Data augmentation for models based on rejection sampling.

Area of Science:

• Statistics
• Computational Statistics
• Bayesian Inference

Background:

• Rejection sampling is common in statistical modeling but can lead to intractable posterior distributions.
• Markov chain Monte Carlo (MCMC) methods are essential for Bayesian inference but face challenges with complex models.
• Doubly-intractable problems, where likelihood evaluation is difficult, require advanced sampling techniques.

Purpose of the Study:

• To introduce a novel data augmentation scheme for MCMC inference in models with rejection sampling.
• To simplify the joint probability distribution of observed and rejected variables.
• To address challenges in Bayesian analysis of complex statistical models, including doubly-intractable problems.

Main Methods:

• A data augmentation technique that instantiates rejected proposals prior to each observed data point.
• Application of the scheme to flow-cytometry data with truncation.
• Bayesian analysis of the matrix Langevin distribution on the Stiefel manifold.
• Bayesian inference for a nonparametric Gaussian process density model.

Main Results:

• The proposed method simplifies the joint probability distribution compared to the marginal distribution of observed variables.
• Demonstrated superior performance against existing state-of-the-art sampling algorithms.
• Successfully applied to flow-cytometry, matrix Langevin, and Gaussian process density models.

Conclusions:

• The data augmentation scheme effectively handles rejection sampling in MCMC inference.
• This method offers a significant improvement for doubly-intractable problems.
• The approach provides a more tractable alternative for complex Bayesian modeling.