pCN#
- class cuqi.sampler.pCN(target, scale=None, x0=None, **kwargs)#
Preconditioned Crank-Nicolson sampler
- Parameters:
target (cuqi.distribution.Posterior or tuple of likelihood and prior objects) – If target is of type cuqi.distribution.Posterior, it represents the posterior distribution. If target is a tuple of (cuqi.likelihood.Likelihood, cuqi.distribution.Distribution) objects, the first element is considered the likelihood and the second is considered the prior.
scale (int)
x0 (np.ndarray) – Initial point for the sampler
callback (callable, Optional) – If set this function will be called after every sample. The signature of the callback function is callback(sample, sample_index), where sample is the current sample and sample_index is the index of the sample. An example is shown in demos/demo31_callback.py.
Example
This uses a custom logpdf and sample function.
# Parameters dim = 5 # Dimension of distribution mu = np.arange(dim) # Mean of Gaussian std = 1 # standard deviation of Gaussian # Logpdf function of likelihood logpdf_func = lambda x: -1/(std**2)*np.sum((x-mu)**2) # sample function of prior N(0,I) sample_func = lambda : 0 + 1*np.random.randn(dim,1) # Define as UserDefinedDistributions likelihood = cuqi.likelihood.UserDefinedLikelihood(dim=dim, logpdf_func=logpdf_func) prior = cuqi.distribution.UserDefinedDistribution(dim=dim, sample_func=sample_func) # Set up sampler sampler = cuqi.sampler.pCN((likelihood,prior), scale = 0.1) # Sample samples = sampler.sample(5000)
Example
This uses CUQIpy distributions.
# Parameters dim = 5 # Dimension of distribution mu = np.arange(dim) # Mean of Gaussian std = 1 # standard deviation of Gaussian # Define as UserDefinedDistributions model = cuqi.model.Model(lambda x: x, range_geometry=dim, domain_geometry=dim) likelihood = cuqi.distribution.Gaussian(mean=model, cov=np.ones(dim)).to_likelihood(mu) prior = cuqi.distribution.Gaussian(mean=np.zeros(dim), cov=1) target = cuqi.distribution.Posterior(likelihood, prior) # Set up sampler sampler = cuqi.sampler.pCN(target, scale = 0.1) # Sample samples = sampler.sample(5000)
- __init__(target, scale=None, x0=None, **kwargs)#
Methods
__init__(target[, scale, x0])sample(N[, Nb])sample_adapt(N[, Nb])single_update(x_t, loglike_eval_t)step(x)Perform a single MCMC step
step_tune(x, *args, **kwargs)Perform a single MCMC step and tune the sampler.
tune()Tune the sampler parameters.
Attributes