Multiparameter Univariate Bayesian Analysis

Abstract Bayesian analysis using Monte Carlo integration is a powerful method for univariate inference. This approach makes possible multiparameter flexibility within families of univariate distributions. These distributions are defined in this article by increasing spline functions superimposed on probability paper coordinate systems. Smoothing is controlled by the prior distribution. The prior distribution also can express uncertainties about the form of the tails when extrapolation beyond the range of the data is required. The handling of difficult forms of data (e.g., quantal response data) is straightforward. Posterior distributions for functions of the parameters can be easily computed. Key Words: Bayesian analysisMultiparameter univariate distributionsMonte Carlo integrationSmoothingExtrapolationSpline functions