Marginal Bayesian Posterior Inference using Recurrent Neural Networks with Application to Sequential Models.

Area of Science:

• Statistics
• Machine Learning
• Computational Science

Background:

• Evaluating posterior quantiles is crucial in Bayesian analysis, especially for forming posterior intervals.
• Traditional methods like Markov chain Monte-Carlo (MCMC) and Approximate Bayesian Computation (ABC) struggle with multi-dimensional problems and non-conjugate priors.
• These methods often require computationally intensive sampling or analytic approximations.

Purpose of the Study:

• To develop a novel, efficient method for approximating posterior quantiles in Bayesian data analysis.
• To reframe the quantile evaluation as a multi-task learning problem solvable with deep neural networks.
• To overcome the limitations of existing methods in complex, multi-dimensional scenarios.

Main Methods:

• Utilized recurrent deep neural networks (RNNs) to approximate posterior quantiles.
• Framed the problem as a multi-task learning challenge.
• Developed a risk-minimization approach that bypasses the need for posterior sampling or likelihood computation.

Main Results:

• Demonstrated the efficacy of RNNs in approximating posterior quantiles for Bayesian inference.
• Showcased the method's applicability in time-series data due to RNNs' sequential information processing.
• Validated the approach through several illustrative examples.

Conclusions:

• Recurrent deep neural networks offer a powerful and efficient alternative for approximating posterior quantiles in Bayesian analysis.
• The proposed method simplifies complex Bayesian computations by avoiding direct posterior sampling and likelihood evaluation.
• This deep learning approach shows significant promise, particularly for time-series and high-dimensional Bayesian problems.