Bayesian Update with Importance Sampling: Required Sample Size

Area of Science:

• Computational statistics
• Bayesian inference
• Machine learning

Background:

• Importance sampling is a key technique for approximating Bayes' rule in computational statistics.
• It is widely applied in Bayesian inverse problems, data assimilation, and machine learning.

Purpose of the Study:

• To investigate the sample size requirements for importance sampling.
• To analyze the impact of target-proposal divergence on sample size.
• To explore the influence of model parameters on Bayesian updates via importance sampling.

Main Methods:

• Review and investigation of importance sampling methodologies.
• Analysis of sample size based on chi-squared divergence.
• Illustrative examples demonstrating parameter influence.

Main Results:

• The study quantifies sample size needs for importance sampling based on divergence metrics.
• Demonstrates how dimensionality, noise, and model parameters affect Bayesian update accuracy.
• Provides a direct comparison of standard and optimal proposals for particle filtering.

Conclusions:

• Understanding sample size requirements is crucial for efficient importance sampling.
• Model parameters significantly influence the performance of importance sampling in Bayesian computations.
• Optimal proposals enhance particle filtering accuracy.