Nonlinear quasi-bayesian theory and inverse linear regression

Abstract

We generalize Wedderburn's (1974) notion of quasi-likelihood to define a quasi-Bayesian approach for nonlinear estimation problems by allowing the full distributional assumptions about the random component in the classical Bayesian approach to be replaced by much weaker assumptions in which only the first and second moments of the prior distribution are specified. The formulas given are based on the Gauss-Newton estimating procedure and require only the first and second moments of the distributions involved. The use of GLIM package to solve for the estimation problems considered is discussed. Applications are made to estimation problems in inverse linear regression, regression models with both variables subject to error and also to the estimation of the size of animal populations. Some numerical illustrations are reported. For the inverse linear regression problem, comparisons with ordinary Bayesianand other techniques are considered.