Michiel branch

Project.toml

@@ -4,6 +4,7 @@ DifferentialEquations = "0c46a032-eb83-5123-abaf-570d42b7fbaa"
 Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f"
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
 GlobalSensitivity = "af5da776-676b-467e-8baf-acd8249e4f0f"
+Interpolations = "a98d9a8b-a2ab-59e6-89dd-64a1c18fca59"
 LaTeXStrings = "b964fa9f-0449-5b57-a5c2-d3ea65f4040f"
 Latexify = "23fbe1c1-3f47-55db-b15f-69d7ec21a316"
 Measurements = "eff96d63-e80a-5855-80a2-b1b0885c5ab7"

examples/censored.jl

@@ -12,7 +12,7 @@ md"""
 
 # Censored
 
-Researchers are studying a new drug designed to cure a specific type of skin condition. They monitor 15 patients undergoing treatment for five months, recording the time it takes for patients to show no signs of the disease. Of the 15, seven were cured in the five-month study period, at `[2.1, 4.7, 1.6, 2.8, 4.3, 1.9, 4.2]` months. Eight patients might not achieve remission within the five-year study period (this is censored data). You may assume that these persons were cured at some later, unspecified time after the five-year period. Given a Gamma prior on the rate parameter $\lambda$, what is its posterior distribution? 
+Researchers are studying a new drug designed to cure a specific type of skin condition. They monitor 15 patients undergoing treatment for five months, recording the time it takes for patients to show no signs of the condition. Of the 15, seven were cured in the five-month study period, at `[2.1, 4.7, 1.6, 2.8, 4.3, 1.9, 4.2]` months. Eight patients were not achieve cured within the five-month study period (this is censored data). You may assume that these persons were cured at some later, unspecified time after the five-month trial. Given a Gamma prior on the rate parameter $\lambda$, what is its posterior distribution? 
 
 Give a 95% credibility interval.
 

examples/citations.jl

@@ -0,0 +1,99 @@
+### A Pluto.jl notebook ###
+# v0.20.3
+
+using Markdown
+using InteractiveUtils
+
+# ╔═╡ 2fb807d8-f555-41cf-a374-8ff9cadf9533
+using Pkg; Pkg.activate("..")
+
+# ╔═╡ 6613efca-d42c-11ef-0e77-716f85ded3df
+using Turing, PlutoUI, StatsPlots
+
+# ╔═╡ e89d9c26-0ffe-48ca-ad39-93655d6868a4
+md"Consider the following model:"
+
+# ╔═╡ 19fcf183-322a-44c4-8c3c-987f667d882e
+@model function citations()
+	X ~ Normal(0, 1)
+	Y ~ Normal(1, 2)
+	Z ~ Poisson(exp(0.8X + 1.2Y + 0.2X*Y))
+end
+
+# ╔═╡ 8197a2a1-86fb-44eb-a09f-d4e8511167b2
+md"Generate a sample of 10,000 observations of this distribution. 
+
+Use this sample to create a histogram of `Z` and compute its quantiles. Additionally, compute the 99% quantile (this is the top-1% value of `Z`).
+
+Next, compute the correlation between `X` and `Y` and draw a scatter plot. Does this match your observation?
+"
+
+# ╔═╡ aa73f4fa-23ca-41ff-b3cf-4bab0740d157
+prior = sample(citations(), Prior(), 10_000)
+
+# ╔═╡ e40b92ad-2a9a-414e-b8ee-cc658d505212
+summarize(prior)
+
+# ╔═╡ fba7efbd-8ad0-4fa3-aeb9-5a674e0295ce
+histogram(prior[:Z])
+
+# ╔═╡ a737c4c1-c27d-4800-9d0a-e71d4503025b
+histogram(prior[:Z], yscale=:log10)
+
+# ╔═╡ b1d4d0a6-6d1d-4cf2-b21e-51705c167b86
+quantile(prior, q = [0.025, 0.25, 0.5, 0.75, 0.975, 0.99])
+
+# ╔═╡ 4196765c-b2bd-4093-963b-82fb0ec2e343
+cor(prior[:X], prior[:Y])
+
+# ╔═╡ 5b4ef7a2-790e-46ba-89f1-136a1c9e7fdb
+scatter(prior[:X], prior[:Y], xlab="X", ylab="Y")
+
+# ╔═╡ b0bef20d-a10c-457b-ac8c-1e8caddc54e1
+md"Now, make a conditional model `high_citation` in which you fix `Z = 100`. Use the No-U-Turn sampler to obtain 10,000 posterior samples.
+
+Using this conditional sample, again compute the correlation between `X` and `Y` together with the scatter plot. What do you observe?
+"
+
+# ╔═╡ bb1681c5-ff86-497c-8cb8-f5e2bd638536
+high_citation = citations() | (Z=100,)
+
+# ╔═╡ 03f48a27-f0ce-46e7-989d-ab57cfc5babe
+post = sample(high_citation, NUTS(), 10_000)
+
+# ╔═╡ d5e6bd69-6a49-4d6a-8c37-9cda7fb97bb5
+quantile(post)
+
+# ╔═╡ 72577ba4-e20c-4eb1-af34-1d702957f1e3
+cor(post[:X], post[:Y])
+
+# ╔═╡ 0a64b09b-fd71-4628-8b7d-7df3c4b45a15
+scatter(post[:X], post[:Y], xlabel="X", ylabel="Y")
+
+# ╔═╡ bf8ac4d6-5a6e-49ff-b75e-6a0f7ad7ff4d
+md"Now for some context, the model is represents the number of citations a journal article can attract after being published (`Z`). `X` represents a metric of **quality**, how well the study was done and whether everything was done correctly. `Y` represents the spectacularity or excitedness of the claims, i.e., whether its results would be of general interest. Re-interpret you results in light of this new information."
+
+# ╔═╡ 830e9980-3f01-4f54-b29f-7247bb4531f4
+plot(post)
+
+# ╔═╡ Cell order:
+# ╠═6613efca-d42c-11ef-0e77-716f85ded3df
+# ╠═2fb807d8-f555-41cf-a374-8ff9cadf9533
+# ╠═e89d9c26-0ffe-48ca-ad39-93655d6868a4
+# ╠═19fcf183-322a-44c4-8c3c-987f667d882e
+# ╠═8197a2a1-86fb-44eb-a09f-d4e8511167b2
+# ╠═aa73f4fa-23ca-41ff-b3cf-4bab0740d157
+# ╠═e40b92ad-2a9a-414e-b8ee-cc658d505212
+# ╠═fba7efbd-8ad0-4fa3-aeb9-5a674e0295ce
+# ╠═a737c4c1-c27d-4800-9d0a-e71d4503025b
+# ╠═b1d4d0a6-6d1d-4cf2-b21e-51705c167b86
+# ╠═4196765c-b2bd-4093-963b-82fb0ec2e343
+# ╠═5b4ef7a2-790e-46ba-89f1-136a1c9e7fdb
+# ╠═b0bef20d-a10c-457b-ac8c-1e8caddc54e1
+# ╠═bb1681c5-ff86-497c-8cb8-f5e2bd638536
+# ╠═03f48a27-f0ce-46e7-989d-ab57cfc5babe
+# ╠═d5e6bd69-6a49-4d6a-8c37-9cda7fb97bb5
+# ╠═72577ba4-e20c-4eb1-af34-1d702957f1e3
+# ╠═0a64b09b-fd71-4628-8b7d-7df3c4b45a15
+# ╠═bf8ac4d6-5a6e-49ff-b75e-6a0f7ad7ff4d
+# ╠═830e9980-3f01-4f54-b29f-7247bb4531f4