On identifiability of parametric statistical models

Summary This is a review article on statistical identifiability. Besides the definition of the main concepts, we deal with several questions relevant to the statistician: parallelism between parametric identifiability and sample sufficiency; relationship of identifiability with measures of sample information and with the inferential concept of estimability; several strategies of making inferences in unidentifiable models with emphasis on the distinct behaviour of the classical and Bayesian approaches. The concepts, ideas and methods discussed are illustrated with simple examples of statistical models. Centro de Análise e Processamento de Sinais da UTL