Haario ACMC

class pints.HaarioACMC(x0, sigma0=None)

Adaptive Metropolis MCMC, which is algorithm 4 in [1] and is described in the text in [2].

This algorithm differs from HaarioBardenetACMC only through its use of alpha in the updating of log_lambda (rather than a binary accept/reject).

Initialise:

mu
Sigma
adaptation_count = 0
log lambda = 0

In each adaptive iteration (t):

adaptation_count = adaptation_count + 1
gamma = (adaptation_count)^-eta
theta* ~ N(theta_t, lambda * Sigma)
alpha = min(1, p(theta*|data) / p(theta_t|data))
u ~ uniform(0, 1)
if alpha > u:
    theta_(t+1) = theta*
    accepted = 1
else:
    theta_(t+1) = theta_t
    accepted = 0

mu = (1 - gamma) mu + gamma theta_(t+1)
Sigma = (1 - gamma) Sigma + gamma (theta_(t+1) - mu)(theta_(t+1) - mu)
log lambda = log lambda + gamma (alpha - self._target_acceptance)
gamma = adaptation_count^-eta

Extends AdaptiveCovarianceMC, does not use sensitivities.

References

[1]

A tutorial on adaptive MCMC Christophe Andrieu and Johannes Thoms, Statistical Computing, 2008, 18: 343-373. https://doi.org/10.1007/s11222-008-9110-y

[2]

An adaptive Metropolis algorithm Heikki Haario, Eero Saksman, and Johanna Tamminen (2001) Bernoulli.

acceptance_rate()

Returns the current (measured) acceptance rate.

ask()

See SingleChainMCMC.ask().

eta()

Returns eta which controls the rate of adaptation decay adaptations**(-eta), where eta > 0 to ensure asymptotic ergodicity.

in_initial_phase()

See pints.MCMCSampler.in_initial_phase().

n_hyper_parameters()

See TunableMethod.n_hyper_parameters().

classmethod name()

See pints.MCMCSampler.name().

needs_initial_phase()

See pints.MCMCSampler.needs_initial_phase().

needs_sensitivities()

Returns True if this methods needs sensitivities to be passed in to tell along with the evaluated logpdf.

replace(current, current_log_pdf, proposed=None)

See pints.SingleChainMCMC.replace().

set_eta(eta)

Updates eta which controls the rate of adaptation decay adaptations**(-eta), where eta > 0 to ensure asymptotic ergodicity.

set_hyper_parameters(x)

The hyper-parameter vector is [eta].

See TunableMethod.set_hyper_parameters().

set_initial_phase(initial_phase)

See pints.MCMCSampler.set_initial_phase().

set_target_acceptance_rate(rate=0.234)

Sets the target acceptance rate.

target_acceptance_rate()

Returns the target acceptance rate.

tell(fx)

See pints.SingleChainMCMC.tell().