Understanding and Addressing the Unbounded “Likelihood” Problem

摘要: The joint probability density function, evaluated at the observed data, is commonly used as likelihood function to compute maximum estimates. For some models, however, there exist paths in parameter space along which this density-approximation goes infinity and estimation breaks down. In all applications, data are really discrete due round-off or grouping error of measurements. “correct likelihood” based on interval censoring can eliminate problem an unbounded likelihood. This article categorizes models leading likelihoods into three groups illustrates breakdown with specific examples. Although it usually possible infer how given were rounded, when not possible, one must choose width for censoring, so we study effect estimation. We also give sufficient conditions provide same likel...