# Probability Measures

• ### Probabilistic Risk Assessment Procedures Guide for NASA Managers and Practitioners

Probabilistic Risk Assessment (PRA) is a comprehensive, structured, and logical analysis method aimed at identifying and assessing risks in complex technological systems for the purpose of cost-effectively improving their safety and performance. NASA’s objective is to better understand and effectively manage risk, and thus more effectively ensure mission and programmatic success, and to achieve and maintain high safety standards at NASA. This PRA Procedures Guide, in the present second edition, is neither a textbook nor an exhaustive sourcebook of PRA methods and techniques. It provides a set of recommended procedures, based on the experience of the authors, that are applicable to different levels and types of PRA that are performed for aerospace applications.

• ### Bayesian Inference for NASA Probabilistic Risk and Reliability Analysis

This NASA-HANDBOOK is published by the National Aeronautics and Space Administration (NASA) to provide a Bayesian foundation for framing probabilistic problems and performing inference on these problems. It is aimed at scientists and engineers and provides an analytical structure for combining data and information from various sources to generate estimates of the parameters of uncertainty distributions used in risk and reliability models. The overall approach taken in this document is to give both a broad perspective on data analysis issues and a narrow focus on the methods required to implement a comprehensive database repository.

• ### Collection: Statistical Calculators

Free statistical calculators online.  Our basic statistical calculators will help you in common tasks you might encounter and deal mostly with simple distributions.

• ### Models for Matched Pairs

This presentation is a part of a series of lessons on the Analysis of Categorical Data.  This lecture overs the following:  odds ratio, dependent proportion, marginal homogeneity, McNemar's Test, marginal homogeneity for greater than 2 levels, measures of agreement, and the kappa coefficient (weighted vs. unweighted).

• ### Logit Models for Multinomial Responses Part II

This presentation is a part of a series of lessons on the Analysis of Categorical Data. This lecture covers the following: ordinal regression models, cumulative probabilities, non-proportional odds, score stat for proportionl odds, MLEs, the adjacent categories logit, and proportional odds model.

• ### Introduction to Categorical Data Analysis

This presentation is a part of a series of lessons on the Analysis of Categorical Data.  This lecture provides a review of probability and statistical concepts such as conditional probabilities, Bayes Theorem, sensitivity and specificity, and binomial and poisson distributions.

• ### Brilliant.org - Lessons in Probability

How can we accurately model the unpredictable world around us? How can we reason precisely about randomness? This course will guide you through the most important and enjoyable ideas in probability to help you cultivate a more quantitative worldview.

By the end of this course, you’ll master the fundamentals of probability and random variables, and you’ll apply them to a wide array of problems, from games and sports to economics and science.  This course includes 62 interactive quizzes and more than 400 probabilty-based problems with solutions.  Access to this course requires users to sign up for a free account.

• ### The International Society for Bayesian Analysis

The International Society for Bayesian Analysis (ISBA) was founded in 1992 to promote the development and application of Bayesian analysis. By sponsoring and organizing meetings, publishing the electronic journal Bayesian Analysis, and other activities, ISBA provides an international community for those interested in Bayesian analysis and its applications.

• ### Psychological Statistics

This site offers separate webpages about statistical topics relevant to those studying psychology such as research design, representing data with graphs, hypothesis testing, and many more elementary statistics concepts.  Homework problems are provided for each section.

• ### A First Lesson in Bayesian Inference (uses Shiny Apps)

This page supports an in-class exercise that highlights several key Bayesian concepts. The scenario is as follows: a large paper bag contains pieces of candy with wrappings of different color, and we are interested in learning about the unknown proportion of yellow-wrapped pieces of candy. After completing the exercises, we will be familiar with the following concepts and ideas: probability distributions can quantify degree of beliefprior distributionposterior distributionsequential updatingconjugacy, Cromwell’s Rule (http://en.wikipedia.org/wiki/Cromwell's_rule), the data overwhelm the prior, Bayes factors, Savage-Dickey density ratio, sensitivity analysiscoherence.