Hierarchical Bayes Approach and Implementation of MCMC in an Ecological Study
The Bayesian paradigm for analysing data has gained unmatched popularity at most of the fields of statistical application in the late twentieth century. Bayesian methods permits one to construct statistical models by simultaneously using the current data and all the prior information on hand to make inference about the unknown nature of the underlying process, in a marvellously simple way. But the real reason for the popularity of Bayesian methods is the ability to solve real world data related problems by using the hierarchical structure and Markov Chain Monte Carlo (MCMC). An enormous number of problems that were deemed to be computational nightmares now cracked like open eggs by the rebirth of MCMC. We will show some examples to show the usefulness of MCMC and how much cautious the experimenter should be before expecting MAGIC!
- The talk begins by stating a research problem in ecology. The characteristics of the problem will be explained with the types of inferences we are interested in. I will also show the unavailability of any closed form solutions for them.
- This will be followed by a brief introduction to Bayesian methods of analysis and by Bayesian approach of learning from data. I will explain how hierarchical structure helps in modelling data. Next will be a description of a generic set of Markov Chain Monte Carlo algorithms that is frequently used to fit the hierarchical models.
- Then I will go back to the problem described at the beginning of the talk and use hierarchical Bayesian approach with MCMC to solve it. I will explain usefulness and some drawbacks of MCMC under Bayesian approach. The talk will end after a discussion on generality and robustness of Bayesian paradigm.
- `Inside every nonBayesian there is a Bayesian struggling to get out.’ - Dennis V. Lindley
- `The practising Bayesian is well advised to become friends with as many numerical analysts as possible.’ - James O. Berger
- Familiarity with the Bayesian and frequentist approach of inference
- Familiarity with the analytical evaluation of a joint, conditional and marginal density function
Soumen Dey is currently a research scholar in Indian Statistical Institute, Bangalore. He has about 4 years of experience in handling ecological data and building statistical models. His research interests include model selection, modelling of data from multiple sources, Bayesian statistics.