Piecewise Approximate Bayesian Computation: fast inference for discretely observed Markov models using a factorised...

Area of Science:

• Statistics
• Computational Statistics
• Bayesian Inference

Background:

• Likelihood-based inference is challenging for complex stochastic models.
• Approximate Bayesian Computation (ABC) is used when likelihoods are intractable.
• Standard ABC methods can be computationally expensive and introduce bias due to summary statistics and tolerances.

Purpose of the Study:

• To propose a new

Main Methods:

• A "piecewise" ABC approach is developed for discretely observed Markov models.
• The posterior density is decomposed into factors, with ABC applied to each subset of data.
• Two methods for estimating the posterior density from ABC samples are investigated: Gaussian approximation and kernel density estimation.

Main Results:

• The piecewise ABC approach avoids the need for summary statistics selection.
• It allows for stringent tolerances, leading to less approximate posteriors.
• Both Gaussian approximation and kernel density estimation methods provide effective posterior estimation, with kernel density estimation offering consistency.

Conclusions:

• The piecewise ABC approach offers a computationally efficient and accurate alternative for Bayesian inference in complex models.
• It successfully addresses limitations of traditional ABC methods, particularly for discretely observed Markov models.
• The method demonstrates fast and accurate inference across various examples.