Southwest Technology Consultants

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 ●Data Analysis
Applied Bayesian Statistics
Introduction

The test and evaluation of complex systems often centers on reliability—the probability that a component, subsystem, or system perform successfully for a given period of time under specified conditions. Efforts to reduce test and evaluation costs at many facilities have resulted in fewer tests, which places greater emphasis on the need to use all available pertinent information. Bayesian statistical methods provide the analyst with a powerful tool for incorporating such information in situations such as this as well as numerous other settings.

Bayesian methods are characterized by probabilistic models rather than confidence intervals that are used in classical statistics. For example, the failure rate q could be expressed as

 P(a < q < b) = 0.95

in a Bayesian analysis, where a and b represent two quantiles from the probability distribution for q . In contrast, classical statistics provides an interval (c, d) with the accompanying statement that there is 95% confidence that the true, but unknown, failure rate q , is contained in the interval. In reality, the interval (c, d) either contains the true value of q or it does not contain it and there is no probabilistic interpretation for the interval.

Bayesian methods require an understanding of probability, statistics, and classical reliability. These topics will be reviewed in this short course. Bayesian methods will be presented and illustrated with many examples. The role of the prior distribution will be reviewed with special emphasis on noninformative priors.

What You Will Learn

Course participants will gain an understanding of the power and usefulness of Bayesian methods in test and evaluation applications. In particular, attendees will learn how to:

  • Formulate probability models
  • Contrast classical and Bayesian analyses
  • Formulate the prior distribution
  • Formulate the likelihood function
  • Update the posterior distribution with new test data
  • Interpret the posterior distribution
  • Communicate results to decision makers
Course Content

The following topics will be covered:

  • A review of probability models
  • A review of statistics
  • A review of reliability
  • Principles of Bayesian inference in reliability
  • The reproductive property of the beta-binomial model
  • The reproductive property of the gamma-Poisson model

Contact Information

Phone: 505 856-6500

Email: stc@swtechcon.com