ABC-SMC sampler

class pints.ABCSMC(log_prior, perturbation_kernel=None, nr_samples=100, error_schedule=[1])

Implements the ABC-SMC algorithm as described in [1]. This algorithm is also referred to as ABC Population Monte Carlo (ABC PMC) [2].

In this algorithm there are going to be several rounds of ABC, each with a different proposal distribution. For each round, we try to obtain nr_samples samples at once. In order to transition between each set of nr_samples, we have intermediate distributions \(p_t(\theta)\) from which we sample the candidates for the new distribution. In particular, \(p_0(\theta)\) is the prior and for \(t>0\) \(p_t(\theta)\) proposes sample \(\theta^{t-1}_i\) with weight \(\w^{t-1}_i\) (which is computed at the end of the iteration). In particular, at each iteration of the algorithm the following steps occur:

\[\begin{split}\begin{align} & \theta^* \sim p_{t-1}(\theta) \textrm{, i.e. sample parameters from previous intermediate distribution} \\ & \theta^{**} \sim K(\theta|\theta^{*}), \textrm{i.e. perturb } \theta^{*} \textrm{ to obtain to new point } x \sim p(x|\theta^{**})\textrm{, i.e. sample data from sampling distribution} \\ & \textrm{if } s(x) < \textrm{threshold}_(t), \theta^* \textrm{ add to list of samples[t]} \end{align}\end{split}\]

After we have obtained nr_samples samples, t is advanced, and weights are calculated for samples[t-1]. At the last error threshold, samples are returned whenever they are accepted.

Parameters:

• log_prior – A pints.LogPrior that specifies the logarithmic prior for the set of parameters that will be sampled.

• perturbation_kernel – A pints.LogPrior used for perturbing the particles sampled from the previous generation. By default a multivariate Gaussian distribution is used with mean I and 0.001 * I as covariance.

• nr_samples – The number of samples requested for intermediate distributions.

• error_schedule – The schedule of error threshold distance for all distributions.

References

[1]

Toni, Welch, Strelkowa, Ipsem, Stumpf. Approximate Bayesian computation scheme for parameter inference and model selection in dynamical systems. Journal of the Royal Society Interface, 6.31: 187-202, 2009. https://doi.org/10.1098/rsif.2008.0172

[2]

Beaumont, Cornuet, Marin, Robert. Adaptive approximate Bayesian computation. Biometrika, 96.4: 983-990, 2009. https://doi.org/10.48550/arXiv.0805.2256

ask(n_samples)

See ABCSampler.ask().

n_hyper_parameters()

Returns the number of hyper-parameters for this method (see TunableMethod).

name()

See pints.ABCSampler.name().

set_hyper_parameters(x)

Sets the hyper-parameters for the method with the given vector of values (see TunableMethod).

Parameters:

x – An array of length n_hyper_parameters used to set the hyper-parameters.

set_intermediate_size(n)

Sets the size of the intermediate distributions, after we find n acceptable samples then we will progress to the next threshold values in the schedule.

set_perturbation_kernel(perturbation_kernel)

Sets the perturbation kernel used for perturbing particles that are sampled from the previous generations. It must implement the pints.LogPrior class.

set_threshold_schedule(schedule)

Sets a schedule for the threshold error distance that determines if a sample is accepted (if error < threshold). Schedule should be a list of float values.

tell(fx)

See ABCSampler.tell().