Differential Evolution MCMC

class pints.DifferentialEvolutionMCMC(chains, x0, sigma0=None)

Uses differential evolution MCMC as described in [1] to perform posterior sampling from the posterior.

In each step of the algorithm n chains are evolved using the evolution equation:

x_proposed = x[i,r] + gamma * (X[i,r1] - x[i,r2]) + epsilon

where r1 and r2 are random chain indices chosen (without replacement) from the n available chains, which must not equal i or each other, where i indicates the current time step, and epsilon ~ N(0,b) where d is the dimensionality of the parameter vector.

If x_proposed / x[i,r] > u ~ U(0,1), then x[i+1,r] = x_proposed; otherwise, x[i+1,r] = x[i].

Extends MultiChainMCMC.

Note

This sampler requires a number of chains \(n \ge 3\), and recommends \(n \ge 1.5 d\).

References

[1]

“A Markov Chain Monte Carlo version of the genetic algorithm Differential Evolution: easy Bayesian computing for real parameter spaces”. Cajo J. F. Ter Braak (2006) Statistical Computing https://doi.org/10.1007/s11222-006-8769-1

ask()

See pints.MultiChainMCMC.ask().

current_log_pdfs()

Returns the log pdf values of the current points (i.e. of the most recent points returned by tell()).

gamma()

Returns the coefficient gamma used in updating the position of each chain.

gamma_switch_rate()

Returns the number of steps between iterations where gamma is set to 1 (then reset immediately afterwards).

gaussian_error()

Returns whether a Gaussian versus uniform error process is used.

in_initial_phase()

For methods that need an initial phase (see needs_initial_phase()), this method returns True if the method is currently configured to be in its initial phase. For other methods a NotImplementedError is returned.

n_hyper_parameters()

See TunableMethod.n_hyper_parameters().

name()

See pints.MCMCSampler.name().

needs_initial_phase()

Returns True if this method needs an initial phase, for example an adaptation-free period for adaptive covariance methods, or a warm-up phase for DREAM.

needs_sensitivities()

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

relative_scaling()

Returns whether an error process whose standard deviation scales relatively is used (False indicates absolute scale).

scale_coefficient()

Sets the scale coefficient b of the error process used in updating the position of each chain.

set_gamma(gamma)

Sets the coefficient gamma used in updating the position of each chain.

set_gamma_switch_rate(gamma_switch_rate)

Sets the number of steps between iterations where gamma is set to 1 (then reset immediately afterwards).

set_gaussian_error(gaussian_error)

If True sets the error process to be a gaussian error, N(0, b*); if False, it uses a uniform error U(-b*, b*); where b* = b if absolute scaling used and b* = mu * b if relative scaling is used instead.

set_hyper_parameters(x)

The hyper-parameter vector is [gamma, gaussian_scale_coefficient, gamma_switch_rate, gaussian_error, relative_scaling].

See TunableMethod.set_hyper_parameters().

set_initial_phase(in_initial_phase)

For methods that need an initial phase (see needs_initial_phase()), this method toggles the initial phase algorithm. For other methods a NotImplementedError is returned.

set_relative_scaling(relative_scaling)

Sets whether to use an error process whose standard deviation scales relatively (scale = self._mu * self_b) or absolutely (scale = self._b in all dimensions).

set_scale_coefficient(b)

Sets the scale coefficient b of the error process used in updating the position of each chain.

tell(proposed_log_pdfs)

See pints.MultiChainMCMC.tell().