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
|
#! /usr/bin/env python
import openturns as ot
import openturns.experimental as otexp
import openturns.testing as ott
import math as m
ot.TESTPREAMBLE()
ot.RandomGenerator.SetSeed(1)
# Sample from a target distribution defined through its log-PDF
# (defined up to some additive constant) and its support:
log_density = ot.SymbolicFunction("x", "log(2 + sin(x)^2)")
support = ot.Interval([0.0], [2.0 * m.pi])
# Apply a Metropolis adjusted Langevin algorithm (MALA).
initialState = [2.5]
proposal = ot.Normal()
h = 0.1
std_deviation = m.sqrt(h)
# The mean of the proposal normal distribution is the current state,
# but moved according to the derivative of the target log-density.
def python_link(x):
derivative_log_density = log_density.getGradient().gradient(x)[0, 0]
mean = x[0] + h / 2 * derivative_log_density
return [mean, std_deviation]
link = ot.PythonFunction(1, 2, python_link)
mala = otexp.UserDefinedMetropolisHastings(
log_density, support, initialState, proposal, link
)
# %%
# Get a sample
sampleSize = 100000
sample = mala.getSample(sampleSize)
# %%
# Compute sample mean and median
mean_ref = m.pi
sample_mean = sample.computeMean()[0]
ott.assert_almost_equal(sample_mean, mean_ref, 1e-2, 0.0)
median_ref = m.pi
sample_median = sample.computeQuantile(0.5)[0]
ott.assert_almost_equal(sample_median, median_ref, 1e-1, 0.0)
|
