Conditional particle filters with diffuse initial distributions.

Area of Science:

• Statistics
• Computational Statistics
• Machine Learning

Background:

• Conditional particle filters (CPFs) are effective for nonlinear/non-Gaussian hidden Markov models.
• CPFs face challenges with diffuse initial distributions, common in statistical applications.
• Existing methods may be inefficient or difficult to implement in such scenarios.

Purpose of the Study:

• To develop a generally applicable auxiliary variable method for efficient inference with CPFs.
• To address the challenges posed by diffuse initial distributions in hidden Markov models.
• To improve the mixing properties of smoothing algorithms.

Main Methods:

• Proposed a simple auxiliary variable method compatible with Conditional Particle Filters (CPFs).
• Utilized simulatable Markov transitions reversible with respect to the initial distribution (potentially improper).
• Focused on random walk and autoregressive kernels, incorporating online adaptations like covariance and acceptance rate adjustments.

Main Results:

• The proposed method demonstrated reliable performance with minimal user input across various models.
• Achieved substantially better mixing compared to direct particle Gibbs algorithms.
• Validated theoretical properties of online adaptations for random walk transitions.

Conclusions:

• The auxiliary variable method effectively enhances Conditional Particle Filters for diffuse initial distributions.
• This approach offers a practical and efficient solution for complex hidden Markov models.
• The method shows significant improvements in computational efficiency and mixing.