Automated Bayesian Posterior Sampling with Stationarity Diagnostics
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Solution Overview
Problem
Current Bayesian sampling methods require manual intervention and expertise for parameter tuning and testing, which can be time-consuming and prone to errors, especially in generating stationary and accurate posterior samples.
Innovation Solution
Automated techniques for Bayesian sampling that initialize and adjust input parameters such as burn-in values, tuning samples, and posterior samples, using tests like Geweke, Heidelberger-Welch, and Raftery-Lewis to ensure stationarity and accuracy, and leverage parallel computing for efficient sample generation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If manual parameter tuning and testing is performed for Bayesian sampling, then expertise and control are required, but the process becomes time-consuming and error-prone
Solution Approach 1:
The system performs self-diagnosis and self-tuning through automated execution of stationarity tests (Geweke, Heidelberger-Welch, Raftery-Lewis) and accuracy tests, eliminating the need for manual expert intervention. The algorithm automatically adjusts parameters such as burn-in periods and sample sizes based on test results, enabling the system to service itself without external input.
Solution Approach 2:
The system performs preliminary diagnostic testing and parameter tuning before actual Bayesian sampling begins. By conducting stationarity and accuracy tests on initial samples and pre-adjusting parameters, the system prepares optimal sampling configurations in advance, preventing time losses during the main sampling process.
2Ease of operation
If automated techniques are used for Bayesian sampling, then the need for human intervention is reduced, but complexity of the system increases
Solution Approach 1:
The system introduces automated diagnostic tools and testing mechanisms as intermediaries between the user and the Bayesian sampling process. These intermediaries (Geweke test, Heidelberger-Welch test, Raftery-Lewis test) automatically handle the complex tasks of verifying stationarity and accuracy, shielding users from underlying complexities while ensuring rigorous statistical validation.
Solution Approach 2:
The complex automated system is segmented into distinct, modular testing components: stationarity testing module, accuracy testing module, and parameter adjustment module. Each module performs a specific function and can be independently executed, making the overall complex system manageable and easier to operate through clear separation of concerns.
3Measurement precision
If multiple stationarity and accuracy tests are performed, then sample quality is ensured, but computational resources and time increase
Solution Approach 1:
The system performs a sufficient number of tests to ensure sample quality without being excessively thorough. It executes essential stationarity tests (Geweke, Heidelberger-Welch, Raftery-Lewis) and accuracy tests on representative sample subsets, achieving adequate precision in assessment without conducting every possible test on the entire dataset, thus balancing quality assurance with computational efficiency.
Data Source
AI summary
Techniques for automated Bayesian posterior sampling using Markov Chain Monte Carlo and related schemes are described. In an embodiment, one or more values in a stationarity phase for a system configured for Bayesian sampling may be initialized. Sampling may be performed in the stationarity phase based upon the one or more values to generate a plurality of samples. The plurality of samples may be evaluated based upon one or more stationarity criteria. The stationarity phase may be exited when the plurality of samples meets the one or more stationarity criteria. Other embodiments are described and claimed.