This course will introduce you to the basic ideas of Bayesian Statistics. In Bayesian statistics, population parameters are considered random variables having probability distributions. These probabilities measure “degree of belief”. The rules of probability (Bayes’ theorem) are used to revise our belief, given the observed data.
You will learn how to perform Bayesian analysis for a binomial proportion, a normal mean, the difference between normal means, the difference between proportions, and for a simple linear regression model.
Bayesian methods will be contrasted with the comparable frequentist methods, demonstrating the advantages this approach offers. These include:
- Bayesian statistics uses both prior and sample information. Usually something is known about possible parameter values before the experiment is performed, and it is wasteful not to use this prior information.
- The Bayesian approach allows direct probability interpretations of the parameters, given the observed data. All probability statements in the frequentists approach are about possible data that could have been observed, but were not. These statements aren’t of much scientific use.
- Bayesian statistics uses a single tool, Bayes’ theorem. Frequentists procedures require many different tools.
- Bayesian methods often out perform the corresponding frequentists methods even when evaluated using frequentists criteria.
- Bayesian statistics has a straightforward method for dealing with nuisance parameters. It integrates them out of the joint posterior distribution. There is no single corresponding method in frequentists’ statistics, and nuisance parameters are harder to deal with.
- Bayes’ theorem gives the general way to find the predictive distribution of future observations. There is no such general method in frequentists statistics, only a collection of methods that sometimes work
- Week 1: Introduction to Bayesian Statistics
- Week 2: Bayesian Inference For Binomial Proportion and Poisson Mean
- Week 3: Bayesian Inference For Normal Mean
- Week 4: Modeling
January 30, 2015 to February 27, 2015
About 15 hours per week, at times of your choosing.
INR 37,740 (assuming $ = INR 60)
Part Time/Full Time:
Biostatisticians, those designing and analyzing clinical trials, social science statisticians, environmental and geophysical scientists; nearly all fields of statistical analysis are amenable to a Bayesian approach.
- William M. Bolstad