Bayesian methods of data analysis

Bayesian methods are used in the analysis of evidence and the more standard analysis of data. In the latter we have been examining the Maxent method.

Trawl tomography

We have been investigating an alternative to the Maxent method of modelling fish density distributions. We assume the fish are in schools of finite dimensions and try to determine the position and size using a bayesian tomographic method. It is possible to detect more than one school. Descriptions of the S-PLUS functions are in thetechnical note S-PLUS code for Estimating fish concentrations using trawl data
Further work, still ongoing, into developments of the simple model is reported in Estimating fish concentration and location using trawl data with proportional errors. In this work, errors are assumed to be proportional to the size of the catch.
Jackie Honeysett and I are also examining the use of Fourier series to model fish concentrations using the trawl data. This work currently uses ordinary frequentist statistical methods.

The following diagram shows contour plots of the density of hoki for a sequence of weeks through the 1991 fishing season, as extracted by our method.

Publications

Vignaux, G.A., Gresham, D. and Paul, S. (2001) 'Estimating fish concentrations using trawl data', pp. 257-263 in Rychert, J.T., Erickson, G.J. and Smith, C.R. (eds) Bayesian inference and Maximum entropy Methods in science and engineering; 19th International Workshop, Boise, Idaho, 1999. AIP Conference Proceedings, vol 567 Melville, New York: American Institute of Physics (2001).
This reports on attempts to make allowances for uncertainties in the trawl tracks and to develop a parametric model for fish schools.
M Vignaux, G A Vignaux, S Lizamore, D Gresham, Fine scale mapping of fish distribution from commercial catch and effort data using maximum entropy tomography, Canadian Journal of Fisheries and Aquatic Sciences , vol 55 no 5, p.1220-1227, May 1998
Suzette Clare Lizamore, Topics in Maximum Entropy Applications MSc thesis, Victoria University of Wellington, 1995 (warning: 7.6MB)
David Gresham, Techniques for fine resolution MaxEnt image analysis MSc thesis, Victoria University of Wellington, 1998 (1.4MB)
Sue Paul, Estimation of Fish density and Location using trawl data MSc thesis, Victoria University of Wellington, 2000 (1.6MB)

MaxEnt Methods

The MaxEnt, or Maximum Entropy, methods of assigning prior distributions in bayesian methods were introduced by Jaynes. His approach to probability is set out in his book Probability theory - The Logic of Science.

We have been using maxent in using information from random commercial trawls to determine the spacial density of hoki fish schools in the seas off the West Coast of New Zealand. Suzette Lizamore has completed an MSc thesis including an analysis of this problem. It was presented as a paper (postscript, 602K) to the 1995 Maxent Workshop in Santa Fe

Image Analysis

Bevan Flack's MSc thesis topic is combining images from several satellites to make use of all the data in their detector channels to distinguish sea and land and high and low cloud. The satellites used are both geostationary and polar-orbiting. The image below is a picture from two satellites over a very cloudy New Zealand classified in this way into the four types from a series of satellite images.

New Zealand
Satellite Picture

MaxEnt Links

An abstract of our paper to the 1994 maxEnt conference is available. The MaxEnt Conference abstracts are available and much material on Maxent is kept in Carlos Rodriguez's page.

Last updated on 1999 May 28