API

SMC(n[, resampler = ResampleWithESSThreshold()])
SMC(n, [resampler = resample_systematic, ]threshold)

Create a sequential Monte Carlo (SMC) sampler with n particles.

If the algorithm for the resampling step is not specified explicitly, systematic resampling is performed if the estimated effective sample size per particle drops below 0.5.

PG(n, [resampler = ResampleWithESSThreshold()])
PG(n, [resampler = resample_systematic, ]threshold)

Create a Particle Gibbs sampler with n particles.

If the algorithm for the resampling step is not specified explicitly, systematic resampling is performed if the estimated effective sample size per particle drops below 0.5.

resample_multinomial(rng, weights, n)

Return a vector of n samples x₁, ..., xₙ from the numbers 1, ..., length(weights), generated by multinomial resampling.

The new indices are sampled from the multinomial distribution with probabilities equal to weights

resample_residual(rng, weights, n)

Return a vector of n samples x₁, ..., xₙ from the numbers 1, ..., length(weights), generated by residual resampling.

In residual resampling we start by duplicating all the particles whose weight is bigger than 1/n. We copy each of these particles $N_i$ times where

$N_i = \left\lfloor n w_i \right\rfloor$

We then duplicate the $R_t = n - \sum_i N_i$ missing particles using multinomial resampling with the residual weights given by:

$\tilde{w} = w_i - \frac{N_i}{N}$

resample_stratified(rng, weights, n)

Return a vector of n samples x₁, ..., xₙ from the numbers 1, ..., length(weights), generated by stratified resampling.

In stratified resampling n ordered random numbers u₁, ..., uₙ are generated, where

$uₖ \sim U[(k - 1) / n, k / n)$.

Based on these numbers the samples x₁, ..., xₙ are selected according to the multinomial distribution defined by the normalized weights, i.e., xᵢ = j if and only if

$uᵢ \in \left[\sum_{s=1}^{j-1} weights_{s}, \sum_{s=1}^{j} weights_{s}\right)$.

resample_systematic(rng, weights, n)

Return a vector of n samples x₁, ..., xₙ from the numbers 1, ..., length(weights), generated by systematic resampling.

In systematic resampling a random number $u \sim U[0, 1)$ is used to generate n ordered numbers u₁, ..., uₙ where

$uₖ = (u + k − 1) / n$.

Based on these numbers the samples x₁, ..., xₙ are selected according to the multinomial distribution defined by the normalized weights, i.e., xᵢ = j if and only if

$uᵢ \in \left[\sum_{s=1}^{j-1} weights_{s}, \sum_{s=1}^{j} weights_{s}\right)$

ResampleWithESSThreshold{R,T<:Real}

Perform resampling using R if the effective sample size is below T. By default we use resample_systematic with a threshold of 0.5

TracedRNG{R,N,T}

Wrapped random number generator from Random123 to keep track of random streams during model evaluation

split(key::Integer, n::Integer=1)

Split key into n new keys

load_state!(r::TracedRNG)

Load state from current model iteration. Random streams are now replayed

save_state!(r::TracedRNG)

Add current key of the inner rng in r to keys.

Data structure for particle filters

• effectiveSampleSize(pc :: ParticleContainer): Return the effective sample size of the particles in pc

sweep!(rng, pc::ParticleContainer, resampler)

Perform a particle sweep and return an unbiased estimate of the log evidence.

The resampling steps use the given resampler.

Reference

Del Moral, P., Doucet, A., & Jasra, A. (2006). Sequential monte carlo samplers. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 68(3), 411-436.