Applied Statistics

• Compute conditional probabilities using Bayes’ Theorem.
• Compute conditional distributions using Bayes’ Theorem, demonstrate understanding of prior and posterior distributions, and compute conditional expectations using conditional distributions.
• Apply methods for conjugate priors to perform Bayesian analyses for one proportion and for one mean. 
• Fit a simple linear regression model using Bayesian methods.
• Report and interpret credible intervals for estimating one proportion and one mean. 
• Report and interpret Bayes’ factors for testing one proportion and one mean. 
• Compute and interpret a predictive distribution, and use the predictive distribution to generate predictions. 
• Utilize simulation-based methods such as Markov Chain Monte Carlo to estimate conditional distributions.
• Apply Bayesian methods to a data analysis problem, and present the results in written and oral form.

Review of conditional probability and Bayes’ Theorem, conditional distributions and conditional expectations, and likelihood functions; Prior and posterior distributions; Conjugate priors; Credible intervals; Bayes’ factors; Bayesian estimation in linear models; Predictive analysis; Markov Chain Monte Carlo methods. Use of appropriate technology. Prerequisites: STA 506 and STA 511. 

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