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#! /usr/bin/env python
import openturns as ot
import openturns.testing as ott
import math
ot.TESTPREAMBLE()
ot.RandomGenerator.SetSeed(0)
# %%
# Test independentMetropolisHastings 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.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 IMH sampler
initialState = [p]
imh_sampler = ot.IndependentMetropolisHastings(
prior, initialState, ot.Uniform(-1.0, 1.0), [0]
)
slf = ot.SymbolicFunction(["x"], [str(n), "x"])
imh_sampler.setLikelihood(model, x, slf)
# %%
# Generate posterior distribution sample
sampleSize = 10000
xSample = imh_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),
)
# %%
# Draw the unnormalized probability density
# -----------------------------------------
ot.RandomGenerator.SetSeed(1)
lower_bound = 0.0
print(lower_bound)
upper_bound = 2.0 * math.pi
print(upper_bound)
# %%
# Independent Metropolis-Hastings
# -------------------------------
# Let us use a mixture distribution to approximate the target distribution.
#
# This approximation will serve as the instrumental distribution
# in the independent Metropolis-Hastings algorithm.
exp = ot.Exponential(1.0)
normal = ot.Normal(5.3, 0.4)
instrumentalDistribution = ot.Mixture([exp, normal], [0.9, 0.1])
print(instrumentalDistribution.getWeights())
# %%
# MetropolisHastings classes expect to receive the logarithm to the target density.
log_density = ot.SymbolicFunction(
"x", "log(2 + sin(x)^2) - (2 + cos(3*x)^3 + sin(2*x)^3) * x"
)
initialState = ot.Point([3.0]) # not important in this case
support = ot.Interval([lower_bound], [upper_bound])
independentMH = ot.IndependentMetropolisHastings(
log_density, support, initialState, instrumentalDistribution, [0]
)
print(independentMH.getRealization())
# %%
# Get a sample
sampleSize = 1000000
sample = independentMH.getSample(sampleSize)
# %%
# Compute posterior mean
mean_ref = 1.22498
posterior_mean = sample.computeMean()[0]
ott.assert_almost_equal(posterior_mean, mean_ref, 1e-5, 0)
std_ref = 1.61558
posterior_std = sample.computeStandardDeviation()[0]
ott.assert_almost_equal(posterior_std, std_ref, 1e-5, 0)
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