Modeling Lake-Chemistry Distributions: Approximate Bayesian Methods for Estimating a Finite-Mixture Model

A modification of the Laplace method is presented and applied to estimation of posterior functions in a Bayesian analysis of finite-mixture distributions. The technique is nonsequential yet relatively fast and provides estimates of mixture-model parameters and classification probabilities. The method is applied to a regional distribution of lake-chemistry data for north central Wisconsin. A mixture density of two lognormal populations is estimated for the acid-neutralizing capacity of lakes in the region, using several other lake characteristics as explanatory variables for classification into lake subpopulations. The fitted mixture model provides a good representation of the observed distribution. Separation into subpopulations based solely on the other lake characteristics matches the mixture-model classification relatively well.