# MCMC¶

## MCMC¶

class MCMC(kernel, num_samples, warmup_steps=0)[source]

Wrapper class for Markov Chain Monte Carlo algorithms. Specific MCMC algorithms are TraceKernel instances and need to be supplied as a kernel argument to the constructor.

Parameters: kernel – An instance of the TraceKernel class, which when given an execution trace returns another sample trace from the target (posterior) distribution. num_samples (int) – The number of samples that need to be generated, excluding the samples discarded during the warmup phase. warmup_steps (int) – Number of warmup iterations. The samples generated during the warmup phase are discarded.

## HMC¶

class HMC(model, step_size=None, trajectory_length=None, num_steps=None, adapt_step_size=False, transforms=None)[source]

Bases: pyro.infer.mcmc.trace_kernel.TraceKernel

Simple Hamiltonian Monte Carlo kernel, where step_size and num_steps need to be explicitly specified by the user.

References

[1] MCMC Using Hamiltonian Dynamics, Radford M. Neal

Parameters: model – Python callable containing Pyro primitives. step_size (float) – Determines the size of a single step taken by the verlet integrator while computing the trajectory using Hamiltonian dynamics. If not specified, it will be set to 1. trajectory_length (float) – Length of a MCMC trajectory. If not specified, it will be set to step_size x num_steps. In case num_steps is not specified, it will be set to $$2\pi$$. num_steps (int) – The number of discrete steps over which to simulate Hamiltonian dynamics. The state at the end of the trajectory is returned as the proposal. This value is always equal to int(trajectory_length / step_size). adapt_step_size (bool) – A flag to decide if we want to adapt step_size during warm-up phase using Dual Averaging scheme. transforms (dict) – Optional dictionary that specifies a transform for a sample site with constrained support to unconstrained space. The transform should be invertible, and implement log_abs_det_jacobian. If not specified and the model has sites with constrained support, automatic transformations will be applied, as specified in torch.distributions.constraint_registry.

Example:

>>> true_coefs = torch.tensor([1., 2., 3.])
>>> data = torch.randn(2000, 3)
>>> dim = 3
>>> labels = dist.Bernoulli(logits=(true_coefs * data).sum(-1)).sample()
>>>
>>> def model(data):
...     coefs_mean = torch.zeros(dim)
...     coefs = pyro.sample('beta', dist.Normal(coefs_mean, torch.ones(3)))
...     y = pyro.sample('y', dist.Bernoulli(logits=(coefs * data).sum(-1)), obs=labels)
...     return y
>>>
>>> hmc_kernel = HMC(model, step_size=0.0855, num_steps=4)
>>> mcmc_run = MCMC(hmc_kernel, num_samples=500, warmup_steps=100).run(data)
>>> posterior = EmpiricalMarginal(mcmc_run, 'beta')
>>> posterior.mean
tensor([ 0.9819,  1.9258,  2.9737])

cleanup()[source]
diagnostics()[source]
end_warmup()[source]
initial_trace()[source]
sample(trace)[source]
setup(*args, **kwargs)[source]

## NUTS¶

class NUTS(model, step_size=None, adapt_step_size=False, transforms=None)[source]

Bases: pyro.infer.mcmc.hmc.HMC

No-U-Turn Sampler kernel, which provides an efficient and convenient way to run Hamiltonian Monte Carlo. The number of steps taken by the integrator is dynamically adjusted on each call to sample to ensure an optimal length for the Hamiltonian trajectory [1]. As such, the samples generated will typically have lower autocorrelation than those generated by the HMC kernel. Optionally, the NUTS kernel also provides the ability to adapt step size during the warmup phase.

Refer to the baseball example to see how to do Bayesian inference in Pyro using NUTS.

References

[1] The No-U-turn sampler: adaptively setting path lengths in Hamiltonian Monte Carlo, Matthew D. Hoffman, and Andrew Gelman

Parameters: model – Python callable containing Pyro primitives. step_size (float) – Determines the size of a single step taken by the verlet integrator while computing the trajectory using Hamiltonian dynamics. If not specified, it will be set to 1. adapt_step_size (bool) – A flag to decide if we want to adapt step_size during warm-up phase using Dual Averaging scheme. transforms (dict) – Optional dictionary that specifies a transform for a sample site with constrained support to unconstrained space. The transform should be invertible, and implement log_abs_det_jacobian. If not specified and the model has sites with constrained support, automatic transformations will be applied, as specified in torch.distributions.constraint_registry.

Example:

>>> true_coefs = torch.tensor([1., 2., 3.])
>>> data = torch.randn(2000, 3)
>>> dim = 3
>>> labels = dist.Bernoulli(logits=(true_coefs * data).sum(-1)).sample()
>>>
>>> def model(data):
...     coefs_mean = torch.zeros(dim)
...     coefs = pyro.sample('beta', dist.Normal(coefs_mean, torch.ones(3)))
...     y = pyro.sample('y', dist.Bernoulli(logits=(coefs * data).sum(-1)), obs=labels)
...     return y
>>>

sample(trace)[source]