# output must be a 1d list or array in order to create a PythonFunction
return res.reshape(-1)
nor0posterior = ot.PythonFunction(2 + N, 2, nor0post)
nor1posterior = ot.PythonFunction(2 + N, 2, nor1post)
zposterior = ot.PythonFunction(2 + N, N, zpost)
# We can now construct the Gibbs algorithm
initialState = [0.0] * (N + 2)
sampler0 = ot.RandomVectorMetropolisHastings(ot.RandomVector(ot.Normal()),
initialState, [0], nor0posterior)
sampler1 = ot.RandomVectorMetropolisHastings(ot.RandomVector(ot.Normal()),
initialState, [1], nor1posterior)
big_bernoulli = ot.ComposedDistribution([ot.Bernoulli()] * N)
sampler2 = ot.RandomVectorMetropolisHastings(ot.RandomVector(big_bernoulli),
initialState, range(2, N + 2),
zposterior)
gibbs = ot.Gibbs([sampler0, sampler1, sampler2])
# Run the Gibbs algorithm
s = gibbs.getSample(10000)
# Extract the relevant marginals: the first (:math:`mu_0`) and the second (:math:`\mu_1`).
posterior_sample = s[:, 0:2]
mean = posterior_sample.computeMean()
stddev = posterior_sample.computeStandardDeviation()
print(mean, stddev)
ott.assert_almost_equal(mean, [-0.0788226, 2.80322])
ott.assert_almost_equal(stddev, [0.0306272, 0.0591087])
# start from te mean x0=(0.,0.,0.)
print('x0=', mu0)
# conditional distribution y~N(z, 1.0)
conditional = ot.Normal()
print('y~', conditional)
# create a gibbs sampler
mh_coll = [
ot.RandomWalkMetropolisHastings(prior, mu0, instrumental, [i])
for i in range(chainDim)
]
for mh in mh_coll:
mh.setLikelihood(conditional, y_obs, linkFunction, p)
sampler = ot.Gibbs(mh_coll)
sampler.setThinning(4)
sampler.setBurnIn(2000)
# get a realization
realization = sampler.getRealization()
print('y1=', realization)
# try to generate a sample
sampleSize = 1000
sample = sampler.getSample(sampleSize)
x_mu = sample.computeMean()
x_sigma = sample.computeStandardDeviation()
# compute covariance
std_prior = ot.Dirac(2.0) # standard dev is known
prior = ot.ComposedDistribution([mean_prior, std_prior])
# choose the initial state within the prior
initialState = prior.getRealization()
# conditional distribution
conditional = ot.Normal()
# create a Gibbs sampler
mean_sampler = ot.RandomWalkMetropolisHastings(prior, initialState,
mean_instrumental, [0])
mean_sampler.setLikelihood(conditional, data)
std_sampler = ot.RandomWalkMetropolisHastings(prior, initialState,
std_instrumental, [1])
std_sampler.setLikelihood(conditional, data)
sampler = ot.Gibbs([mean_sampler, std_sampler])
sampler.setThinning(2)
sampler.setBurnIn(500)
realization = sampler.getRealization()
sigmay = ot.ConditionalDistribution(ot.Normal(),
prior).getStandardDeviation()[0]
w = size * sigma0**2. / (size * sigma0**2. + sigmay**2.0)
print("prior variance= %.12g" % (sigma0**2.))
print(" realization=", realization)
print(" w= %.12g" % w)
# the posterior for mu is analytical
mu_exp = (w * data.computeMean()[0] + (1. - w) * mu0)