This document provides a brief tutorial on Bayesian inference. It explains that the tutorial is organized into two sections that cover the different role probability plays in Bayesian statistics compared to other approaches, and how probability distributions can be represented using Monte Carlo ensembles. The tutorial is intended to provide an introduction to Bayesian inference for data scientists, business analysts, and statisticians who want to learn more about the topic.

1. A brief tutorial on Bayesian inference
Steven L. Scott
March 9 2018
Are you a data scientist, business analyst, or statistician who has heard about Bayesian inference and
wants to know more? This post will help you get you started. Once you’re done here, you’ll be ready to try
a few examples yourself, but keep in mind that Bayesian data analysis is a large topic that really deserves
its own book. Good elementary introductions can be found in Kruschke (2015), Albert (2009), and Congdon
(2014). Advanced readers can consult Gelman et al. (2014) for practical matters, and Bernardo and Smith
(1994) for more theoretical questions. Although its examples are exclusively from Marketing, Rossi et al.
(2005) offers a pithy and complete description of the Bayesian paradigm for advanced readers with an applied
bent.
This tutorial is organized around two broad conceptual challenges faced by people new to Bayesian
statistics. The first is coming to grips with the different role that probability plays in the Bayesian setting,
relative to the non-Bayesian approach. The second is becoming comfortable with the idea of representing
probability distributions using a Monte Carlo ensemble. Each of these gets a section, so first section discusses
the role of probability in Bayesian inference. The section section tackles Monte Carlo.
References
Albert, J. (2009). Bayesian Computation with R. Springer, 2nd edn.
Bernardo, J. M. and Smith, A. F. M. (1994). Bayesian Theory. John Wiley & Sons.
Congdon, P. (2014). Applied Bayesian Modelling. Wiley, 2nd edn.
Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., and Rubin, D. B. (2014). Bayesian Data
Analysis. Chapman & Hall, 3rd edn.
Kruschke, J. (2015). Doing Bayesian Data Analysis, Second Edition: A Tutorial with R, JAGS, and Stan.
Academic Press, 2nd edn.
Rossi, P., Allenby, G., and McCulloch, R. (2005). Bayesian Statistics in Marketing. John Wiley and Sons.
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