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A collection of weighted samples, or particles.

Explicit representation of the weighted sample with weights in the log domain.

deprecated synonym

Explicit representation of the weighted sample with weights in the log domain.

Explicit representation of the weighted sample.

Initialize Population with a concrete weighted sample.

Increase the sample size by a given factor. The weights are adjusted such that their sum is preserved. It is therefore safe to use spawn in arbitrary places in the program without introducing bias.

Multinomial sampler. Sample from \(0, \ldots, n - 1\) \(n\) times drawn at random according to the weights where \(n\) is the length of vector of weights.

Resample the population using the underlying monad and a multinomial resampling scheme. The total weight is preserved.

Systematic sampler. Sample \(n\) values from \((0,1]\) as follows \[ \begin{aligned} u^{(1)} &\sim U\left(0, \frac{1}{n}\right] \\ u^{(i)} &=u^{(1)}+\frac{i-1}{n}, \quad i=2,3, \ldots, n \end{aligned} \] and then pick integers \(m\) according to \[ Q^{(m-1)}<u^{(n)} \leq Q^{(m)} \] where \[ Q^{(m)}=\sum_{k=1}^{m} w^{(k)} \] and \(w^{(k)}\) are the weights. See also Comparison of Resampling Schemes for Particle Filtering.

Resample the population using the underlying monad and a systematic resampling scheme. The total weight is preserved.

Stratified sampler.

Sample \(n\) values from \((0,1]\) as follows \[ u^{(i)} \sim U\left(\frac{i-1}{n}, \frac{i}{n}\right], \quad i=1,2, \ldots, n \] and then pick integers \(m\) according to \[ Q^{(m-1)}<u^{(n)} \leq Q^{(m)} \] where \[ Q^{(m)}=\sum_{k=1}^{m} w^{(k)} \] and \(w^{(k)}\) are the weights.

The conditional variance of stratified sampling is always smaller than that of multinomial sampling and it is also unbiased - see Comparison of Resampling Schemes for Particle Filtering.

Resample the population using the underlying monad and a stratified resampling scheme. The total weight is preserved.

Separate the sum of weights into the Weighted transformer. Weights are normalized after this operation.

Push the evidence estimator as a score to the transformed monad. Weights are normalized after this operation.

A properly weighted single sample, that is one picked at random according to the weights, with the sum of all weights.

Model evidence estimator, also known as pseudo-marginal likelihood.

Applies a transformation to the inner monad.

Picks one point from the population and uses model evidence as a score in the transformed monad. This way a single sample can be selected from a population without introducing bias.

Population average of a function, computed using unnormalized weights.