THE ROLE OF CONDITIONAL INFERENCE

Abstract

summaryThe fact that unconditional sampling theoretic inference is sometimes misleading is illustrated with some examples. Each of these examples involves a sequential sampling procedure and it is suggested here that meaningful inferences can be obtained in these examples by viewing the sequential components of the experiment as though they are separate and independent experiments. Inferences are then made with reference to hypothetical repetitions of the components of the current experiment, rather than referring to hypothetical repetitions of the experiment as a whole. In essence this involves combining the conditional inferences from the components as though they are independent. The approach involves the same likelihood and asymptotic likelihood inference remains essentially the same. However, the finite sampling properties of estimators and tests are changed. A by‐product of the use of this alternative reference set is that it resolves problems arising from the arbitrariness of stopping rules. This approach to sampling theoretic inference is not merely a device for overcoming difficulties arising in a few examples, it has relevance in all problems of statistical inference.