On predictive inference for intractable models via approximate Bayesian computation.

Area of Science:

• Statistics
• Computational Statistics
• Bayesian Inference

Background:

• Approximate Bayesian computation (ABC) is widely used for parameter estimation and model comparison in statistical modeling.
• Traditional ABC methods are often limited to scenarios where the likelihood function is intractable.
• Predictive inference, crucial for forecasting and handling missing data, has seen less exploration with ABC.

Purpose of the Study:

• To investigate the feasibility of Approximate Bayesian computation (ABC) as a general method for predictive inference.
• To develop and evaluate ABC approaches for computing posterior predictive distributions for intractable models.
• To identify optimal summary statistics for ABC-based predictive inference.

Main Methods:

• Three distinct ABC approaches were developed, differing in assumptions about sampling from predictive densities.
• Particular attention was given to a method using simulation from the joint density of observed and future data.
• The study explored an ABC prediction approach leveraging latent variable representations and adapted common ABC sampling algorithms.

Main Results:

• The research demonstrates that minimal predictive sufficient statistics are ideal for certain ABC predictive inference settings.
• The proposed ABC methods are shown to be effective for computing posterior predictive distributions.
• The applicability of the methods was validated using both simple time-series models and complex intractable dynamic models.

Conclusions:

• Approximate Bayesian computation (ABC) is a viable and effective tool for predictive inference with intractable models.
• The study provides novel ABC methodologies and insights into optimal statistical summaries for predictive tasks.
• These findings expand the utility of ABC beyond parameter estimation and model comparison.