# sequential Monte Carlo

(2.3 hours to learn)

## Summary

Sequential Monte Carlo is a general framework for Monte Carlo algorithms which involve sampling from a sequence of distributions. It encompasses sequential importance sampling, particle filters, and annealed importance sampling as special cases.

## Context

This concept has the prerequisites:

- particle filter (The particle filter is a canonical example of a sequential Monte Carlo algorithm.)
- importance sampling (Importance sampling is one step of sequential Monte Carlo algorithms.)
- expectation and variance (Sequential Monte Carlo algorithms yield unbiased estimators of expectations.)
- Markov chain Monte Carlo (The rejuvenation step involves applying an MCMC operator.)

## Goals

- Learn the general formulation of sequential Monte Carlo samplers

- Understand why each of the following operators preserves weighted samples:
- importance weighting
- sampling from the sampling (proposal) distribution
- resampling
- rejuvenation

- Know how to use SMC to estimate the normalizing constant of a distribution

- What is the optimal sampling (proposal) distribution?
- Know how this can be approximated using look-ahead

## Core resources (read/watch one of the following)

## -Free-

→ Sequential Monte Carlo samplers

## -Paid-

→ Monte Carlo Strategies in Scientific Computing (2001)

A monograph on Monte Carlo methods.

Location:
Section 3.4, "A general framework," pages 67-76

Other notes:

- Sections 3.1 through 3.3 discuss instructive examples of the framework.

## See also

-No Additional Notes-