This model is based on data of the !Kung San people (Howell, 2010). The prior assumes that the height of a man is most likely to be 178 cm because McElreath has that lenght.
In Edition 2, McElreath defines the model as
import CSV
using DataFrames
using Random
using Turing
using TuringModels
Random.seed!(1)
data_path = joinpath(TuringModels.project_root, "data", "Howell1.csv")
df = CSV.read(data_path, DataFrame; delim=';')
df = filter(row -> row.age >= 18, df);
For df, see Section df.
@model function line(height)
μ ~ Normal(178, 20)
σ ~ Uniform(0, 50)
height ~ Normal(μ, σ)
end
model = line(df.height);
chns = sample(model, NUTS(), 1000)
Chains MCMC chain (1000×14×1 Array{Float64, 3}):
Iterations = 501:1:1500
Number of chains = 1
Samples per chain = 1000
Wall duration = 4.78 seconds
Compute duration = 4.78 seconds
parameters = μ, σ
internals = lp, n_steps, is_accept, acceptance_rate, log_density, hamiltonian_energy, hamiltonian_energy_error, max_hamiltonian_energy_error, tree_depth, numerical_error, step_size, nom_step_size
Summary Statistics
parameters mean std naive_se mcse ess rhat ess_per_sec
Symbol Float64 Float64 Float64 Float64 Float64 Float64 Float64
μ 154.6053 0.4132 0.0131 0.0121 1030.1379 0.9991 215.4199
σ 7.7694 0.2958 0.0094 0.0102 753.0792 0.9990 157.4821
Quantiles
parameters 2.5% 25.0% 50.0% 75.0% 97.5%
Symbol Float64 Float64 Float64 Float64 Float64
μ 153.7747 154.3235 154.6145 154.8901 155.4439
σ 7.2390 7.5562 7.7573 7.9728 8.3750
using StatsPlots
StatsPlots.plot(chns)
"/home/runner/work/TuringModels.jl/TuringModels.jl/__site/assets/models/height/code/output/chns.svg"
"""
Iterations = 1:1000
Thinning interval = 1
Chains = 1,2,3,4
Samples per chain = 1000
Empirical Posterior Estimates:
Mean SD Naive SE MCSE ESS
alpha 154.597086 0.27326431 0.0043206882 0.0036304132 1000
beta 0.906380 0.04143488 0.0006551430 0.0006994720 1000
sigma 5.106643 0.19345409 0.0030587777 0.0032035103 1000
Quantiles:
2.5% 25.0% 50.0% 75.0% 97.5%
alpha 154.0610000 154.4150000 154.5980000 154.7812500 155.1260000
beta 0.8255494 0.8790695 0.9057435 0.9336445 0.9882981
sigma 4.7524368 4.9683400 5.0994450 5.2353100 5.5090128
""";
df
352×4 DataFrame
Row │ height weight age male
│ Float64 Float64 Float64 Int64
─────┼──────────────────────────────────
1 │ 151.765 47.8256 63.0 1
2 │ 139.7 36.4858 63.0 0
3 │ 136.525 31.8648 65.0 0
4 │ 156.845 53.0419 41.0 1
5 │ 145.415 41.2769 51.0 0
6 │ 163.83 62.9926 35.0 1
7 │ 149.225 38.2435 32.0 0
8 │ 168.91 55.48 27.0 1
9 │ 147.955 34.8699 19.0 0
10 │ 165.1 54.4877 54.0 1
11 │ 154.305 49.8951 47.0 0
12 │ 151.13 41.2202 66.0 1
13 │ 144.78 36.0322 73.0 0
14 │ 149.9 47.7 20.0 0
15 │ 150.495 33.8493 65.3 0
16 │ 163.195 48.5627 36.0 1
17 │ 157.48 42.3258 44.0 1
18 │ 143.942 38.3569 31.0 0
19 │ 161.29 48.9879 39.0 1
20 │ 156.21 42.7227 29.0 0
21 │ 146.4 35.4936 56.0 1
22 │ 148.59 37.9033 45.0 0
23 │ 147.32 35.4652 19.0 0
24 │ 147.955 40.313 29.0 1
25 │ 161.925 55.1114 30.0 1
26 │ 146.05 37.5064 24.0 0
27 │ 146.05 38.4986 35.0 0
28 │ 152.705 46.6066 33.0 0
29 │ 142.875 38.8388 27.0 0
30 │ 142.875 35.5786 32.0 0
31 │ 147.955 47.4004 36.0 0
32 │ 160.655 47.8823 24.0 1
33 │ 151.765 49.4132 30.0 1
34 │ 162.865 49.3848 24.0 1
35 │ 171.45 56.5573 52.0 1
36 │ 147.32 39.1223 42.0 0
37 │ 147.955 49.8951 19.0 0
38 │ 154.305 41.2485 55.0 1
39 │ 143.51 38.5553 43.0 0
40 │ 146.7 42.4 20.0 1
41 │ 157.48 44.6505 18.0 1
42 │ 165.735 58.5984 42.0 1
43 │ 152.4 46.72 44.0 0
44 │ 141.605 44.2252 60.0 0
45 │ 158.8 50.9 20.0 0
46 │ 155.575 54.3176 37.0 0
47 │ 164.465 45.8978 50.0 1
48 │ 151.765 48.0241 50.0 0
49 │ 161.29 52.2198 31.0 1
50 │ 154.305 47.6272 25.0 0
51 │ 145.415 45.6427 23.0 0
52 │ 145.415 42.4109 52.0 0
53 │ 152.4 36.4858 79.3 1
54 │ 163.83 55.9336 35.0 1
55 │ 144.145 37.1945 27.0 0
56 │ 153.67 48.3075 38.0 1
57 │ 142.875 37.3363 39.0 0
58 │ 167.005 47.1736 30.0 1
59 │ 158.42 47.287 24.0 0
60 │ 165.735 57.5495 51.0 1
61 │ 149.86 37.9316 46.0 0
62 │ 154.94 47.2019 22.0 0
63 │ 160.96 43.2046 29.0 1
64 │ 161.925 50.2637 38.0 1
65 │ 147.955 39.3775 30.0 0
66 │ 159.385 50.689 45.0 1
67 │ 148.59 39.4342 47.0 0
68 │ 136.525 36.2874 79.0 0
69 │ 158.115 46.2664 45.0 1
70 │ 144.78 42.2691 54.0 0
71 │ 156.845 47.6272 31.0 1
72 │ 179.07 55.7068 23.0 1
73 │ 170.18 48.5627 41.0 1
74 │ 146.05 42.8077 23.0 0
75 │ 147.32 35.0683 36.0 0
76 │ 162.56 56.7557 30.0 0
77 │ 152.4 51.2559 34.0 0
78 │ 160.02 47.2303 44.0 1
79 │ 149.86 40.9367 43.0 0
80 │ 142.875 32.7153 73.3 0
81 │ 167.005 57.0675 38.0 1
82 │ 159.385 42.9778 43.0 1
83 │ 154.94 39.9444 33.0 0
84 │ 162.56 45.9545 35.0 1
85 │ 152.4 41.1068 29.0 0
86 │ 170.18 47.5988 58.0 1
87 │ 146.05 37.5064 53.0 0
88 │ 159.385 45.019 51.0 1
89 │ 151.13 42.2691 48.0 0
90 │ 160.655 54.8563 29.0 1
91 │ 169.545 53.5239 41.0 1
92 │ 158.75 52.1914 81.75 1
93 │ 149.86 42.4109 35.0 0
94 │ 153.035 49.5833 46.0 0
95 │ 161.925 41.7305 29.0 1
96 │ 162.56 56.0186 42.0 1
97 │ 149.225 42.1557 27.0 0
98 │ 163.195 53.0986 22.0 1
99 │ 161.925 50.2353 43.0 1
100 │ 145.415 42.5243 53.0 0
101 │ 163.195 49.1013 43.0 1
102 │ 151.13 38.4986 41.0 0
103 │ 150.495 49.8101 50.0 0
104 │ 170.815 59.7607 33.0 1
105 │ 157.48 47.939 62.0 1
106 │ 152.4 39.2924 49.0 0
107 │ 147.32 36.8827 22.0 0
108 │ 145.415 42.1274 29.0 0
109 │ 157.48 44.5654 33.0 1
110 │ 154.305 47.854 34.0 0
111 │ 167.005 55.1965 42.0 1
112 │ 142.875 32.9988 40.0 0
113 │ 152.4 40.88 27.0 0
114 │ 160.0 51.2 25.0 1
115 │ 159.385 49.0446 29.0 1
116 │ 149.86 53.4388 45.0 0
117 │ 160.655 54.0908 26.0 1
118 │ 160.655 55.3666 45.0 1
119 │ 149.225 42.2408 45.0 0
120 │ 140.97 40.9367 85.6 0
121 │ 154.94 49.6967 26.0 1
122 │ 141.605 44.3386 24.0 0
123 │ 160.02 45.9545 57.0 1
124 │ 150.165 41.9573 22.0 0
125 │ 155.575 51.4827 24.0 0
126 │ 156.21 44.1118 21.0 0
127 │ 153.035 32.205 79.0 0
128 │ 167.005 56.7557 50.0 1
129 │ 149.86 52.6734 40.0 0
130 │ 147.955 36.4858 64.0 0
131 │ 159.385 48.8462 32.0 1
132 │ 161.925 56.9541 38.7 1
133 │ 155.575 42.099 26.0 0
134 │ 159.385 50.1786 63.0 1
135 │ 146.685 46.5499 62.0 0
136 │ 172.72 61.8019 22.0 1
137 │ 166.37 48.9879 41.0 1
138 │ 141.605 31.5246 19.0 1
139 │ 151.765 35.2951 74.0 0
140 │ 156.845 45.6427 41.0 1
141 │ 148.59 43.885 33.0 0
142 │ 157.48 45.5576 53.0 0
143 │ 149.86 39.0089 18.0 0
144 │ 147.955 41.1635 37.0 0
145 │ 153.035 45.2458 61.0 0
146 │ 160.655 53.6373 44.0 1
147 │ 149.225 52.3048 35.0 0
148 │ 138.43 39.094 23.0 0
149 │ 162.56 45.6994 55.0 1
150 │ 149.225 40.398 53.0 0
151 │ 158.75 51.4827 59.0 1
152 │ 149.86 38.6687 57.0 0
153 │ 158.115 39.2357 35.0 1
154 │ 156.21 44.3386 29.0 0
155 │ 148.59 39.5192 62.0 1
156 │ 143.51 31.0711 18.0 0
157 │ 154.305 46.7767 51.0 0
158 │ 157.48 40.6248 19.0 1
159 │ 157.48 50.1786 42.0 1
160 │ 154.305 41.2769 25.0 0
161 │ 168.275 54.6 41.0 1
162 │ 145.415 44.9907 37.0 0
163 │ 149.225 35.8054 82.0 1
164 │ 154.94 45.2175 28.0 1
165 │ 162.56 48.1091 50.0 1
166 │ 156.845 45.671 43.0 0
167 │ 161.011 48.4209 31.0 1
168 │ 144.78 41.1918 67.0 0
169 │ 143.51 38.4136 39.0 0
170 │ 149.225 42.1274 18.0 0
171 │ 149.86 38.2435 48.0 0
172 │ 165.735 48.3359 30.0 1
173 │ 144.145 38.9239 64.0 0
174 │ 157.48 40.0295 72.0 1
175 │ 154.305 50.207 68.0 0
176 │ 163.83 54.2893 44.0 1
177 │ 156.21 45.6 43.0 0
178 │ 144.145 39.4342 34.0 0
179 │ 162.56 43.2046 62.0 1
180 │ 146.05 31.8648 44.0 0
181 │ 154.94 45.4442 31.0 1
182 │ 144.78 38.045 29.0 0
183 │ 146.685 36.0889 62.0 0
184 │ 152.4 40.88 67.0 0
185 │ 163.83 47.9107 57.0 1
186 │ 165.735 47.7122 32.0 1
187 │ 156.21 46.3798 24.0 0
188 │ 152.4 41.1635 77.0 1
189 │ 140.335 36.5992 62.0 0
190 │ 163.195 48.1375 67.0 1
191 │ 151.13 36.7126 70.0 0
192 │ 171.12 56.5573 37.0 1
193 │ 149.86 38.6971 58.0 0
194 │ 163.83 47.4854 35.0 1
195 │ 141.605 36.2023 30.0 0
196 │ 149.225 41.2769 26.0 0
197 │ 146.05 44.7639 21.0 0
198 │ 161.29 50.4338 41.0 1
199 │ 162.56 55.2815 46.0 1
200 │ 145.415 37.9316 49.0 0
201 │ 170.815 58.4567 28.0 1
202 │ 159.385 44.4237 83.0 0
203 │ 159.4 44.4 54.0 1
204 │ 153.67 44.5654 54.0 0
205 │ 160.02 44.6221 68.0 1
206 │ 150.495 40.4831 68.0 0
207 │ 149.225 44.0835 56.0 0
208 │ 142.875 34.4163 57.0 0
209 │ 142.113 32.772 22.0 0
210 │ 147.32 35.9472 40.0 0
211 │ 162.56 49.5549 19.0 1
212 │ 164.465 53.1837 41.0 1
213 │ 160.02 37.0811 75.9 1
214 │ 153.67 40.5114 73.9 0
215 │ 167.005 50.6039 49.0 1
216 │ 151.13 43.9701 26.0 1
217 │ 153.035 49.89 88.0 1
218 │ 139.065 33.5942 68.0 0
219 │ 152.4 43.8567 33.0 1
220 │ 154.94 48.1375 26.0 0
221 │ 147.955 42.751 56.0 0
222 │ 144.145 33.906 34.0 0
223 │ 155.575 39.7176 74.0 1
224 │ 150.495 35.9472 69.0 0
225 │ 155.575 50.9157 50.0 1
226 │ 154.305 45.7561 44.0 0
227 │ 157.48 49.2147 18.0 0
228 │ 168.91 58.8252 41.0 1
229 │ 150.495 43.4598 27.0 0
230 │ 160.02 51.9646 38.0 1
231 │ 167.64 50.6889 57.0 1
232 │ 144.145 34.2462 64.5 0
233 │ 145.415 39.3775 42.0 0
234 │ 160.02 59.5623 24.0 1
235 │ 164.465 52.1631 71.0 1
236 │ 153.035 39.9728 49.5 0
237 │ 149.225 43.9417 33.0 1
238 │ 160.02 54.6011 28.0 0
239 │ 149.225 45.0757 47.0 0
240 │ 153.67 41.3336 27.0 0
241 │ 150.495 41.9006 55.0 0
242 │ 151.765 42.524 83.4 1
243 │ 158.115 43.1479 63.0 1
244 │ 149.225 40.8233 52.0 0
245 │ 151.765 42.8644 49.0 1
246 │ 154.94 46.2097 31.0 0
247 │ 161.29 47.854 35.0 1
248 │ 148.59 42.5243 35.0 0
249 │ 160.655 48.506 24.0 1
250 │ 157.48 45.8695 41.0 1
251 │ 167.005 52.9002 32.0 1
252 │ 157.48 47.5705 43.0 1
253 │ 152.4 43.5448 63.0 0
254 │ 152.4 43.4314 21.0 0
255 │ 161.925 53.212 55.0 0
256 │ 152.4 44.6788 38.0 0
257 │ 159.385 47.2019 28.0 1
258 │ 142.24 31.6664 36.0 0
259 │ 168.91 56.4439 38.0 1
260 │ 160.02 55.7918 48.0 1
261 │ 158.115 47.4854 45.0 1
262 │ 152.4 45.1608 38.0 0
263 │ 155.575 45.5293 21.0 0
264 │ 154.305 48.8745 50.0 0
265 │ 156.845 46.5782 41.0 1
266 │ 156.21 43.885 30.0 0
267 │ 168.275 56.047 21.0 1
268 │ 147.955 40.0862 38.0 0
269 │ 157.48 50.8023 19.0 0
270 │ 160.7 46.3 31.0 1
271 │ 161.29 49.3565 21.0 1
272 │ 150.495 44.1118 50.0 0
273 │ 163.195 51.0291 39.0 1
274 │ 148.59 40.7666 44.0 1
275 │ 148.59 37.5631 36.0 0
276 │ 161.925 51.5961 36.0 1
277 │ 153.67 44.8206 18.0 0
278 │ 151.13 43.4031 58.0 0
279 │ 163.83 46.72 58.0 1
280 │ 153.035 39.5476 33.0 0
281 │ 151.765 34.7848 21.5 0
282 │ 156.21 39.2924 26.0 1
283 │ 140.335 37.4497 22.0 0
284 │ 158.75 48.6761 28.0 1
285 │ 142.875 35.607 42.0 0
286 │ 151.943 43.7149 21.0 1
287 │ 161.29 48.1942 19.0 1
288 │ 160.985 50.9724 48.0 1
289 │ 144.78 43.9984 46.0 0
290 │ 160.02 48.1942 25.0 1
291 │ 160.985 46.6916 51.0 1
292 │ 165.989 56.4155 25.0 1
293 │ 157.988 48.591 28.0 1
294 │ 154.94 48.2225 26.0 0
295 │ 160.655 47.4854 54.0 1
296 │ 147.32 35.5503 66.0 0
297 │ 146.7 36.6 20.0 0
298 │ 147.32 48.9596 25.0 0
299 │ 172.999 51.2559 38.0 1
300 │ 158.115 46.5215 51.0 1
301 │ 147.32 36.9677 48.0 0
302 │ 165.989 48.6477 27.0 1
303 │ 149.86 38.045 22.0 0
304 │ 161.925 47.287 60.0 1
305 │ 163.83 55.3949 43.0 1
306 │ 160.02 54.2042 27.0 1
307 │ 154.94 48.4776 30.0 1
308 │ 152.4 43.0629 29.0 0
309 │ 146.05 34.1895 23.0 0
310 │ 151.994 49.9518 30.0 0
311 │ 151.765 44.3386 41.0 0
312 │ 144.78 33.4524 42.0 0
313 │ 160.655 47.287 43.0 1
314 │ 151.13 46.1246 35.0 0
315 │ 153.67 47.4004 75.5 1
316 │ 147.32 40.8516 64.0 0
317 │ 139.7 50.3487 38.0 1
318 │ 157.48 45.1324 24.2 0
319 │ 154.94 42.2408 26.0 1
320 │ 143.51 41.6454 19.0 0
321 │ 158.115 45.2175 43.0 1
322 │ 147.32 51.2559 38.0 0
323 │ 160.02 49.2714 23.0 1
324 │ 165.1 51.1992 49.0 1
325 │ 154.94 43.8567 41.0 0
326 │ 153.67 35.5219 23.0 0
327 │ 141.605 42.8854 43.0 0
328 │ 163.83 46.7767 21.0 1
329 │ 161.29 41.8722 24.0 1
330 │ 154.9 38.2 20.0 1
331 │ 161.3 43.3 20.0 1
332 │ 170.18 53.6373 34.0 1
333 │ 149.86 42.9778 29.0 0
334 │ 160.655 39.7743 65.0 1
335 │ 154.94 43.3464 46.0 0
336 │ 166.37 52.6734 43.0 1
337 │ 148.285 38.4419 39.0 0
338 │ 151.765 42.8077 43.0 0
339 │ 148.59 35.8905 70.0 0
340 │ 153.67 44.2252 26.0 0
341 │ 146.685 38.0734 48.0 0
342 │ 154.94 44.1118 44.0 1
343 │ 156.21 44.0268 33.0 0
344 │ 160.655 47.8823 41.0 1
345 │ 146.05 39.4058 37.4 0
346 │ 156.21 41.0501 53.0 1
347 │ 152.4 40.8233 49.0 0
348 │ 162.56 47.0318 27.0 0
349 │ 142.875 34.2462 31.0 0
350 │ 162.56 52.1631 31.0 1
351 │ 156.21 54.0625 21.0 0
352 │ 158.75 52.5316 68.0 1
Howell, N. (2010). Life Histories of the Dobe !Kung: Food, Fatness, and Well-being over the Life-span. Origins of Human Behavior and Culture. University of California Press