Bayesian Analysis in R/STAN
In an era of reduced budgets and limited testing, verifying that requirements have been met in a single test period can be challenging, particularly using traditional analysis methods that ignore all available information. The Bayesian paradigm is tailor made for these situations, allowing for the combination of multiple sources of data and resulting in more robust inference and uncertainty quantification. This tutorial is meant to introduce the basic concepts of Bayesian analysis. Further illustration of the flexibility and applicability of these methods is shown with examples from the T&E community, including implementation details. The course consists of four sections:
- Fundamentals of Bayesian Analysis: This section provides the basic concepts common to all Bayesian analyses, including the specifications of prior distributions, likelihood functions, and posterior distributions. A simple example is used for demonstrative purposes, including a short sensitivity study.
- Case study: Littoral Combat Ship (LCS). This section extends the simple component/subsystem level system reliability calculation. Here, LCS has a functional area reliability requirement, but data were collected on various subsystems of different data types. Implementation details are given in code snippets.
- Case Study: Bio-chemical Detection System (BDS). This example takes the simple modeling case from the introduction and introduces factors of interest. A logistic regression model is fit to determine the probability of detection across different concentration levels of various chemical or biological agent/matrix concentrations. Implementation details are provided, along with a list of R packages that can aid in the fitting of these types of models.