Nested Random Walk Sampler

Create a nested random walk sampler, which uses a symmetric proposal for separable sections of a model to move around in parameter space. This sampler supports sampling from models where the likelihood is only computable randomly (e.g., for pmcmc), and requires that models support the has_parameter_groups property.

Usage

monty_sampler_nested_random_walk(vcv, boundaries = "reflect")

Arguments

vcv

A list of variance covariance matrices. We expect this to be a list with elements base and groups corresponding to the covariance matrix for base parameters (if any) and groups.

boundaries

Control the behaviour of proposals that are outside the model domain. The supported options are:

• "reflect" (the default): we reflect proposed parameters that lie outside the domain back into the domain (as many times as needed)

• "reject": we do not evaluate the density function, and return -Inf for its density instead.

• "ignore": evaluate the point anyway, even if it lies outside the domain.

The initial point selected will lie within the domain, as this is enforced by monty_sample.

Value

A monty_sampler object, which can be used with monty_sample

Details

The intended use case for this sampler is for models where the density can be decomposed at least partially into chunks that are independent from each other. Our motivating example for this is a model of COVID-19 transmission where some parameters region-specific (e.g., patterns and rates of contact between individuals), and some parameters are shared across all regions (e.g., intrinsic properties of the disease such as incubation period).

The strategy is to propose all the shared parameters as a deviation from the current point in parameter space as a single move and accept or reject as a block. Then we generate points for all the region-specific parameters, compute the density and then accept or reject these updates independently. This is possible because the change in likelihood in region A is independent from region B.

We expect that this approach will be beneficial in limited situations, but where it is beneficial it is likely to result in fairly large speed-ups:

• You probably need more than three regions; as the number of regions increases the benefit of independently accepting or rejecting densities increases (with 1000 separate regions your chains will mix very slowly for example).

• Your model is fairly computationally heavy so that the density calculation completely dominates the sampling process.

• You do not have access to gradient information for your model; we suspect that HMC will outperform this approach by some margin because it already includes this independence via the gradients.

• You can compute your independent calculations in parallel, which help this method reduce your walk time.