GeneralisedFilters.jl

GeneralisedFilters is a flexible, modular framework for state-space inference in Julia. State-space models describe an unobserved process that evolves over time and is measured through noisy observations. The package provides filtering to estimate the current state, smoothing to infer past states, and particle Gibbs to jointly infer state trajectories and model parameters.

Models and inference algorithms are defined separately. You can combine prior, transition and observation models, then choose an analytical filter, a particle filter, or a combination of the two. Custom processes and algorithms can extend the same interface.

Rao–Blackwellised inference

Many models have a part that is difficult to integrate out and another part that becomes linear and Gaussian once the first is known. For example, a model of inflation might have an unknown trend and changing volatility. Given the volatility trajectory, a Kalman filter can integrate out the trend.

A Rao–Blackwellised particle filter uses this structure: particles sample the volatility, while each particle carries a conditional Gaussian distribution for the trend. This reduces the number of states that must be sampled and can give more accurate estimates for a given number of particles.

This combination is a particular focus of GeneralisedFilters. A particle filter and an analytical filter can be composed directly:

using GeneralisedFilters

pf = RBPF(BF(100), KF())  # 100 outer particles, each with an inner Kalman filter

For joint state and parameter inference, particle Gibbs alternates trajectory updates with parameter updates. The Turing.jl integration lets you specify parameter priors in a Turing model and use HMC or NUTS for the parameter update. ForwardDiff and Mooncake provide forward and reverse mode differentiation of the likelihood after integrating out the Gaussian states. StaticArrays are supported for small, fixed-dimensional states.

Getting started

The documentation overview introduces the model and algorithm interface with a complete filtering example. From there:

• Models and conditioning explains how to define models and their Rao–Blackwellised structure.
• Particle Gibbs and Turing covers joint inference for trajectories and parameters.
• Recording filtering results shows manual loops and particle ancestry storage.
• The trend inflation example applies Rao–Blackwellised filtering to a model with stochastic volatility.
• The static arrays example benchmarks the speed-up from using StaticArrays for small states.

This repository contains both GeneralisedFilters and SSMProblems, which supplies the shared state-space model interface. GeneralisedFilters re-exports that interface, so most users only need to load GeneralisedFilters.