Safe Probability: restricted conditioning and extended marginalization

Abstract. Updating probabilities by conditioning can lead to bad predictions, unless one explicitly takes into account the mechanisms that determine (1) what is observed and (2) what has to be predicted. Analogous to the observation-CAR (coarsening at random) condition, used in existing analyses of (1), we propose a new prediction task-CAR condition to analyze (2). We redefine conditioning so that it remains valid if the mechanisms (1) and (2) are unknown. This will often update a singleton distribution to an imprecise set of probabilities, leading to dilation, but we show how to mitigate this problem by marginalization. We illustrate our notions using the Monty Hall Puzzle.

Inferences for the ratio: Fieller’s interval, log ratio, and large sample based confidence intervals

Fieller’s interval, Ratio estimation, Variance estimation, Sample surveys, Small sample inference,

Analysis of rounded data from dependent sequences

10.1007/s10463-009-0224-6Annals of the Institute of Statistical Mathematics6261143-1173AISX

Decision-analytical modelling in health-care economic evaluations

Decision analysis, Markov model, Economic evaluation, Cost-effectiveness analysis,