1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
|
#! /usr/bin/env python
import openturns as ot
import openturns.testing as ott
import math
ot.RandomGenerator.SetSeed(0)
ot.TESTPREAMBLE()
# %%
# Test RandomVectorMetropolisHastings on Beta-Binomial conjugate model
# Define Beta-binomial model
a, b, lower, upper = 1.0, 1.0, 0.0, 1.0
n, p = 10, 0.5
prior = ot.RandomVector(ot.Beta(a, b, lower, upper))
model = ot.Binomial(n, p)
# %%
# Simulate data and compute analytical posterior
x = model.getSample(1)
posterior = ot.Beta(a + x[0, 0], b + n - x[0, 0], lower, upper)
# %%
# Define RVMH sampler
# Here, the random vector is defined with repsect to the prior law
# this effectively implements the IMH algorithm using the prior
# as an instrumental distribution
initialState = [p]
rvmh_sampler = ot.RandomVectorMetropolisHastings(prior, initialState, [0])
slf = ot.SymbolicFunction(["x"], [str(n), "x"])
rvmh_sampler.setLikelihood(model, x, slf)
# %%
# Generate posterior distribution sample
sampleSize = 10000
xSample = rvmh_sampler.getSample(sampleSize)
# %%
# Compare empirical to theoretical moments
ott.assert_almost_equal(
xSample.computeMean(), posterior.getMean(), 0.0, 10.0 / math.sqrt(sampleSize)
)
ott.assert_almost_equal(
xSample.computeStandardDeviation(),
posterior.getStandardDeviation(),
0.0,
10.0 / math.sqrt(sampleSize),
)
# %%
randomVector = ot.RandomVector(ot.Normal())
initialState = [0.0]
sampler = ot.RandomVectorMetropolisHastings(randomVector, initialState)
x = sampler.getSample(10000)
mean = x.computeMean()
stddev = x.computeStandardDeviation()
ott.assert_almost_equal(mean, [0.0], 0.0, 0.03)
ott.assert_almost_equal(stddev, [1.0], 0.03, 0.0)
# with link function
slf = ot.SymbolicFunction(["x"], ["0.5", "0.1"])
sampler = ot.RandomVectorMetropolisHastings(randomVector, initialState, [0], slf)
x = sampler.getSample(10000)
mean = x.computeMean()
stddev = x.computeStandardDeviation()
ott.assert_almost_equal(mean, [0.5], 0.0, 0.003)
ott.assert_almost_equal(stddev, [0.1], 0.03, 0.0)
|
