This page describes the combination of Bayesian Statistics with Genetic Algorithms. This allows prior information to effect the results of an experiment.

Bayes' equation is used to provide a near-optimal statistic for deciding which model (from a selection of possible models) is best supported by both the available data and any prior information. Typically, the selection of possible models is one particular model, but with varied parameters. For example, in fitting a straight line to some data, the "base" model would be y_data = m * x_data + c, where m and c are parameters of the model. The selection of possible models would be the set of y_data = m * x_data + c for all acceptable values of m and c.

It would be possible to compair different models against each other. This would just result with a larger selection of possible models. The statistic from Bayes' equation would calculate the model which is best supported by the data. In the above example, this would allow the possibility of y_data = c. The possibility of there being no x_data dependancy of the data is included, and the model that is supported by the data is chosen.

Given the statistic, finding the global (or true) minimum of the statistic is a hard problem. One method of solving such problems is inversion of the equations; however, this only works for a subset of problems. The class of technique is called solving the reverse problem.

Another method for solving difficult problems is to solve the forward problem. This is where no properties of the function is used other than the value of the function at specific points. At no point are gradients (for example) used to determine what might be a better (lower value) point. One algorithm that can be used for forward problems is Genetic Algorithms.

Genetic Algorithms are good at finding close to the global minimum of the function. They use redundancy in the calculations to cover an effective area in parameter space than much greater than the number of calculated points would suggest.

Webmaster Paul Millar email paulm@astro.gla.ac.uk