Sequential Monte Carlo Methods

• Particle filter - flexible particle filter for general Feynman-Kac models.
• Marginal particle filter - \(O(N^2)\) variant of the particle filter.
• Backward sampler - flexible backward smoothing using approaches in cuthbertlib.smc.smoothing.

The core atomic functions can be found in cuthbertlib.smc.

Feynman-Kac Models

Sequential Monte Carlo methods provide particle approximations to general Feynman-Kac models:

\[ \mathbb{Q}_{t}(x_{0:t}) \propto \mathbb{M}_0(x_0) \, G_0(x_0) \prod_{s=1}^{t} M_s(x_s \mid x_{s-1}) \, G_s(x_{s-1}, x_s), \quad t \in \{ 0, \dots, T\}, \]

where \(M_{s}\) are probability kernels and \(G_{s}\) are positive and bounded functions.