Approximating multivariate posterior distribution functions from Monte Carlo samples for sequential Bayesian...

Area of Science:

• Statistics
• Computational Statistics

Background:

• Bayesian statistics enables sequential inference, where posterior distributions from one dataset inform subsequent analyses.
• Monte Carlo sampling methods generate samples from posterior distributions, posing challenges for direct sequential updates.

Purpose of the Study:

• To assess the accuracy of sequential Bayesian inference compared to joint inference when using Monte Carlo sampling.
• To evaluate various density approximation methods for representing posterior distributions in sequential inference.

Main Methods:

• Investigated sequential inference accuracy using kernel density estimates, Gaussian mixtures, mixtures of factor analyzers, vine copulas, and Gaussian processes.
• Compared the performance of these approximations against direct sample reweighting in sequential Bayesian analysis.

Main Results:

• Posterior approximations generally yield more accurate results than direct sample reweighting in sequential inference.
• Gaussian processes excel in low-dimensional settings, while Gaussian mixtures, mixtures of factor analyzers, and vine copulas perform better in higher dimensions.
• Joint inference is consistently more accurate than sequential inference, though the latter is viable with appropriate density approximations.

Conclusions:

• Sequential Bayesian inference using posterior approximations is a viable alternative to direct sample reweighting.
• The choice of density approximation method for sequential inference is dependent on data dimensionality.
• Joint inference remains the preferred approach for accuracy when computationally feasible.