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170 | 170 |
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171 | 171 | # ╔═╡ e15efdfa-e64f-4f5b-a94c-6c5e135a9ec2
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172 | 172 | let
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| 173 | + W = 6 |
| 174 | + L = 3 |
| 175 | + x = collect(range(0, 1; length=101)) |
| 176 | + b1 = Beta(W+1, L+1) |
| 177 | + plot(x, pdf.(b1, x); label = "β") |
| 178 | + |
173 | 179 | map2_0 = optimize(m2_0(W, L), MAP())
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174 | 180 | μ = coef(map2_0)[:p]
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175 | 181 | σ = sqrt(vcov(map2_0)[:p, :p])
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178 | 184 | label="Normal($(round(μ; digits=2)), $(round(σ; digits=2)))")
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179 | 185 | end
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180 | 186 |
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| 187 | +# ╔═╡ 56f8237f-69d2-4725-bb48-8c62e70085dc |
| 188 | +let |
| 189 | + W = 6 |
| 190 | + L = 3 |
| 191 | + x = collect(range(0, 1; length=101)) |
| 192 | + b1 = Beta(W+1, L+1) |
| 193 | + plot(x, pdf.(b1, x); label = "β") |
| 194 | + |
| 195 | + chains = sample(m2_0(W, L), NUTS(), 1000) |
| 196 | + global df = DataFrame(chains) |
| 197 | + |
| 198 | + global map2_0 = optimize(m2_0(W, L), MAP()) |
| 199 | + μ = coef(map2_0)[:p] |
| 200 | + σ = sqrt(vcov(map2_0)[:p, :p]) |
| 201 | + b = Normal(μ, σ) |
| 202 | + σ1 = std(df.p; mean=μ) |
| 203 | + b1 = Normal(μ, σ1) |
| 204 | + plot!(x, pdf.(b, x); style=:dash, |
| 205 | + label="Normal($(round(μ; digits=2)), $(round(σ; digits=2)))") |
| 206 | + plot!(x, pdf.(b1, x); style=:dash, |
| 207 | + label="Normal($(round(μ; digits=2)), $(round(σ1; digits=2)))") |
| 208 | +end |
| 209 | + |
| 210 | +# ╔═╡ 141da211-65cf-4bc2-9684-f469b13eff6b |
| 211 | +vcov(map2_0) |
| 212 | + |
| 213 | +# ╔═╡ 3bddae59-4998-4b87-ae43-8343f6a9350f |
| 214 | +vcov(map2_0)[:p, :p] |
| 215 | + |
| 216 | +# ╔═╡ 3c64eda4-fcbe-46ee-aafc-0d0b89e5f8fb |
| 217 | +√vcov(map2_0) |
| 218 | + |
| 219 | +# ╔═╡ e0440e29-ab5d-43b9-8151-2b824645b90b |
| 220 | +let |
| 221 | + μ = coef(map2_0)[:p] |
| 222 | + std(df.p; mean=μ) |
| 223 | +end |
| 224 | + |
| 225 | +# ╔═╡ 8b367ce6-fe0a-4e47-ac25-d2a20ea06e48 |
| 226 | +let |
| 227 | + chains = sample(m2_0(W, L), NUTS(), 1000) |
| 228 | + DataFrame(chains) |
| 229 | +end |
| 230 | + |
181 | 231 | # ╔═╡ 8c7de4e1-b5b1-44c4-9718-b8044a6397ef
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182 | 232 | md"### Code 2.9"
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183 | 233 |
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221 | 271 | # ╠═443044d5-02a3-4bfc-955b-54b0c12c63e2
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222 | 272 | # ╟─3276b558-7dc7-4869-a083-472716a8a2ab
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223 | 273 | # ╠═e15efdfa-e64f-4f5b-a94c-6c5e135a9ec2
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| 274 | +# ╠═56f8237f-69d2-4725-bb48-8c62e70085dc |
| 275 | +# ╠═141da211-65cf-4bc2-9684-f469b13eff6b |
| 276 | +# ╠═3bddae59-4998-4b87-ae43-8343f6a9350f |
| 277 | +# ╠═3c64eda4-fcbe-46ee-aafc-0d0b89e5f8fb |
| 278 | +# ╠═e0440e29-ab5d-43b9-8151-2b824645b90b |
| 279 | +# ╠═8b367ce6-fe0a-4e47-ac25-d2a20ea06e48 |
224 | 280 | # ╟─20e03a5e-3321-4019-97a5-44a0fd77a831
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225 | 281 | # ╠═4a47f055-842c-451c-bc75-072708588f9a
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226 | 282 | # ╟─8c7de4e1-b5b1-44c4-9718-b8044a6397ef
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