Lectures (Professor Malcolm Faddy)

Dispersion Modelling for Count Data

Abstract: The binomial, Poisson and negative binomial distributions are what might be termed “standard” discrete probability distributions. They have quite specific dispersion properties, and many attempts have been made to generalise them to get more or less dispersion. Mixture distributions generally result in increased dispersion; to get less dispersion requires alternatives that can involve a certain artifice, such as weighting or truncation. A more unifying approach to constructing over- and under-dispersed distributions can be developed using Markov counting (or pure birth) processes, where the distribution is that of the state of the process after a fixed time has elapsed; here the binomial distribution corresponds to a linearly decreasing sequence of birth rates, the Poisson to a constant sequence and the negative binomial to a linearly increasing sequence. By generalising such simple forms of these sequences probability distributions with quite general dispersion properties can be constructed, and the structure of the underlying stochastic process can offer potentially useful insights.

The series of lectures will start with an overview of classical models for over and under-dispersion, including mixture distributions and weighted distributions. The counting process methodology will then be introduced with a discussion of properties of the resulting probability distributions; analysis of example data-sets will be used to illustrate the modelling. Recent work on generalisations of the binomial distribution to describe predation in functional response will be covered, where the focus is on interpretation of the components of the model estimated from available data. Further generalisations involve bivariate processes to simultaneously model both the number of (binary) trials and the number of successes.

Lectures will be held as follows:

Tuesday 6 December, Professor M Faddy	11.00 - 12.00hrs (Rm A1.01)
Thursday 8 December, Professor M Faddy	14.00 - 15.00hrs (Rm A1.01)
Monday 12 December, Professor M Faddy	11.00 - 12.00hrs (Rm A1.01)
Wednesday 14 December, Profess M Faddy	14.00 - 15.00hrs (Rm A1.01)

All lectures will take place in Rm A1.01, unless otherwise stated.