diff --git a/.github/workflows/DocPreviewCleanup.yml b/.github/workflows/DocPreviewCleanup.yml
new file mode 100644
index 0000000..1568024
--- /dev/null
+++ b/.github/workflows/DocPreviewCleanup.yml
@@ -0,0 +1,28 @@
+name: Doc Preview Cleanup
+
+on:
+  pull_request:
+    types: [closed]
+
+jobs:
+  doc-preview-cleanup:
+    runs-on: ubuntu-latest
+    steps:
+      - name: Checkout gh-pages branch
+        uses: actions/checkout@v2
+        with:
+          ref: gh-pages
+
+      - name: Delete preview and history
+        run: |
+            git config user.name "Documenter.jl"
+            git config user.email "documenter@juliadocs.github.io"
+            git rm -rf "previews/PR$PRNUM"
+            git commit -m "delete preview"
+            git branch gh-pages-new $(echo "delete history" | git commit-tree HEAD^{tree})
+        env:
+            PRNUM: ${{ github.event.number }}
+
+      - name: Push changes
+        run: |
+            git push --force origin gh-pages-new:gh-pages
diff --git a/bors.toml b/bors.toml
index 5e4a4e3..4e0be23 100644
--- a/bors.toml
+++ b/bors.toml
@@ -12,6 +12,8 @@ status = [
   "Documentation"
 ]
 delete_merged_branches = true
+# Squash commits before merging.
+use_squash_merge = true
 # Uncomment this to use a two hour timeout.
 # The default is one hour.
 #timeout_sec = 7200
diff --git a/docs/Manifest.toml b/docs/Manifest.toml
index fe1dc94..41eb209 100644
--- a/docs/Manifest.toml
+++ b/docs/Manifest.toml
@@ -1,16 +1,208 @@
 # This file is machine-generated - editing it directly is not advised
 
+[[AbstractFFTs]]
+deps = ["LinearAlgebra"]
+git-tree-sha1 = "8ed9de2f1b1a9b1dee48582ad477c6e67b83eb2c"
+uuid = "621f4979-c628-5d54-868e-fcf4e3e8185c"
+version = "1.0.0"
+
+[[AbstractPlotting]]
+deps = ["Animations", "ColorBrewer", "ColorSchemes", "ColorTypes", "Colors", "Contour", "Distributions", "DocStringExtensions", "FFMPEG", "FileIO", "FixedPointNumbers", "Formatting", "FreeType", "FreeTypeAbstraction", "GeometryBasics", "GridLayoutBase", "ImageIO", "IntervalSets", "Isoband", "KernelDensity", "LinearAlgebra", "Markdown", "Match", "Observables", "Packing", "PlotUtils", "PolygonOps", "Printf", "Random", "Serialization", "Showoff", "SignedDistanceFields", "SparseArrays", "StaticArrays", "Statistics", "StatsBase", "StructArrays", "UnicodeFun"]
+git-tree-sha1 = "5000fe26eaa31cdd63390e5764dfe13ef6e678ce"
+uuid = "537997a7-5e4e-5d89-9595-2241ea00577e"
+version = "0.15.1"
+
+[[Adapt]]
+deps = ["LinearAlgebra"]
+git-tree-sha1 = "345a14764e43fe927d6f5c250fe4c8e4664e6ee8"
+uuid = "79e6a3ab-5dfb-504d-930d-738a2a938a0e"
+version = "2.4.0"
+
+[[Animations]]
+deps = ["Colors"]
+git-tree-sha1 = "e81c509d2c8e49592413bfb0bb3b08150056c79d"
+uuid = "27a7e980-b3e6-11e9-2bcd-0b925532e340"
+version = "0.4.1"
+
+[[Artifacts]]
+deps = ["Pkg"]
+git-tree-sha1 = "c30985d8821e0cd73870b17b0ed0ce6dc44cb744"
+uuid = "56f22d72-fd6d-98f1-02f0-08ddc0907c33"
+version = "1.3.0"
+
+[[AxisAlgorithms]]
+deps = ["LinearAlgebra", "Random", "SparseArrays", "WoodburyMatrices"]
+git-tree-sha1 = "a4d07a1c313392a77042855df46c5f534076fab9"
+uuid = "13072b0f-2c55-5437-9ae7-d433b7a33950"
+version = "1.0.0"
+
 [[Base64]]
 uuid = "2a0f44e3-6c83-55bd-87e4-b1978d98bd5f"
 
+[[BinaryProvider]]
+deps = ["Libdl", "Logging", "SHA"]
+git-tree-sha1 = "ecdec412a9abc8db54c0efc5548c64dfce072058"
+uuid = "b99e7846-7c00-51b0-8f62-c81ae34c0232"
+version = "0.5.10"
+
+[[Bzip2_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "c3598e525718abcc440f69cc6d5f60dda0a1b61e"
+uuid = "6e34b625-4abd-537c-b88f-471c36dfa7a0"
+version = "1.0.6+5"
+
+[[CEnum]]
+git-tree-sha1 = "215a9aa4a1f23fbd05b92769fdd62559488d70e9"
+uuid = "fa961155-64e5-5f13-b03f-caf6b980ea82"
+version = "0.4.1"
+
+[[CSV]]
+deps = ["CategoricalArrays", "DataFrames", "Dates", "Mmap", "Parsers", "PooledArrays", "SentinelArrays", "Tables", "Unicode"]
+git-tree-sha1 = "b1f60ea404dc40a76e7f539672ce651079a5a190"
+uuid = "336ed68f-0bac-5ca0-87d4-7b16caf5d00b"
+version = "0.7.10"
+
+[[Cairo]]
+deps = ["Cairo_jll", "Colors", "Glib_jll", "Graphics", "Libdl", "Pango_jll"]
+git-tree-sha1 = "d0b3f8b4ad16cb0a2988c6788646a5e6a17b6b1b"
+uuid = "159f3aea-2a34-519c-b102-8c37f9878175"
+version = "1.0.5"
+
+[[CairoMakie]]
+deps = ["AbstractPlotting", "Cairo", "Colors", "FFTW", "FileIO", "FreeType", "GeometryBasics", "LinearAlgebra", "StaticArrays"]
+git-tree-sha1 = "0e4922f4e8cc892537b3c08f7b3daaaa822c6e41"
+uuid = "13f3f980-e62b-5c42-98c6-ff1f3baf88f0"
+version = "0.3.10"
+
+[[Cairo_jll]]
+deps = ["Artifacts", "Bzip2_jll", "Fontconfig_jll", "FreeType2_jll", "Glib_jll", "JLLWrappers", "LZO_jll", "Libdl", "Pixman_jll", "Pkg", "Xorg_libXext_jll", "Xorg_libXrender_jll", "Zlib_jll", "libpng_jll"]
+git-tree-sha1 = "e2f47f6d8337369411569fd45ae5753ca10394c6"
+uuid = "83423d85-b0ee-5818-9007-b63ccbeb887a"
+version = "1.16.0+6"
+
+[[CalibrationErrors]]
+deps = ["DataStructures", "Distances", "KernelFunctions", "LinearAlgebra", "Reexport", "Statistics", "StatsBase", "UnPack"]
+path = ".."
+uuid = "33913031-fe46-5864-950f-100836f47845"
+version = "0.5.9"
+
+[[CategoricalArrays]]
+deps = ["DataAPI", "Future", "JSON", "Missings", "Printf", "Statistics", "StructTypes", "Unicode"]
+git-tree-sha1 = "2ac27f59196a68070e132b25713f9a5bbc5fa0d2"
+uuid = "324d7699-5711-5eae-9e2f-1d82baa6b597"
+version = "0.8.3"
+
+[[ChainRulesCore]]
+deps = ["LinearAlgebra", "MuladdMacro", "SparseArrays"]
+git-tree-sha1 = "15081c431bb25848ad9b0d172a65794f3a3e197a"
+uuid = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
+version = "0.9.24"
+
+[[ColorBrewer]]
+deps = ["Colors", "JSON", "Test"]
+git-tree-sha1 = "61c5334f33d91e570e1d0c3eb5465835242582c4"
+uuid = "a2cac450-b92f-5266-8821-25eda20663c8"
+version = "0.4.0"
+
+[[ColorSchemes]]
+deps = ["ColorTypes", "Colors", "FixedPointNumbers", "Random", "StaticArrays"]
+git-tree-sha1 = "3141757b5832ee7a0386db87997ee5a23ff20f4d"
+uuid = "35d6a980-a343-548e-a6ea-1d62b119f2f4"
+version = "3.10.2"
+
+[[ColorTypes]]
+deps = ["FixedPointNumbers", "Random"]
+git-tree-sha1 = "4bffea7ed1a9f0f3d1a131bbcd4b925548d75288"
+uuid = "3da002f7-5984-5a60-b8a6-cbb66c0b333f"
+version = "0.10.9"
+
+[[ColorVectorSpace]]
+deps = ["ColorTypes", "Colors", "FixedPointNumbers", "LinearAlgebra", "SpecialFunctions", "Statistics", "StatsBase"]
+git-tree-sha1 = "4d17724e99f357bfd32afa0a9e2dda2af31a9aea"
+uuid = "c3611d14-8923-5661-9e6a-0046d554d3a4"
+version = "0.8.7"
+
+[[Colors]]
+deps = ["ColorTypes", "FixedPointNumbers", "InteractiveUtils", "Reexport"]
+git-tree-sha1 = "ac5f2213e56ed8a34a3dd2f681f4df1166b34929"
+uuid = "5ae59095-9a9b-59fe-a467-6f913c188581"
+version = "0.12.6"
+
+[[Compat]]
+deps = ["Base64", "Dates", "DelimitedFiles", "Distributed", "InteractiveUtils", "LibGit2", "Libdl", "LinearAlgebra", "Markdown", "Mmap", "Pkg", "Printf", "REPL", "Random", "SHA", "Serialization", "SharedArrays", "Sockets", "SparseArrays", "Statistics", "Test", "UUIDs", "Unicode"]
+git-tree-sha1 = "919c7f3151e79ff196add81d7f4e45d91bbf420b"
+uuid = "34da2185-b29b-5c13-b0c7-acf172513d20"
+version = "3.25.0"
+
+[[CompilerSupportLibraries_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "8e695f735fca77e9708e795eda62afdb869cbb70"
+uuid = "e66e0078-7015-5450-92f7-15fbd957f2ae"
+version = "0.3.4+0"
+
+[[Contour]]
+deps = ["StaticArrays"]
+git-tree-sha1 = "9f02045d934dc030edad45944ea80dbd1f0ebea7"
+uuid = "d38c429a-6771-53c6-b99e-75d170b6e991"
+version = "0.5.7"
+
+[[Crayons]]
+git-tree-sha1 = "3f71217b538d7aaee0b69ab47d9b7724ca8afa0d"
+uuid = "a8cc5b0e-0ffa-5ad4-8c14-923d3ee1735f"
+version = "4.0.4"
+
+[[DataAPI]]
+git-tree-sha1 = "ad84f52c0b8f05aa20839484dbaf01690b41ff84"
+uuid = "9a962f9c-6df0-11e9-0e5d-c546b8b5ee8a"
+version = "1.4.0"
+
+[[DataDeps]]
+deps = ["BinaryProvider", "HTTP", "Libdl", "Reexport", "SHA", "p7zip_jll"]
+git-tree-sha1 = "9f69dd052eaf292edd42d4bed999dfbd291927a0"
+uuid = "124859b0-ceae-595e-8997-d05f6a7a8dfe"
+version = "0.7.6"
+
+[[DataFrames]]
+deps = ["CategoricalArrays", "Compat", "DataAPI", "Future", "InvertedIndices", "IteratorInterfaceExtensions", "LinearAlgebra", "Markdown", "Missings", "PooledArrays", "PrettyTables", "Printf", "REPL", "Reexport", "SortingAlgorithms", "Statistics", "TableTraits", "Tables", "Unicode"]
+git-tree-sha1 = "b46e1deb4592a5df7416b10dfcd6b01fb194ab9a"
+uuid = "a93c6f00-e57d-5684-b7b6-d8193f3e46c0"
+version = "0.22.2"
+
+[[DataStructures]]
+deps = ["Compat", "InteractiveUtils", "OrderedCollections"]
+git-tree-sha1 = "fb0aa371da91c1ff9dc7fbed6122d3e411420b9c"
+uuid = "864edb3b-99cc-5e75-8d2d-829cb0a9cfe8"
+version = "0.18.8"
+
+[[DataValueInterfaces]]
+git-tree-sha1 = "bfc1187b79289637fa0ef6d4436ebdfe6905cbd6"
+uuid = "e2d170a0-9d28-54be-80f0-106bbe20a464"
+version = "1.0.0"
+
 [[Dates]]
 deps = ["Printf"]
 uuid = "ade2ca70-3891-5945-98fb-dc099432e06a"
 
+[[DelimitedFiles]]
+deps = ["Mmap"]
+uuid = "8bb1440f-4735-579b-a4ab-409b98df4dab"
+
+[[Distances]]
+deps = ["LinearAlgebra", "Statistics"]
+git-tree-sha1 = "e8b13ba5f166e11df2de6fc283e5db7864245df0"
+uuid = "b4f34e82-e78d-54a5-968a-f98e89d6e8f7"
+version = "0.10.0"
+
 [[Distributed]]
 deps = ["Random", "Serialization", "Sockets"]
 uuid = "8ba89e20-285c-5b6f-9357-94700520ee1b"
 
+[[Distributions]]
+deps = ["FillArrays", "LinearAlgebra", "PDMats", "Printf", "QuadGK", "Random", "SparseArrays", "SpecialFunctions", "Statistics", "StatsBase", "StatsFuns"]
+git-tree-sha1 = "5c6a645ea65af6aac4f96b5dedaae660b7b56267"
+uuid = "31c24e10-a181-5473-b8eb-7969acd0382f"
+version = "0.24.10"
+
 [[DocStringExtensions]]
 deps = ["LibGit2", "Markdown", "Pkg", "Test"]
 git-tree-sha1 = "50ddf44c53698f5e784bbebb3f4b21c5807401b1"
@@ -23,53 +215,535 @@ git-tree-sha1 = "b7715ae18be02110a8cf9cc8ed2ccdb1e3e3aba2"
 uuid = "e30172f5-a6a5-5a46-863b-614d45cd2de4"
 version = "0.26.1"
 
+[[EarCut_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "92d8f9f208637e8d2d28c664051a00569c01493d"
+uuid = "5ae413db-bbd1-5e63-b57d-d24a61df00f5"
+version = "2.1.5+1"
+
+[[EllipsisNotation]]
+git-tree-sha1 = "18ee049accec8763be17a933737c1dd0fdf8673a"
+uuid = "da5c29d0-fa7d-589e-88eb-ea29b0a81949"
+version = "1.0.0"
+
+[[Expat_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "1402e52fcda25064f51c77a9655ce8680b76acf0"
+uuid = "2e619515-83b5-522b-bb60-26c02a35a201"
+version = "2.2.7+6"
+
+[[FFMPEG]]
+deps = ["FFMPEG_jll", "x264_jll"]
+git-tree-sha1 = "9a73ffdc375be61b0e4516d83d880b265366fe1f"
+uuid = "c87230d0-a227-11e9-1b43-d7ebe4e7570a"
+version = "0.4.0"
+
+[[FFMPEG_jll]]
+deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "JLLWrappers", "LAME_jll", "LibVPX_jll", "Libdl", "Ogg_jll", "OpenSSL_jll", "Opus_jll", "Pkg", "Zlib_jll", "libass_jll", "libfdk_aac_jll", "libvorbis_jll", "x264_jll", "x265_jll"]
+git-tree-sha1 = "3cc57ad0a213808473eafef4845a74766242e05f"
+uuid = "b22a6f82-2f65-5046-a5b2-351ab43fb4e5"
+version = "4.3.1+4"
+
+[[FFTW]]
+deps = ["AbstractFFTs", "FFTW_jll", "IntelOpenMP_jll", "Libdl", "LinearAlgebra", "MKL_jll", "Reexport"]
+git-tree-sha1 = "c31e446bf3b12aad2ec8fc500fe19528c148d811"
+uuid = "7a1cc6ca-52ef-59f5-83cd-3a7055c09341"
+version = "1.3.1"
+
+[[FFTW_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "5a0d4b6a22a34d17d53543bd124f4b08ed78e8b0"
+uuid = "f5851436-0d7a-5f13-b9de-f02708fd171a"
+version = "3.3.9+7"
+
+[[FileIO]]
+deps = ["Pkg"]
+git-tree-sha1 = "fee8955b9dfa7bec67117ef48085fb2b559b9c22"
+uuid = "5789e2e9-d7fb-5bc7-8068-2c6fae9b9549"
+version = "1.4.5"
+
+[[FillArrays]]
+deps = ["LinearAlgebra", "Random", "SparseArrays"]
+git-tree-sha1 = "ff537e5a3cba92fb48f30fec46723510450f2c0e"
+uuid = "1a297f60-69ca-5386-bcde-b61e274b549b"
+version = "0.10.2"
+
+[[FixedPointNumbers]]
+deps = ["Statistics"]
+git-tree-sha1 = "335bfdceacc84c5cdf16aadc768aa5ddfc5383cc"
+uuid = "53c48c17-4a7d-5ca2-90c5-79b7896eea93"
+version = "0.8.4"
+
+[[Fontconfig_jll]]
+deps = ["Artifacts", "Bzip2_jll", "Expat_jll", "FreeType2_jll", "JLLWrappers", "Libdl", "Libuuid_jll", "Pkg", "Zlib_jll"]
+git-tree-sha1 = "35895cf184ceaab11fd778b4590144034a167a2f"
+uuid = "a3f928ae-7b40-5064-980b-68af3947d34b"
+version = "2.13.1+14"
+
+[[Formatting]]
+deps = ["Printf"]
+git-tree-sha1 = "8339d61043228fdd3eb658d86c926cb282ae72a8"
+uuid = "59287772-0a20-5a39-b81b-1366585eb4c0"
+version = "0.4.2"
+
+[[FreeType]]
+deps = ["CEnum", "FreeType2_jll"]
+git-tree-sha1 = "d5e296dea44f9cfb8cc83681aa3db367e0cbfd4f"
+uuid = "b38be410-82b0-50bf-ab77-7b57e271db43"
+version = "3.0.1"
+
+[[FreeType2_jll]]
+deps = ["Artifacts", "Bzip2_jll", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
+git-tree-sha1 = "cbd58c9deb1d304f5a245a0b7eb841a2560cfec6"
+uuid = "d7e528f0-a631-5988-bf34-fe36492bcfd7"
+version = "2.10.1+5"
+
+[[FreeTypeAbstraction]]
+deps = ["ColorVectorSpace", "Colors", "FreeType", "GeometryBasics", "StaticArrays"]
+git-tree-sha1 = "3d955cfbefd6645ced60091d8c9bfcc96fc32345"
+uuid = "663a7486-cb36-511b-a19d-713bb74d65c9"
+version = "0.8.4"
+
+[[FriBidi_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "0d20aed5b14dd4c9a2453c1b601d08e1149679cc"
+uuid = "559328eb-81f9-559d-9380-de523a88c83c"
+version = "1.0.5+6"
+
+[[Functors]]
+deps = ["MacroTools"]
+git-tree-sha1 = "f40adc6422f548176bb4351ebd29e4abf773040a"
+uuid = "d9f16b24-f501-4c13-a1f2-28368ffc5196"
+version = "0.1.0"
+
+[[Future]]
+deps = ["Random"]
+uuid = "9fa8497b-333b-5362-9e8d-4d0656e87820"
+
+[[GeometryBasics]]
+deps = ["EarCut_jll", "IterTools", "LinearAlgebra", "StaticArrays", "StructArrays", "Tables"]
+git-tree-sha1 = "876f77f0d3253e882ff588af1c95d0e4a86c9766"
+uuid = "5c1252a2-5f33-56bf-86c9-59e7332b4326"
+version = "0.3.5"
+
+[[Gettext_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Libiconv_jll", "Pkg", "XML2_jll"]
+git-tree-sha1 = "8c14294a079216000a0bdca5ec5a447f073ddc9d"
+uuid = "78b55507-aeef-58d4-861c-77aaff3498b1"
+version = "0.20.1+7"
+
+[[Glib_jll]]
+deps = ["Artifacts", "Gettext_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Libiconv_jll", "Libmount_jll", "PCRE_jll", "Pkg", "Zlib_jll"]
+git-tree-sha1 = "04690cc5008b38ecbdfede949220bc7d9ba26397"
+uuid = "7746bdde-850d-59dc-9ae8-88ece973131d"
+version = "2.59.0+4"
+
+[[Graphics]]
+deps = ["Colors", "LinearAlgebra", "NaNMath"]
+git-tree-sha1 = "45d684ead5b65c043ad46bd5be750d61c39d7ef8"
+uuid = "a2bd30eb-e257-5431-a919-1863eab51364"
+version = "1.0.2"
+
+[[Graphite2_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "42adbc6fd39ba41138f894b8ac711146a2b0d986"
+uuid = "3b182d85-2403-5c21-9c21-1e1f0cc25472"
+version = "1.3.13+4"
+
+[[GridLayoutBase]]
+deps = ["GeometryBasics", "InteractiveUtils", "Match", "Observables"]
+git-tree-sha1 = "0702ac06d05e653996a37fea1d631bc7e74512ee"
+uuid = "3955a311-db13-416c-9275-1d80ed98e5e9"
+version = "0.4.1"
+
+[[Grisu]]
+git-tree-sha1 = "03d381f65183cb2d0af8b3425fde97263ce9a995"
+uuid = "42e2da0e-8278-4e71-bc24-59509adca0fe"
+version = "1.0.0"
+
+[[HTTP]]
+deps = ["Base64", "Dates", "IniFile", "MbedTLS", "Sockets", "URIs"]
+git-tree-sha1 = "63055ee44b5c2b95ec1921edcf856c60124ff0c3"
+uuid = "cd3eb016-35fb-5094-929b-558a96fad6f3"
+version = "0.9.2"
+
+[[HarfBuzz_jll]]
+deps = ["Artifacts", "Cairo_jll", "Fontconfig_jll", "FreeType2_jll", "Gettext_jll", "Glib_jll", "Graphite2_jll", "ICU_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Pkg"]
+git-tree-sha1 = "90bed5fc61d12d10832ebf988988104888eebaca"
+uuid = "2e76f6c2-a576-52d4-95c1-20adfe4de566"
+version = "2.6.1+10"
+
+[[ICU_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "6ce9cf3c5490b045710d60ac3fd2fe48188846b3"
+uuid = "a51ab1cf-af8e-5615-a023-bc2c838bba6b"
+version = "67.1.0+3"
+
 [[IOCapture]]
 deps = ["Logging"]
 git-tree-sha1 = "377252859f740c217b936cebcd918a44f9b53b59"
 uuid = "b5f81e59-6552-4d32-b1f0-c071b021bf89"
 version = "0.1.1"
 
+[[ImageCore]]
+deps = ["AbstractFFTs", "Colors", "FixedPointNumbers", "Graphics", "MappedArrays", "MosaicViews", "OffsetArrays", "PaddedViews", "Reexport"]
+git-tree-sha1 = "79badd979fbee9b8980cd995cd5a86a9e93b8ad7"
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+
+[[ImageIO]]
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+git-tree-sha1 = "0d6d09c28d67611c68e25af0c2df7269c82b73c7"
+uuid = "82e4d734-157c-48bb-816b-45c225c6df19"
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+
+[[IndirectArrays]]
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+
+[[IniFile]]
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+
+[[IntelOpenMP_jll]]
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+git-tree-sha1 = "fb8e1c7a5594ba56f9011310790e03b5384998d6"
+uuid = "1d5cc7b8-4909-519e-a0f8-d0f5ad9712d0"
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+
 [[InteractiveUtils]]
 deps = ["Markdown"]
 uuid = "b77e0a4c-d291-57a0-90e8-8db25a27a240"
 
+[[Interpolations]]
+deps = ["AxisAlgorithms", "LinearAlgebra", "OffsetArrays", "Random", "Ratios", "SharedArrays", "SparseArrays", "StaticArrays", "WoodburyMatrices"]
+git-tree-sha1 = "eb1dd6d5b2275faaaa18533e0fc5f9171cec25fa"
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+
+[[IntervalSets]]
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+
+[[InvertedIndices]]
+deps = ["Test"]
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+
+[[Isoband]]
+deps = ["isoband_jll"]
+git-tree-sha1 = "f9b6d97355599074dc867318950adaa6f9946137"
+uuid = "f1662d9f-8043-43de-a69a-05efc1cc6ff4"
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+
+[[IterTools]]
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+
+[[IteratorInterfaceExtensions]]
+git-tree-sha1 = "a3f24677c21f5bbe9d2a714f95dcd58337fb2856"
+uuid = "82899510-4779-5014-852e-03e436cf321d"
+version = "1.0.0"
+
+[[JLLWrappers]]
+git-tree-sha1 = "04b49c556240b62d5a799e94c63d5fc14d3c07cd"
+uuid = "692b3bcd-3c85-4b1f-b108-f13ce0eb3210"
+version = "1.1.4"
+
 [[JSON]]
 deps = ["Dates", "Mmap", "Parsers", "Unicode"]
 git-tree-sha1 = "81690084b6198a2e1da36fcfda16eeca9f9f24e4"
 uuid = "682c06a0-de6a-54ab-a142-c8b1cf79cde6"
 version = "0.21.1"
 
+[[KernelDensity]]
+deps = ["Distributions", "DocStringExtensions", "FFTW", "Interpolations", "StatsBase"]
+git-tree-sha1 = "09aeec87bdc9c1fa70d0b508dfa94a21acd280d9"
+uuid = "5ab0869b-81aa-558d-bb23-cbf5423bbe9b"
+version = "0.6.2"
+
+[[KernelFunctions]]
+deps = ["Compat", "Distances", "Functors", "InteractiveUtils", "LinearAlgebra", "Random", "Requires", "SpecialFunctions", "StatsBase", "StatsFuns", "Test", "ZygoteRules"]
+git-tree-sha1 = "e9152dff713b5e17e458403ab67cec33a9ff00d3"
+uuid = "ec8451be-7e33-11e9-00cf-bbf324bd1392"
+version = "0.8.11"
+
+[[LAME_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "df381151e871f41ee86cee4f5f6fd598b8a68826"
+uuid = "c1c5ebd0-6772-5130-a774-d5fcae4a789d"
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+
+[[LZO_jll]]
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+git-tree-sha1 = "f128cd6cd05ffd6d3df0523ed99b90ff6f9b349a"
+uuid = "dd4b983a-f0e5-5f8d-a1b7-129d4a5fb1ac"
+version = "2.10.0+3"
+
 [[LibGit2]]
 deps = ["Printf"]
 uuid = "76f85450-5226-5b5a-8eaa-529ad045b433"
 
+[[LibVPX_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "85fcc80c3052be96619affa2fe2e6d2da3908e11"
+uuid = "dd192d2f-8180-539f-9fb4-cc70b1dcf69a"
+version = "1.9.0+1"
+
 [[Libdl]]
 uuid = "8f399da3-3557-5675-b5ff-fb832c97cbdb"
 
+[[Libffi_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "a2cd088a88c0d37eef7d209fd3d8712febce0d90"
+uuid = "e9f186c6-92d2-5b65-8a66-fee21dc1b490"
+version = "3.2.1+4"
+
+[[Libgcrypt_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Libgpg_error_jll", "Pkg"]
+git-tree-sha1 = "b391a18ab1170a2e568f9fb8d83bc7c780cb9999"
+uuid = "d4300ac3-e22c-5743-9152-c294e39db1e4"
+version = "1.8.5+4"
+
+[[Libgpg_error_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "ec7f2e8ad5c9fa99fc773376cdbc86d9a5a23cb7"
+uuid = "7add5ba3-2f88-524e-9cd5-f83b8a55f7b8"
+version = "1.36.0+3"
+
+[[Libiconv_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "8e924324b2e9275a51407a4e06deb3455b1e359f"
+uuid = "94ce4f54-9a6c-5748-9c1c-f9c7231a4531"
+version = "1.16.0+7"
+
+[[Libmount_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "51ad0c01c94c1ce48d5cad629425035ad030bfd5"
+uuid = "4b2f31a3-9ecc-558c-b454-b3730dcb73e9"
+version = "2.34.0+3"
+
+[[Libuuid_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "f879ae9edbaa2c74c922e8b85bb83cc84ea1450b"
+uuid = "38a345b3-de98-5d2b-a5d3-14cd9215e700"
+version = "2.34.0+7"
+
+[[LinearAlgebra]]
+deps = ["Libdl"]
+uuid = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
+
 [[Logging]]
 uuid = "56ddb016-857b-54e1-b83d-db4d58db5568"
 
+[[MKL_jll]]
+deps = ["IntelOpenMP_jll", "Libdl", "Pkg"]
+git-tree-sha1 = "eb540ede3aabb8284cb482aa41d00d6ca850b1f8"
+uuid = "856f044c-d86e-5d09-b602-aeab76dc8ba7"
+version = "2020.2.254+0"
+
+[[MacroTools]]
+deps = ["Markdown", "Random"]
+git-tree-sha1 = "6a8a2a625ab0dea913aba95c11370589e0239ff0"
+uuid = "1914dd2f-81c6-5fcd-8719-6d5c9610ff09"
+version = "0.5.6"
+
+[[MappedArrays]]
+deps = ["FixedPointNumbers"]
+git-tree-sha1 = "b92bd220c95a8bbe89af28f11201fd080e0e3fe7"
+uuid = "dbb5928d-eab1-5f90-85c2-b9b0edb7c900"
+version = "0.3.0"
+
 [[Markdown]]
 deps = ["Base64"]
 uuid = "d6f4376e-aef5-505a-96c1-9c027394607a"
 
+[[Match]]
+git-tree-sha1 = "5cf525d97caf86d29307150fcba763a64eaa9cbe"
+uuid = "7eb4fadd-790c-5f42-8a69-bfa0b872bfbf"
+version = "1.1.0"
+
+[[MbedTLS]]
+deps = ["Dates", "MbedTLS_jll", "Random", "Sockets"]
+git-tree-sha1 = "1c38e51c3d08ef2278062ebceade0e46cefc96fe"
+uuid = "739be429-bea8-5141-9913-cc70e7f3736d"
+version = "1.0.3"
+
+[[MbedTLS_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "0eef589dd1c26a3ac9d753fe1a8bcad63f956fa6"
+uuid = "c8ffd9c3-330d-5841-b78e-0817d7145fa1"
+version = "2.16.8+1"
+
+[[Missings]]
+deps = ["DataAPI"]
+git-tree-sha1 = "ed61674a0864832495ffe0a7e889c0da76b0f4c8"
+uuid = "e1d29d7a-bbdc-5cf2-9ac0-f12de2c33e28"
+version = "0.4.4"
+
 [[Mmap]]
 uuid = "a63ad114-7e13-5084-954f-fe012c677804"
 
+[[MosaicViews]]
+deps = ["MappedArrays", "OffsetArrays", "PaddedViews"]
+git-tree-sha1 = "614e8d77264d20c1db83661daadfab38e8e4b77e"
+uuid = "e94cdb99-869f-56ef-bcf0-1ae2bcbe0389"
+version = "0.2.4"
+
+[[MuladdMacro]]
+git-tree-sha1 = "c6190f9a7fc5d9d5915ab29f2134421b12d24a68"
+uuid = "46d2c3a1-f734-5fdb-9937-b9b9aeba4221"
+version = "0.2.2"
+
+[[NaNMath]]
+git-tree-sha1 = "bfe47e760d60b82b66b61d2d44128b62e3a369fb"
+uuid = "77ba4419-2d1f-58cd-9bb1-8ffee604a2e3"
+version = "0.3.5"
+
+[[Netpbm]]
+deps = ["ColorVectorSpace", "FileIO", "ImageCore"]
+git-tree-sha1 = "03472ec5ea8884b791c6340712f3261c0f393691"
+uuid = "f09324ee-3d7c-5217-9330-fc30815ba969"
+version = "1.0.0"
+
+[[Observables]]
+git-tree-sha1 = "3469ef96607a6b9a1e89e54e6f23401073ed3126"
+uuid = "510215fc-4207-5dde-b226-833fc4488ee2"
+version = "0.3.3"
+
+[[OffsetArrays]]
+deps = ["Adapt"]
+git-tree-sha1 = "5b9ed21d50a91bb783c87f37c8da9266f0265504"
+uuid = "6fe1bfb0-de20-5000-8ca7-80f57d26f881"
+version = "1.4.4"
+
+[[Ogg_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "a42c0f138b9ebe8b58eba2271c5053773bde52d0"
+uuid = "e7412a2a-1a6e-54c0-be00-318e2571c051"
+version = "1.3.4+2"
+
+[[OpenSSL_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "71bbbc616a1d710879f5a1021bcba65ffba6ce58"
+uuid = "458c3c95-2e84-50aa-8efc-19380b2a3a95"
+version = "1.1.1+6"
+
+[[OpenSpecFun_jll]]
+deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "9db77584158d0ab52307f8c04f8e7c08ca76b5b3"
+uuid = "efe28fd5-8261-553b-a9e1-b2916fc3738e"
+version = "0.5.3+4"
+
+[[Opus_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "f9d57f4126c39565e05a2b0264df99f497fc6f37"
+uuid = "91d4177d-7536-5919-b921-800302f37372"
+version = "1.3.1+3"
+
+[[OrderedCollections]]
+git-tree-sha1 = "cf59cfed2e2c12e8a2ff0a4f1e9b2cd8650da6db"
+uuid = "bac558e1-5e72-5ebc-8fee-abe8a469f55d"
+version = "1.3.2"
+
+[[PCRE_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "1b556ad51dceefdbf30e86ffa8f528b73c7df2bb"
+uuid = "2f80f16e-611a-54ab-bc61-aa92de5b98fc"
+version = "8.42.0+4"
+
+[[PDMats]]
+deps = ["LinearAlgebra", "SparseArrays", "SuiteSparse", "Test"]
+git-tree-sha1 = "95a4038d1011dfdbde7cecd2ad0ac411e53ab1bc"
+uuid = "90014a1f-27ba-587c-ab20-58faa44d9150"
+version = "0.10.1"
+
+[[PNGFiles]]
+deps = ["Base64", "CEnum", "ImageCore", "IndirectArrays", "OffsetArrays", "libpng_jll"]
+git-tree-sha1 = "aa6e87a2361c2fe5a63b1a6a4b567f13aa108991"
+uuid = "f57f5aa1-a3ce-4bc8-8ab9-96f992907883"
+version = "0.3.5"
+
+[[Packing]]
+deps = ["GeometryBasics"]
+git-tree-sha1 = "f4049d379326c2c7aa875c702ad19346ecb2b004"
+uuid = "19eb6ba3-879d-56ad-ad62-d5c202156566"
+version = "0.4.1"
+
+[[PaddedViews]]
+deps = ["OffsetArrays"]
+git-tree-sha1 = "91d229e113e8975a399e40d7c0b1ddf4da6d3c59"
+uuid = "5432bcbf-9aad-5242-b902-cca2824c8663"
+version = "0.5.7"
+
+[[PalmerPenguins]]
+deps = ["CSV", "DataDeps"]
+git-tree-sha1 = "d44224354c5d31262b4402d6f9fef79a715b1dce"
+uuid = "8b842266-38fa-440a-9b57-31493939ab85"
+version = "0.1.1"
+
+[[Pango_jll]]
+deps = ["Artifacts", "Cairo_jll", "Fontconfig_jll", "FreeType2_jll", "FriBidi_jll", "Glib_jll", "HarfBuzz_jll", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "9a336dee51d20d1ed890c4a8dca636e86e2b76ca"
+uuid = "36c8627f-9965-5494-a995-c6b170f724f3"
+version = "1.42.4+10"
+
 [[Parsers]]
 deps = ["Dates"]
 git-tree-sha1 = "50c9a9ed8c714945e01cd53a21007ed3865ed714"
 uuid = "69de0a69-1ddd-5017-9359-2bf0b02dc9f0"
 version = "1.0.15"
 
+[[Pixman_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "6a20a83c1ae86416f0a5de605eaea08a552844a3"
+uuid = "30392449-352a-5448-841d-b1acce4e97dc"
+version = "0.40.0+0"
+
 [[Pkg]]
 deps = ["Dates", "LibGit2", "Libdl", "Logging", "Markdown", "Printf", "REPL", "Random", "SHA", "UUIDs"]
 uuid = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
 
+[[PlotUtils]]
+deps = ["ColorSchemes", "Colors", "Dates", "Printf", "Random", "Reexport", "Statistics"]
+git-tree-sha1 = "6a59c282058f46967069972d74526a68d27a9012"
+uuid = "995b91a9-d308-5afd-9ec6-746e21dbc043"
+version = "1.0.8"
+
+[[PolygonOps]]
+git-tree-sha1 = "c031d2332c9a8e1c90eca239385815dc271abb22"
+uuid = "647866c9-e3ac-4575-94e7-e3d426903924"
+version = "0.1.1"
+
+[[PooledArrays]]
+deps = ["DataAPI"]
+git-tree-sha1 = "b1333d4eced1826e15adbdf01a4ecaccca9d353c"
+uuid = "2dfb63ee-cc39-5dd5-95bd-886bf059d720"
+version = "0.5.3"
+
+[[PrettyTables]]
+deps = ["Crayons", "Formatting", "Markdown", "Reexport", "Tables"]
+git-tree-sha1 = "237170206bf38a66fee4d845f4ae57f63788eeb0"
+uuid = "08abe8d2-0d0c-5749-adfa-8a2ac140af0d"
+version = "0.10.1"
+
 [[Printf]]
 deps = ["Unicode"]
 uuid = "de0858da-6303-5e67-8744-51eddeeeb8d7"
 
+[[QuadGK]]
+deps = ["DataStructures", "LinearAlgebra"]
+git-tree-sha1 = "12fbe86da16df6679be7521dfb39fbc861e1dc7b"
+uuid = "1fd47b50-473d-5c70-9696-f719f8f3bcdc"
+version = "2.4.1"
+
 [[REPL]]
 deps = ["InteractiveUtils", "Markdown", "Sockets"]
 uuid = "3fa0cd96-eef1-5676-8a61-b3b8758bbffb"
@@ -78,22 +752,281 @@ uuid = "3fa0cd96-eef1-5676-8a61-b3b8758bbffb"
 deps = ["Serialization"]
 uuid = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 
+[[Ratios]]
+git-tree-sha1 = "37d210f612d70f3f7d57d488cb3b6eff56ad4e41"
+uuid = "c84ed2f1-dad5-54f0-aa8e-dbefe2724439"
+version = "0.4.0"
+
+[[Reexport]]
+deps = ["Pkg"]
+git-tree-sha1 = "7b1d07f411bc8ddb7977ec7f377b97b158514fe0"
+uuid = "189a3867-3050-52da-a836-e630ba90ab69"
+version = "0.2.0"
+
+[[Requires]]
+deps = ["UUIDs"]
+git-tree-sha1 = "cfbac6c1ed70c002ec6361e7fd334f02820d6419"
+uuid = "ae029012-a4dd-5104-9daa-d747884805df"
+version = "1.1.2"
+
+[[Rmath]]
+deps = ["Random", "Rmath_jll"]
+git-tree-sha1 = "86c5647b565873641538d8f812c04e4c9dbeb370"
+uuid = "79098fc4-a85e-5d69-aa6a-4863f24498fa"
+version = "0.6.1"
+
+[[Rmath_jll]]
+deps = ["Libdl", "Pkg"]
+git-tree-sha1 = "d76185aa1f421306dec73c057aa384bad74188f0"
+uuid = "f50d1b31-88e8-58de-be2c-1cc44531875f"
+version = "0.2.2+1"
+
 [[SHA]]
 uuid = "ea8e919c-243c-51af-8825-aaa63cd721ce"
 
+[[SentinelArrays]]
+deps = ["Dates", "Random"]
+git-tree-sha1 = "6ccde405cf0759eba835eb613130723cb8f10ff9"
+uuid = "91c51154-3ec4-41a3-a24f-3f23e20d615c"
+version = "1.2.16"
+
 [[Serialization]]
 uuid = "9e88b42a-f829-5b0c-bbe9-9e923198166b"
 
+[[SharedArrays]]
+deps = ["Distributed", "Mmap", "Random", "Serialization"]
+uuid = "1a1011a3-84de-559e-8e89-a11a2f7dc383"
+
+[[Showoff]]
+deps = ["Dates", "Grisu"]
+git-tree-sha1 = "ee010d8f103468309b8afac4abb9be2e18ff1182"
+uuid = "992d4aef-0814-514b-bc4d-f2e9a6c4116f"
+version = "0.3.2"
+
+[[SignedDistanceFields]]
+deps = ["Random", "Statistics", "Test"]
+git-tree-sha1 = "d263a08ec505853a5ff1c1ebde2070419e3f28e9"
+uuid = "73760f76-fbc4-59ce-8f25-708e95d2df96"
+version = "0.4.0"
+
 [[Sockets]]
 uuid = "6462fe0b-24de-5631-8697-dd941f90decc"
 
+[[SortingAlgorithms]]
+deps = ["DataStructures", "Random", "Test"]
+git-tree-sha1 = "03f5898c9959f8115e30bc7226ada7d0df554ddd"
+uuid = "a2af1166-a08f-5f64-846c-94a0d3cef48c"
+version = "0.3.1"
+
+[[SparseArrays]]
+deps = ["LinearAlgebra", "Random"]
+uuid = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
+
+[[SpecialFunctions]]
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+[[Statistics]]
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 [[Test]]
 deps = ["Distributed", "InteractiveUtils", "Logging", "Random"]
 uuid = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
+[[URIs]]
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+
 [[UUIDs]]
 deps = ["Random", "SHA"]
 uuid = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"
 
+[[UnPack]]
+git-tree-sha1 = "387c1f73762231e86e0c9c5443ce3b4a0a9a0c2b"
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 [[Unicode]]
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+
+[[x264_jll]]
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+
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diff --git a/docs/Project.toml b/docs/Project.toml
index 101c2b6..4093589 100644
--- a/docs/Project.toml
+++ b/docs/Project.toml
@@ -1,5 +1,15 @@
 [deps]
+AbstractPlotting = "537997a7-5e4e-5d89-9595-2241ea00577e"
+CairoMakie = "13f3f980-e62b-5c42-98c6-ff1f3baf88f0"
+DataFrames = "a93c6f00-e57d-5684-b7b6-d8193f3e46c0"
 Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4"
+JSON = "682c06a0-de6a-54ab-a142-c8b1cf79cde6"
+PalmerPenguins = "8b842266-38fa-440a-9b57-31493939ab85"
 
 [compat]
+AbstractPlotting = "0.15"
+CairoMakie = "0.3.10"
+DataFrames = "0.22"
 Documenter = "0.26"
+JSON = "0.21"
+PalmerPenguins = "0.1"
diff --git a/docs/make.jl b/docs/make.jl
index 403d381..e506579 100644
--- a/docs/make.jl
+++ b/docs/make.jl
@@ -1,5 +1,19 @@
-using CalibrationErrors
 using Documenter
+import JSON
+
+if haskey(ENV, "GITHUB_ACTIONS")
+    # Print `@debug` statements (https://github.com/JuliaDocs/Documenter.jl/issues/955)
+    ENV["JULIA_DEBUG"] = "Documenter"
+    # Bypass the accept download prompt
+    ENV["DATADEPS_ALWAYS_ACCEPT"] = "true"
+end
+
+using CalibrationErrors
+
+# Avoid font caching warning in docs
+using CairoMakie
+CairoMakie.activate!()
+scatter(rand(10), rand(10))
 
 makedocs(;
     modules = [CalibrationErrors],
@@ -12,11 +26,50 @@ makedocs(;
         assets=String[],
     ),
     pages = [
-        "Home" => "index.md",
+        "index.md",
+        "introduction.md",
+        "ece.md",
+        "kce.md",
     ],
 )
 
+# Obtain PR from commit message
+function pr_from_commit()
+    # Check if action is caused by bors on the "trying" branch
+    get(ENV, "GITHUB_ACTOR", "") == "bors[bot]" || return
+    get(ENV, "GITHUB_REF", "") == "refs/heads/trying" || return
+
+    # Parse event payload
+    event_path = get(ENV, "GITHUB_EVENT_PATH", nothing)
+    event_path === nothing && return
+    event = JSON.parsefile(event_path)
+    if haskey(event, "head_commit") && haskey(event["head_commit"], "message")
+        m = match(r"^Try #(.*):$", event["head_commit"]["message"])
+        m === nothing && return
+        return m.captures[1]
+    end
+
+    return
+end
+
+# Enable preview on the trying branch
+function deploy_config()
+    if haskey(ENV, "GITHUB_ACTIONS")
+        repo = get(ENV, "GITHUB_REPOSITORY", "")
+        if repo == "devmotion/CalibrationErrors.jl" && (pr = pr_from_commit()) !== nothing
+            return Documenter.GitHubActions(
+                "devmotion/CalibrationErrors.jl",
+                "pull_request",
+                "refs/pull/$pr/merge",
+            )
+        end
+    end
+
+    return Documenter.auto_detect_deploy_system()
+end
+
 deploydocs(;
     repo = "github.com/devmotion/CalibrationErrors.jl.git",
+    deploy_config = deploy_config(),
     push_preview = true,
 )
diff --git a/docs/src/background.md b/docs/src/background.md
deleted file mode 100644
index de2f393..0000000
--- a/docs/src/background.md
+++ /dev/null
@@ -1,38 +0,0 @@
-# Probabilistic setting
-
-## Probabilistic model
-
-A probabilistic model predicts a probability distribution of possible outputs
-for a given input.
-
-A very simple probabilistic model is a model that predicts a uniform
-distribution for a dice roll; there is no input and the possible outputs are
-the numbers $1,2,3,4,5,6$. A probably more complicated probabilistic model
-would be a model that predicts the distribution of stock price changes from
-the stock prices of last week; here the input are the stock prices of last week
-and the possible outputs are formed by the set of possible stock price changes.
-
-If we assume that for each input there exists an underlying
-unknown probability distribution that captures the relation between the given
-input and the possible outputs, we can aim for a model whose predicted
-distributions are, in some sense, close to these unknown probability distributions.
-
-More mathematically, if we view inputs and outputs as random variables $X$ and $Y$
-on some probability space, we can strive for a model $g$ that satisfies
-```math
-    g(X) \approx \mu_{Y|X}(\cdot|X),
-```
-where $\mu_{Y|X}$ is a version of the conditional distribution of $Y$ given $X$.
-
-Closeness of $g(X)$ and $\mu_{Y|X}(\cdot|X)$ can be measured with distance measures
-of probability distributions. Two prominent families of distances are
-[$\phi$-divergences](https://en.wikipedia.org/wiki/F-divergence)
-and [integral probability metrics](https://arxiv.org/pdf/0901.2698.pdf).
-
-## Classification model
-
-Here we restrict ourselves to classification models, i.e., models for which output
-$Y$ takes only values from a finite set.
-
-The dice roll model above is a classification model, whereas the model that
-predicts stock price changes is not.
diff --git a/docs/src/calibration.md b/docs/src/calibration.md
deleted file mode 100644
index b272aa7..0000000
--- a/docs/src/calibration.md
+++ /dev/null
@@ -1,146 +0,0 @@
-# Calibration
-
-## Motivation
-
-Ideally one would like to have a model that predicts the underlying probability
-distribution for almost every input, i.e., a model $g$ such that almost always
-```math
-    g(X) = \mu_{Y|X}(\cdot|X).
-```
-Unfortunately, if we try to infer the model from a finite data set of inputs and
-outputs that is usually not possible.
-
-In safety-critical applications such as medical decision-making or autonomous
-driving, however, important decisions are based on the predictions of a model.
-Since we are not able to obtain the perfect model, the model has to satisfy
-other properties such that it is deemed trustworthy.
-
-## Definition
-
-One such property is calibration, which is also called reliability. Loosely speaking,
-if we repeatedly predict the same distribution for different pairs of inputs and
-outputs, we would like that in the long run the empirical distribution of the
-observed outputs is similar to the predicted probability distribution. This property
-guarantees that the predicted distribution is not only an arbitrary probability
-distribution but actually makes sense from a frequentist point of view.
-
-A [classic example from the literature](https://www.jstor.org/stable/2987588) is a
-weather forecaster who each morning predicts the probability that it will rain during
-the day. If we assume that the forecaster's predictions are observed for a long time,
-the forecaster is called calibrated "if among those days for which his prediction
-is $x$, the long-run relative frequency of rain is also $x$".
-
-### Common notion
-
-Commonly (see, e.g,
-[Guo et al. (2017)](http://proceedings.mlr.press/v70/guo17a/guo17a.pdf)), only
-calibration of the most-confident predictions $\max_y g_y(x)$ of a model $g$ is
-considered. According to this common notion a model is calibrated if almost
-always
-```math
-    \mathbb{P}[Y = \textrm{arg} \, \max_y g_y(X) \,|\, \max_y g_y(X)] = \max_y g_y(X).
-```
-
-### Strong notion
-
-According to the more general definition by
-[Bröcker (2009)](https://rmets.onlinelibrary.wiley.com/doi/pdf/10.1002/qj.456)
-and [Vaicenavicius et al. (2019)](http://proceedings.mlr.press/v89/vaicenavicius19a/vaicenavicius19a.pdf),
-a probabilistic model $g$ is calibrated if almost always
-```math
-    \mathbb{P}[Y = y \,|\, g(X)] = g_y(X)
-```
-for all classes $y$.
-
-For classification problems with more than two classes, this definition of
-calibration is stronger than the more common one above. By reducing the model
-and applying the strong notion to the simplified model, however, this definition
-still allows to investigate the calibration of the model with respect to only
-certain aspects of interest such as the calibration of the most-confident
-predictions.
-
-Thus in this Julia package and its documentation, we always refer to the strong
-notion of calibration.
-
-Let $y_1, \ldots, y_m$ be the possible outputs. Then we can also define
-calibration in a vectorized form. Equivalently to the definition above, a model
-$g$ is calibrated if and only if
-```math
-    r(g(X)) - g(X) = 0
-```
-holds almost always, where
-```math
-    r(\xi) := (\mathbb{P}[Y = y_1 \,|\, g(X) = \xi], \ldots, \mathbb{P}[Y = y_m \,|\, g(X) = \xi])
-```
-denotes the so-called calibration function.
-
-## Measures
-
-Calibration measures allow a more fine-tuned analysis of calibration and enable
-comparisons of calibration of different models. Intuitively, calibration
-measures quantify the deviation of the left and right hand side in the
-definitions above.
-
-### Expected calibration error (ECE)
-
-The most common calibration measure is the so-called expected calibration error
-(ECE) (see, e.g.,
-[Guo et al. (2017)](http://proceedings.mlr.press/v70/guo17a/guo17a.pdf)).
-Informally, it is defined as the average distance between the left and right
-hand side of the definition above with respect to some metric. Mathematically,
-the expected calibration of model $g$ with respect to distance measure $d$ is
-defined as
-```math
-    \mathrm{ECE}[d, g] := \mathbb{E}[d(r(g(X)), g(X))].
-```
-Here $d$ could be, e.g., the cityblock distance, the total variation distance,
-or the squared Euclidean distance.
-
-If $d(p, q) = 0$ if and only if $p = q$, then the ECE of model $g$ with respect
-to distance measure $d$ is zero if and only if $g$ is calibrated.
-
-### Calibration error (CE)
-
-More generally, Widmann et al. (2019) define the calibration error (CE) of
-a model $g$ with respect to a function class $\mathcal{F} \subset \{f \colon
-\Delta^m \to \mathbb{R}^m\}$ as
-```math
-    \mathrm{CE}[\mathcal{F}, g] := \sup_{f \in \mathcal{F}} \mathbb{E}[(r(g(X)) - g(X))^\intercal f(g(X))].
-```
-
-If model $g$ is calibrated, then the CE is zero, regardless of the choice of
-$\mathcal{F}$. However, for some function spaces (e.g., for
-$\mathcal{F} = \{0\}$) the CE is zero even if $g$ is not calibrated.
-
-Interestingly, the ECE with respect to the cityblock distance, the total
-variation distance, and the squared Euclidean distance are all special cases
-of the CE (Widmann et al. (2019)).
-
-### Kernel calibration error (KCE)
-
-The kernel calibration error (KCE) is another special case of the CE, in which
-the unit ball of a reproducing kernel Hilbert space (RKHS) of vector-valued
-functions is chosen as function space $\mathcal{F}$.
-
-A RKHS of vector-valued functions $f \colon \Delta^m \to \mathbb{R}^m$ can be
-identified with a unique matrix-valued kernel $k \colon \Delta^m \times
-\Delta^m \to \mathbb{R}^{m \times m}$. Then the KCE of a model $g$ with respect
-to kernel $k$ is defined as
-```math
-    \mathrm{KCE}[k, g] := \mathrm{CE}[\mathcal{F}, g],
-```
-where $\mathcal{F}$ is the unit ball of the RKHS corresponding to kernel $k$.
-
-As Widmann et al. (2019) show, for a large class of kernels (so-called universal
-kernels) the KCE is zero if and only if the model $g$ is calibrated. Moreover,
-the KCE can be formulated in terms of the kernel $k$ as
-```math
-    \mathrm{KCE}[k, g] := {\left(\mathbb{E}[(e_Y - g(X))^{\intercal} k(g(X), g(X')) (e_{Y'} - g(X'))]\right)}^{1/2},
-```
-where $(X',Y')$ is an independent copy of $(X,Y)$ and $e_i$ denotes the $i$th
-unit vector.
-
-The so-called maximum mean calibration error (MMCE), proposed by
-[Kumar et al. (2018)](http://proceedings.mlr.press/v80/kumar18a/kumar18a.pdf),
-can be viewed as a special case of the KCE, in which only the most-confident
-predictions are considered (Widmann et al. (2019)).
diff --git a/docs/src/ece.md b/docs/src/ece.md
new file mode 100644
index 0000000..453313d
--- /dev/null
+++ b/docs/src/ece.md
@@ -0,0 +1,49 @@
+# [Expected calibration error (ECE)](@id ece)
+
+## Definition
+
+A common calibration measure is the so-called expected calibration error (ECE).
+In its most general form (see [Widmann et al.](https://openreview.net/pdf?id=-bxf89v3Nx)),
+the ECE with respect to distance measure $d(p, p')$ is defined as
+```math
+\mathrm{ECE}_d := \mathbb{E} d\big(P_X, \mathcal{L}(Y \,|\, P_X)\big).
+```
+
+As implied by its name, the ECE is the expected distance between the left and
+right hand side of the calibration definition with respect to $d$.
+
+Usually, the ECE is used to analyze classification models (see, e.g.,
+[Guo et al. (2017)](http://proceedings.mlr.press/v70/guo17a/guo17a.pdf) and
+[Vaicenavicius et al. (2019)](http://proceedings.mlr.press/v89/vaicenavicius19a/vaicenavicius19a.pdf)).
+In this case, $P_X$ and $\mathcal{L}(Y \,|\, P_X)$ can be identified with vectors
+in the probability simplex and $d$ can be chosen as a the cityblock distance,
+the total variation distance, or the squared Euclidean distance.
+
+For other probabilistic predictive models such as regression models, one has to
+choose a more general distance measure $d$ between probability distributions on the
+target space since the conditional distributions $\mathcal{L}(Y \,|\, P_X)$ can be
+arbitrarily complex in general.
+
+## Estimators
+
+The main challenge in the estimation of the ECE is the estimation of the conditional
+distribution $\mathcal{L}(Y \,|\, P_X)$ from a finite data set of predictions and
+corresponding targets. Typically, predictions are binned and empirical estimates of
+the conditional distributions are calculated for each bin. You can construct such
+estimators with [`ECE`](@ref).
+
+```@docs
+ECE
+```
+
+### Binning algorithms
+
+Currently, two binning algorithms are supported. [`UniformBinning`](@ref) is a binning
+schemes with bins of fixed bins of uniform size whereas [`MedianVarianceBinning`](@ref)
+splits the validation data set of predictions and targets dynamically to reduce the
+variance of the predictions.
+
+```@docs
+UniformBinning
+MedianVarianceBinning
+```
diff --git a/docs/src/estimators.md b/docs/src/estimators.md
deleted file mode 100644
index 08bcbe8..0000000
--- a/docs/src/estimators.md
+++ /dev/null
@@ -1 +0,0 @@
-# Calibration error estimators
diff --git a/docs/src/index.md b/docs/src/index.md
index 3e8079c..930df28 100644
--- a/docs/src/index.md
+++ b/docs/src/index.md
@@ -3,10 +3,3 @@
 *Estimation of calibration errors.*
 
 A package for estimating calibration errors from predictions and targets.
-
-```@index
-```
-
-```@autodocs
-Modules = [CalibrationErrors]
-```
diff --git a/docs/src/introduction.md b/docs/src/introduction.md
new file mode 100644
index 0000000..8bd4ee0
--- /dev/null
+++ b/docs/src/introduction.md
@@ -0,0 +1,129 @@
+# Introduction
+
+## Probabilistic predictive models
+
+A probabilistic predictive model predicts a probability distribution over a set
+of targets for a given feature. By predicting a distribution, one can express
+the uncertainty in the prediction, which might be inherent to the prediction
+task (e.g., if the feature does not contain enough information to determine the
+target with absolute certainty) or caused by insufficient knowledge of the
+underlying relation between feature and target (e.g., if only a small number
+of observations of features and corresponding targets are available).[^1]
+
+The following plot shows measurements of the bill length and the flipper length
+for three different penguin species in the
+[Palmer penguin dataset](https://github.com/allisonhorst/palmerpenguins).
+
+```@setup palmerpenguins
+using CairoMakie
+using DataFrames
+using PalmerPenguins
+using AbstractPlotting.ColorSchemes
+
+penguins = dropmissing(DataFrame(PalmerPenguins.load()))
+
+f = Figure()
+f[1,1] = Axis(f; xlabel = "bill length [mm]", ylabel = "flipper length [mm]")
+scs = map(enumerate(groupby(penguins, :species))) do (i, df)
+    scatter!(
+        df[!, :bill_length_mm], df[!, :flipper_length_mm];
+        color = (ColorSchemes.Dark2_8[i], 0.8),
+    )
+end
+f[1,2] = Legend(f, scs, string.(levels(penguins.species)), "species")
+AbstractPlotting.save("penguins.svg", f)
+```
+
+![](penguins.svg)
+
+There exist many different probabilistic predictive models for predicting the
+probability of the penguin species (*target*) given the bill and flipper length
+(*feature*). We denote the feature by $X$ and the target by $Y$, and let
+$P_X$ be the prediction of a specific model $P$ for a feature $X$. Ideally, we would
+like that
+```math
+P_X = \mathcal{L}(Y \,|\, X) \qquad \text{almost surely},
+```
+i.e., the model should predict the law of target $Y$ given features $X$.[^2] Of course,
+usually it is not possible to achieve this in practice.
+
+A very simple class of models are models that yield the same prediction for all features,
+i.e., they return the same probabilities for the penguin species regardless of the bill and
+flipper length. Clearly, more complicated take into account also the features and might output
+different predictions for different features.
+
+In contrast to probabilistic predictive models, non-probabilistic predictive models
+predict a single target instead of a distribution over targets. In fact, such models can be
+viewed as a special class of probabilistic predictive models that output only Dirac
+distributions, i.e., that always predict 100% probability for one penguin species and
+0% probability for all others.
+
+Some other prediction models output a single target together with a confidence score
+between 0 and 1. Even these models can be reformulated as probabilistic predictive models,
+arguably in a slightly unconventional way: they correspond to a probabilistic model for a
+a binary classification problem whose feature space is extended with the predicted target
+and whose target is the predicted confidence score.
+
+[^1]: It does not matter how the model is obtained. In particular, both Bayesian and frequentist approaches can be used.
+
+[^2]: In classification problems, the law $\mathcal{L}(Y \,|\, X)$ can be identified with a vector in the probability simplex. Therefore often we just consider this equivalent formulation, both for the predictions $P_X$ and the law $\mathcal{L}(Y \,|\, X)$.
+
+## Calibration
+
+The main motivation for using a probabilistic model is that it provides additional
+information about the uncertainty of the predictions, which is valuable for decision
+making. A [classic example are weather forecasts](https://www.jstor.org/stable/2987588)
+that also report the "probability of rain" instead of only if it will rain or not.
+
+Therefore it is not sufficient if the model predicts an arbitrary distribution.
+Instead the predictions should actualy express the involved uncertainties "correctly".
+One desired property is that the predictions are consistent: if the forecasts predict
+an 80% probability of rain for an infinite sequence of days, then ideally on 80% of the
+days it rains.
+
+More generally, mathematically we would like
+```math
+P_X = \mathcal{L}(Y \,|\, P_X) \quad \text{almost surely},
+```
+i.e., the predicted distribution of targets should be equal to the distribution of targets
+conditioned on the predicted distribution.[^3]
+
+This statistical property is called *calibration*. If it is satisfied, a model is
+*calibrated*.
+
+Obviously, the ideal model $P_X = \mathcal{L}(Y \,|\, X)$ is calibrated. However,
+also the naive model $P_X = \mathcal{L}(Y)$ that always predicts the marginal
+distribution of $Y$ independent of the features is calibrated.[^4] In fact, any model of
+the form
+```math
+P_X = \mathcal{L}(Y \,|\, \phi(X)) \quad \text{almost surely},
+```
+where $\phi$ is some measurable function, is calibrated.
+
+[^3]: The general formulation applies not only to classification but to any prediction task with arbitrary target spaces, including regression.
+
+[^4]: In meterology, this model is called the *climatology*.
+
+## Calibration error
+
+Calibration errors such as the [expected calibration error](@ref ece) and the
+[kernel calibration error](@ref kce) measure the calibration, or rather the
+degree of miscalibration, of probabilistic predictive models. They allow a more
+fine-tuned analysis of calibration and enable comparisons of calibration of
+different models. Intuitively, calibration measures quantify the deviation of
+$P_X$ and $\mathcal{L}(Y \,|\, P_X)$, i.e., the left and right hand side in
+the calibration definition.
+
+### Estimation
+
+The calibration error of a model depends on the true conditional distribution of
+targets which is unknown in practice. Therefore calibration errors have to be
+estimated from a validation data set.
+
+Various estimators of different calibration errors such as the
+[expected calibration error](@ref ece) and the [kernel calibration error](@ref kce)
+can be evaluated with [`calibrationerror`](@ref).
+
+```@docs
+calibrationerror
+```
diff --git a/docs/src/kce.md b/docs/src/kce.md
new file mode 100644
index 0000000..45e3274
--- /dev/null
+++ b/docs/src/kce.md
@@ -0,0 +1,86 @@
+# [Kernel calibration error (KCE)](@id kce)
+
+## Definition
+
+The kernel calibration error (KCE) is another calibration error. The KCE with
+respect to a real-valued kernel
+$k \colon (\mathcal{P} \times \mathcal{Y}) \times (\mathcal{P} \times \mathcal{Y}) \to \mathbb{R}$
+on the product space $\mathcal{P} \times \mathcal{Y}$ of predictions and targets
+is defined as
+as
+```math
+\mathrm{KCE}_k := \sup_{f \in \mathcal{B}_k} \bigg| \mathbb{E}_{Y,P_X} f(P_X, Y) - \mathbb{E}_{Z_X,P_X} f(P_X, Z_X)\bigg|,
+```
+where $\mathcal{B}_{k}$ is the unit ball in the
+[reproducing kernel Hilbert space (RKHS)](https://en.wikipedia.org/wiki/Reproducing_kernel_Hilbert_space)
+of $k$, consisting of functions $f \colon \mathcal{P} \times \mathcal{Y} \to \mathbb{R}$,
+and $Z_X$ is a random variable on the target space $\mathcal{Y}$ with conditional distribution
+$P_X$ given $P_X$, i.e., $Z_X \,|\, P_X = \mu \sim \mu$
+([Widmann et al., 2021](https://openreview.net/pdf?id=-bxf89v3Nx)).[^1]
+
+For classification models with $m$ classes, there exists an equivalent formulation of the
+KCE based on matrix-valued kernel
+$\tilde{k} \colon \mathcal{P} \times \mathcal{P} \to \mathbb{R}^{m \times m}$ on
+the space $\mathcal{P}$ of predictions
+([Widmann et al., 2019](https://proceedings.neurips.cc/paper/2019/file/1c336b8080f82bcc2cd2499b4c57261d-Paper.pdf)). The definition above can be rewritten as
+```math
+\mathrm{KCE}_{\tilde{k}} := \sup_{f \in \mathcal{B}_{\tilde{k}}} \bigg| \mathbb{E}_{P_X} \big(\mathcal{L}(Y \,|\, P_X) - P_X\big)^\mathsf{T} f(P_X) \bigg|,
+```
+where the matrix-valued kernel $\tilde{k}$ is given by
+```math
+\tilde{k}_{i,j}(p, q) = k((p, i), (q, j)) \quad (i,j=1,\ldots,m),
+```
+and $\mathcal{B}_{\tilde{k}}$ is the unit ball in the RKHS of $\tilde{k}$, consisting
+of vector-valued functions $f \colon \mathcal{P} \to \mathbb{R}^m$.[^2] However,
+this formulation applies only to classification models whereas the general
+definition above covers all probabilistic predictive models.
+
+For a large class of kernels the KCE is zero if and only if the model is
+calibrated ([Widmann et al., 2021](https://openreview.net/pdf?id=-bxf89v3Nx)).
+Moreover, the squared KCE (SKCE) can be formulated in terms of the kernel $k$ as
+```math
+\begin{aligned}
+\mathrm{SKCE}_{k} := \mathrm{KCE}_k^2 &= \int k(u, v) \, \big(\mathcal{L}(P_X, Y) - \mathcal{L}(P_X, Z_X)\big)(u) \big(\mathcal{L}(P_X, Y) - \mathcal{L}(P_X, Z_X)\big)(v) \\
+&= \mathbb{E} h_k\big((P_X, Y), (P_{X'}, Y')\big),
+\end{aligned}
+```
+where $(X',Y')$ is an independent copy of $(X,Y)$ and
+```math
+\begin{aligned}
+h_k\big((\mu, y), (\mu', y')\big) :={}& k\big((\mu, y), (\mu', y')\big) - \mathbb{E}_{Z \sim \mu} k\big((\mu, Z), (\mu', y')\big) \\
+&- \mathbb{E}_{Z' \sim \mu'} k\big((\mu, y), (\mu', Z')\big) + \mathbb{E}_{Z \sim \mu, Z' \sim \mu'} k\big((\mu, Z), (\mu', Z')\big).
+\end{aligned}
+```
+
+[^1]: The KCE is a special case of calibration errors of the form $\sup_{f \in \mathcal{F}} \big| \mathbb{E}_{Y,P_X} f(P_X, Y) - \mathbb{E}_{Z_X,P_X} f(P_X, Z_X)\big|$, where $\mathcal{F}$ is some space of functions $f \colon \mathcal{P} \times \mathcal{Y} \to \mathbb{R}$ ([Widmann et al., 2021](https://openreview.net/pdf?id=-bxf89v3Nx)). For classification models, the [ECE](@ref ece) with respect to common distances such as the total variation distance or the squared Euclidean distance can be formulated in this way ([Widmann et al., 2019](https://proceedings.neurips.cc/paper/2019/file/1c336b8080f82bcc2cd2499b4c57261d-Paper.pdf)).
+
+[^2]: The maximum mean calibration error (MMCE) ([Kumar et al., 2018](http://proceedings.mlr.press/v80/kumar18a/kumar18a.pdf)) can be viewed as a special case of the KCE, in which only the most-confident predictions are considered ([Widmann et al., 2019](https://proceedings.neurips.cc/paper/2019/file/1c336b8080f82bcc2cd2499b4c57261d-Paper.pdf)).
+
+## Estimators
+
+For the SKCE biased and unbiased estimators exist. In CalibrationErrors.jl
+three types of estimators are available, namely [`BiasedSKCE`](@ref),
+[`UnbiasedSKCE`](@ref), and [`BlockUnbiasedSKCE`](@ref). Unsurprisingly,
+[`BiasedSKCE`](@ref) is a biased estimator whereas the other two
+estimators are unbiased. [`BiasedSKCE`](@ref) and [`UnbiasedSKCE`](@ref)
+have quadratic sample complexity whereas [`BlockUnbiasedSKCE`](@ref)
+is an estimator with linear sample complexity.
+
+### Biased estimators
+
+```@docs
+BiasedSKCE
+BiasedSKCE(::Kernel, ::Kernel)
+```
+
+### Unbiased estimators
+
+```@docs
+UnbiasedSKCE
+UnbiasedSKCE(::Kernel, ::Kernel)
+```
+
+```@docs
+BlockUnbiasedSKCE
+BlockUnbiasedSKCE(::Kernel, ::Kernel)
+```
diff --git a/src/binning/generic.jl b/src/binning/generic.jl
index 184b776..f8360f1 100644
--- a/src/binning/generic.jl
+++ b/src/binning/generic.jl
@@ -81,15 +81,3 @@ function adddata!(bin::Bin, prediction::AbstractVector{<:Real}, target::Integer)
 
     nothing
 end
-
-# distance computations
-
-"""
-    evaluate(distance, bin::Bin)
-
-Evaluate the `distance` between the average prediction and the distribution of targets in
-the `bin`.
-"""
-function Distances.evaluate(distance::SemiMetric, bin::Bin)
-    evaluate(distance, bin.mean_predictions, bin.proportions_targets)
-end
\ No newline at end of file
diff --git a/src/binning/medianvariance.jl b/src/binning/medianvariance.jl
index fc032a0..1e65db4 100644
--- a/src/binning/medianvariance.jl
+++ b/src/binning/medianvariance.jl
@@ -1,3 +1,14 @@
+"""
+    MedianVarianceBinning([minsize::Int = 10, maxbins::Int = typemax(Int)])
+
+Dynamic binning scheme of the probability simplex with at most `maxbins` bins that each
+contain at least `minsize` samples.
+
+The data set is split recursively as long as it is possible to split the bins while
+satisfying these conditions. In each step, the bin with the maximum variance of predicted
+probabilities for any component is selected and split at the median of the predicted
+probability of the component with the largest variance.
+"""
 struct MedianVarianceBinning <: AbstractBinningAlgorithm
     minsize::Int
     maxbins::Int
diff --git a/src/binning/uniform.jl b/src/binning/uniform.jl
index 9c710b3..58635a1 100644
--- a/src/binning/uniform.jl
+++ b/src/binning/uniform.jl
@@ -1,3 +1,9 @@
+"""
+    UniformBinning(nbins::Int)
+
+Binning scheme of the probability simplex with `nbins` bins of uniform width for
+each component.
+"""
 struct UniformBinning <: AbstractBinningAlgorithm
     nbins::Int
 
diff --git a/src/ece.jl b/src/ece.jl
index 4d53375..3890e06 100644
--- a/src/ece.jl
+++ b/src/ece.jl
@@ -8,8 +8,25 @@ end
 """
     ECE(binning[, distance = TotalVariation()])
 
-Create an estimator of the expected calibration error (ECE) with the given `binning`
-algorithm and `distance` function.
+Estimator of the expected calibration error (ECE) for a classification model with
+respect to the given `distance` function using the `binning` algorithm.
+
+For classification models, the predictions ``P_{X_i}`` and targets ``Y_i`` are identified
+with vectors in the probability simplex. The estimator of the ECE is defined as
+```math
+\\frac{1}{B} \\sum_{i=1}^B d\\big(\\overline{P}_i, \\overline{Y}_i\\big),
+```
+where ``B`` is the number of non-empty bins, ``d`` is the distance function, and
+``\\overline{P}_i`` and ``\\overline{Y}_i`` are the average vector of the predictions and
+the average vector of targets in the ``i``th bin. By default, the total variation distance
+is used.
+
+The `distance` has to be a function of the form
+```julia
+distance(pbar::Vector{<:Real}, ybar::Vector{<:Real}).
+```
+In particular, distance measures of the package
+[Distances.jl](https://github.com/JuliaStats/Distances.jl) are supported.
 """
 ECE(binning::AbstractBinningAlgorithm) = ECE(binning, TotalVariation())
 
@@ -33,7 +50,7 @@ function _calibrationerror(ece::ECE, predictions::AbstractVector{<:AbstractVecto
     # evaluate the distance in the first bin
     @inbounds begin
         bin = bins[1]
-        x = evaluate(distance, bin)
+        x = distance(bin.mean_predictions, bin.proportions_targets)
 
         # initialize the estimate
         estimate = x / 1
@@ -43,7 +60,7 @@ function _calibrationerror(ece::ECE, predictions::AbstractVector{<:AbstractVecto
         for i in 2:nbins
             # evaluate the distance
             bin = bins[i]
-            x = evaluate(distance, bin)
+            x = distance(bin.mean_predictions, bin.proportions_targets)
 
             # update the estimate
             m = bin.nsamples
diff --git a/src/mkce/unnormalized.jl b/src/mkce/unnormalized.jl
new file mode 100644
index 0000000..17e7896
--- /dev/null
+++ b/src/mkce/unnormalized.jl
@@ -0,0 +1,78 @@
+struct UnnormalizedMKCE{K<:MatrixKernel,V<:AbstractArray} <: CalibrationErrorEstimator
+    kernel::K
+    witness::V
+end
+
+function _calibrationerror(estimator::UnnormalizedMKCE, predictions::AbstractMatrix{<:Real},
+                          labels::AbstractVector{<:Integer})
+    @unpack kernel, witness = estimator
+
+    # obtain number of samples
+    nclasses, nsamples = size(predictions)
+    nwitness = length(witness)
+
+    T = float(eltype(predictions))
+    cache = Vector{T}(undef, nclasses)
+    meancache = Vector{T}(undef, nclasses)
+
+    s = zero(T)
+    for i in 1:nwitness
+        v = witness[i]
+        fill!(meancache, zero(T))
+
+        for j in 1:nsamples
+            mkce_kernel!(cache, kernel, v, view(predictions, :, j), labels[j])
+            meancache .+= cache
+        end
+        meancache ./= nsamples
+
+        s += sum(abs2, meancache)
+    end
+
+    s / nwitness
+end
+
+"""
+    mkce_kernel!(out, k, v, p, y)
+
+Evaluate kernel function
+```math
+k(v, p) (p - e_y)
+```
+of the mean kernel calibration error for the matrix-valued kernel `k`, witness point `v`
+and prediction `p` with corresponding label `y`.
+
+This method assumes that `v`, `p`, and `y` are valid and specified correctly, and
+does not perform any checks.
+"""
+function mkce_kernel!(out, kernel::MatrixKernel, v::AbstractVector{<:Real},
+                      p::AbstractVector{<:Real}, y::Integer)
+    copyto!(out, p)
+    @inbounds out[y] -= 1
+    lmul!(kernel(v, p), out)
+
+    out
+end
+
+function mkce_kernel!(out, kernel::UniformScalingKernel, v::AbstractVector{<:Real},
+                      p::AbstractVector{<:Real}, y::Integer)
+    @unpack λ = kernel
+
+    copyto!(out, p)
+    @inbounds out[y] -= 1
+    lmul!(λ * kernel.kernel(v, p), out)
+    
+    out
+end
+
+function mkce_kernel!(out, kernel::DiagonalKernel, v::AbstractVector{<:Real},
+                      p::AbstractVector{<:Real}, y::Integer)
+    @unpack diag = kernel
+
+    copyto!(out, p)
+    @inbounds out[y] -= 1
+    k = kernel.kernel(v, p)
+    @. out = k * diag
+    
+    out
+end
\ No newline at end of file
diff --git a/src/skce/biased.jl b/src/skce/biased.jl
index 29cd751..34dd65a 100644
--- a/src/skce/biased.jl
+++ b/src/skce/biased.jl
@@ -1,8 +1,57 @@
+@doc raw"""
+    BiasedSKCE(k)
+
+Biased estimator of the squared kernel calibration error (SKCE) with kernel `k`.
+
+Kernel `k` on the product space of predictions and targets has to be a `Kernel` from the
+Julia package
+[KernelFunctions.jl](https://github.com/JuliaGaussianProcesses/KernelFunctions.jl)
+that can be evaluated for inputs that are tuples of predictions and targets.
+
+# Details
+
+The estimator is biased and guaranteed to be non-negative. Its sample complexity is
+``O(n^2)``, where ``n`` is the total number of samples.
+
+Let ``(P_{X_i}, Y_i)_{i=1,\ldots,n}`` be a data set of predictions and corresponding
+targets. The estimator is defined as
+```math
+\frac{1}{n^2} \sum_{i,j=1}^n h_k\big((P_{X_i}, Y_i), (P_{X_j}, Y_j)\big)
+```
+where
+```math
+\begin{aligned}
+h_k\big((μ, y), (μ', y')\big) ={}&   k\big((μ, y), (μ', y')\big)
+                                   - 𝔼_{Z ∼ μ} k\big((μ, Z), (μ', y')\big) \\
+                                 & - 𝔼_{Z' ∼ μ'} k\big((μ, y), (μ', Z')\big)
+                                   + 𝔼_{Z ∼ μ, Z' ∼ μ'} k\big((μ, Z), (μ', Z')\big).
+\end{aligned}
+```
+
+# References
+
+Widmann, D., Lindsten, F., & Zachariah, D. (2019). [Calibration tests in multi-class
+classification: A unifying framework](https://proceedings.neurips.cc/paper/2019/hash/1c336b8080f82bcc2cd2499b4c57261d-Abstract.html).
+In: Advances in Neural Information Processing Systems (NeurIPS 2019) (pp. 12257–12267).
+
+Widmann, D., Lindsten, F., & Zachariah, D. (2021). [Calibration tests beyond
+classification](https://openreview.net/forum?id=-bxf89v3Nx).
+
+See also: [`UnbiasedSKCE`](@ref), [`BlockUnbiasedSKCE`](@ref)
+"""
 struct BiasedSKCE{K<:Kernel} <: SKCE
     """Kernel of estimator."""
     kernel::K
 end
 
+"""
+    BiasedSKCE(k₁, k₂)
+
+Biased estimator of the squared kernel calibration error (SKCE) with a tensor product
+kernel ``k = k_1 \\otimes k_2``.
+
+See also: [`BiasedSKCE`](@ref)
+"""
 BiasedSKCE(kernel1::Kernel, kernel2::Kernel) = BiasedSKCE(TensorProduct(kernel1, kernel2))
 
 function _calibrationerror(skce::BiasedSKCE,
diff --git a/src/skce/unbiased.jl b/src/skce/unbiased.jl
index 19ae637..8e223e9 100644
--- a/src/skce/unbiased.jl
+++ b/src/skce/unbiased.jl
@@ -1,8 +1,57 @@
+@doc raw"""
+    UnbiasedSKCE(k)
+
+Unbiased estimator of the squared kernel calibration error (SKCE) with kernel `k`.
+
+Kernel `k` on the product space of predictions and targets has to be a `Kernel` from the
+Julia package
+[KernelFunctions.jl](https://github.com/JuliaGaussianProcesses/KernelFunctions.jl)
+that can be evaluated for inputs that are tuples of predictions and targets.
+
+# Details
+
+The estimator is unbiased and not guaranteed to be non-negative. Its sample complexity
+is ``O(n^2)``, where ``n`` is the total number of samples.
+
+Let ``(P_{X_i}, Y_i)_{i=1,\ldots,n}`` be a data set of predictions and corresponding
+targets. The estimator is defined as
+```math
+\frac{2}{n(n-1)} \sum_{1 \leq i < j \leq n} h_k\big((P_{X_i}, Y_i), (P_{X_j}, Y_j)\big),
+```
+where
+```math
+\begin{aligned}
+h_k\big((μ, y), (μ', y')\big) ={}&   k\big((μ, y), (μ', y')\big)
+                                   - 𝔼_{Z ∼ μ} k\big((μ, Z), (μ', y')\big) \\
+                                 & - 𝔼_{Z' ∼ μ'} k\big((μ, y), (μ', Z')\big)
+                                   + 𝔼_{Z ∼ μ, Z' ∼ μ'} k\big((μ, Z), (μ', Z')\big).
+\end{aligned}
+```
+
+# References
+
+Widmann, D., Lindsten, F., & Zachariah, D. (2019). [Calibration tests in multi-class
+classification: A unifying framework](https://proceedings.neurips.cc/paper/2019/hash/1c336b8080f82bcc2cd2499b4c57261d-Abstract.html).
+In: Advances in Neural Information Processing Systems (NeurIPS 2019) (pp. 12257–12267).
+
+Widmann, D., Lindsten, F., & Zachariah, D. (2021). [Calibration tests beyond
+classification](https://openreview.net/forum?id=-bxf89v3Nx).
+
+See also: [`BiasedSKCE`](@ref), [`BlockUnbiasedSKCE`](@ref)
+"""
 struct UnbiasedSKCE{K<:Kernel} <: SKCE
     """Kernel of estimator."""
     kernel::K
 end
 
+"""
+    UnbiasedSKCE(k₁, k₂)
+
+Unbiased estimator of the squared kernel calibration error (SKCE) with a tensor product
+kernel ``k = k_1 \\otimes k_2``.
+
+See also: [`UnbiasedSKCE`](@ref)
+"""
 function UnbiasedSKCE(kernel1::Kernel, kernel2::Kernel)
     return UnbiasedSKCE(TensorProduct(kernel1, kernel2))
 end
@@ -24,6 +73,52 @@ function _calibrationerror(
     return estimate
 end
 
+@doc raw"""
+    BlockUnbiasedSKCE(k[, blocksize = 2])
+
+Unbiased estimator of the squared kernel calibration error (SKCE) with kernel `k` that
+uses blocks with `blocksize` samples.
+
+Kernel `k` on the product space of predictions and targets has to be a `Kernel` from the
+Julia package
+[KernelFunctions.jl](https://github.com/JuliaGaussianProcesses/KernelFunctions.jl)
+that can be evaluated for inputs that are tuples of predictions and targets.
+
+The number of samples per block must be at least 2 and at most the total number of samples.
+Note that samples in the last block are discarded if it is incomplete (see details below).
+
+# Details
+
+The estimator is unbiased and not guaranteed to be non-negative. Its sample complexity
+is ``O(Bn)``, where ``B`` is the block size and ``n`` is the total number of samples.
+
+Let ``(P_{X_i}, Y_i)_{i=1,\ldots,n}`` be a data set of predictions and corresponding
+targets. The estimator with block size ``B`` is defined as
+```math
+{\bigg\lfloor \frac{n}{B} \bigg\rfloor}^{-1} \sum_{b=1}^{\lfloor n/B \rfloor}
+\frac{2}{B(B-1)} \sum_{(b - 1) B < i < j \leq bB} h_k\big((P_{X_i}, Y_i), (P_{X_j}, Y_j)\big),
+```
+where
+```math
+\begin{aligned}
+h_k\big((μ, y), (μ', y')\big) ={}&   k\big((μ, y), (μ', y')\big)
+                                   - 𝔼_{Z ∼ μ} k\big((μ, Z), (μ', y')\big) \\
+                                 & - 𝔼_{Z' ∼ μ'} k\big((μ, y), (μ', Z')\big)
+                                   + 𝔼_{Z ∼ μ, Z' ∼ μ'} k\big((μ, Z), (μ', Z')\big).
+\end{aligned}
+```
+
+# References
+
+Widmann, D., Lindsten, F., & Zachariah, D. (2019). [Calibration tests in multi-class
+classification: A unifying framework](https://proceedings.neurips.cc/paper/2019/hash/1c336b8080f82bcc2cd2499b4c57261d-Abstract.html).
+In: Advances in Neural Information Processing Systems (NeurIPS 2019) (pp. 12257–12267).
+
+Widmann, D., Lindsten, F., & Zachariah, D. (2021). [Calibration tests beyond
+classification](https://openreview.net/forum?id=-bxf89v3Nx).
+
+See also: [`BiasedSKCE`](@ref), [`UnbiasedSKCE`](@ref)
+"""
 struct BlockUnbiasedSKCE{K<:Kernel} <: SKCE
     """Kernel of estimator."""
     kernel::K
@@ -36,6 +131,14 @@ struct BlockUnbiasedSKCE{K<:Kernel} <: SKCE
     end
 end
 
+"""
+    BlockUnbiasedSKCE(k₁, k₂)
+
+Unbiased estimator of the squared kernel calibration error (SKCE) with a tensor product
+kernel ``k = k_1 \\otimes k_2`` that uses blocks with `blocksize` samples.
+
+See also: [`BlockUnbiasedSKCE`](@ref)
+"""
 function BlockUnbiasedSKCE(kernel1::Kernel, kernel2::Kernel, blocksize::Int = 2)
     return BlockUnbiasedSKCE(TensorProduct(kernel1, kernel2), blocksize)
 end
diff --git a/test/binning/generic.jl b/test/binning/generic.jl
index 3e7dd03..4337957 100644
--- a/test/binning/generic.jl
+++ b/test/binning/generic.jl
@@ -24,12 +24,6 @@ Random.seed!(1234)
     @test sum(bin.mean_predictions) ≈ 1
     @test sum(bin.proportions_targets) ≈ 1
 
-    # check distance calculations
-    for distance in (TotalVariation(), Cityblock(), Euclidean(), SqEuclidean())
-        @test evaluate(distance, bin) == evaluate(distance, mean(predictions),
-            proportions(targets, nclasses))
-    end
-
     # compare with adding data
     bin2 = Bin(predictions[1], targets[1])
     for i in 2:nsamples