On Some Basic Patterns of Statistical Inference

Abstract

1. Statistical inference consists in drawing conclusions about the distribution of a random variable X in a population on the basis values of X found in a random sample taken from the population in question. A rule of statistical inference is, therefore, a function associating conclusions concerning the distribution of X with particular sample-values of X. It is the task of statistical theory to formulate such rules of inference, to investigate their properties, and also to answer the question, which of them are to be considered ‘good’ (that is, accepted from some point of view), or possibly ‘the best of all rules’ with respect to a given problem (the problem itself being determined by the set of possible premises, the set of possible conclusions and the probability relation between conclusion and premises).¹