Bayesian Analysis with Excel and R

Leverage the full power of Bayesian analysis for competitive advantage Bayesian methods can solve problems you can't reliably handle any other way. Building on your existing Excel analytics skills and experience, Microsoft Excel MVP Conrad Carlberg helps you make the most of Excel's Bayesian capabilities and move toward R to do even more. Step by step, with real-world examples, Carlberg shows you how to use Bayesian analytics to solve a wide array of real problems. Carlberg clarifies terminology that often bewilders analysts, and offers sample R code to take advantage of the rethinking package in R and its gateway to Stan. As you incorporate these Bayesian approaches into your analytical toolbox, you'll build a powerful competitive advantage for your organization—and yourself. Explore key ideas and strategies that underlie Bayesian analysis Distinguish prior, likelihood, and posterior distributions, and compare algorithms for driving sampling inputs Use grid approximation to solve simple univariate problems, and understand its limits as parameters increase Perform complex simulations and regressions with quadratic approximation and Richard McElreath's quap function Manage text values as if they were numeric Learn today's gold-standard Bayesian sampling technique: Markov Chain Monte Carlo (MCMC) Use MCMC to optimize execution speed in high-complexity problems Discover when frequentist methods fail and Bayesian methods are essential—and when to use both in tandem

Table of Contents:
Preface Chapter 1 Bayesian Analysis and R: An Overview Bayes Comes Back About Structuring Priors Watching the Jargon Priors, Likelihoods, and Posteriors     The Prior     The Likelihood Contrasting a Frequentist Analysis with a Bayesian     The Frequentist Approach     The Bayesian Approach Summary Chapter 2 Generating Posterior Distributions with the Binomial Distribution Understanding the Binomial Distribution Understanding Some Related Functions Working with R's Binomial Functions     Using R's dbinom Function     Using R's pbinom Function     Using R's qbinom Function     Using R's rbinom Function Grappling with the Math Summary Chapter 3 Understanding the Beta Distribution Establishing the Beta Distribution in Excel Comparing the Beta Distribution with the Binomial Distribution Decoding Excel's Help Documentation for BETA.DIST Replicating the Analysis in R     Understanding dbeta     Understanding pbeta     Understanding qbeta     About Confidence Intervals     Applying qbeta to Confidence Intervals     Applying BETA.INV to Confidence Intervals Summary Chapter 4 Grid Approximation and the Beta Distribution More on Grid Approximation     Setting the Prior Using the Results of the Beta Function Tracking the Shape and Location of the Distribution Inventorying the Necessary Functions     Looking Behind the Curtains Moving from the Underlying Formulas to the Functions Comparing Built-in Functions with Underlying Formulas Understanding Conjugate Priors Summary Chapter 5 Grid Approximation with Multiple Parameters Setting the Stage     Global Options     Local Variables     Specifying the Order of Execution     Normal Curves, Mu and Sigma     Visualizing the Arrays     Combining Mu and Sigma Putting the Data Together     Calculating the Probabilities     Folding in the Prior     Inventorying the Results     Viewing the Results from Different Perspectives Summary Chapter 6 Regression Using Bayesian Methods Regression a la Bayes Sample Regression Analysis Matrix Algebra Methods Understanding quap Continuing the Code A Full Example Designing the Multiple Regression Arranging a Bayesian Multiple Regression Summary Chapter 7 Handling Nominal Variables Using Dummy Coding Supplying Text Labels in Place of Codes Comparing Group Means Summary Chapter 8 MCMC Sampling Methods Quick Review of Bayesian Sampling     Grid Approximation     Quadratic Approximation     MCMC Gets Up To Speed A Sample MCMC Analysis     ulam's Output     Validating the Results     Getting Trace Plot Charts Summary and Concluding Thoughts Appendix Installation Instructions for RStan and the rethinking Package on the Windows Platform Glossary   Downloadable Bonus Content Excel Worksheets Book: Statistical Analysis: Microsoft Excel 2016 (PDF)     9780137580989    TOC    10/24/2022