Predictive distributions that mimic frequencies over a restricted subdomain (expanded preprint version)

09/05/2019
by   Frank Lad, et al.
0

A predictive distribution over a sequence of N+1 events is said to be "frequency mimicking" whenever the probability for the final event conditioned on the outcome of the first N events equals the relative frequency of successes among them. Infinitely extendible exchangeable distributions that universally inhere this property are known to have several annoying concomitant properties. We motivate frequency mimicking assertions over a limited subdomain in practical problems of finite inference, and we identify their computable coherent implications. We provide some computed examples using reference distributions, and we introduce computational software to generate any specification. The software derives from an inversion of the finite form of the exchangeability representation theorem. Three new theorems delineate the extent of the usefulness of such distributions, and we show why it may not be appropriate to extend the frequency mimicking assertions for a specified value of N to any arbitrary larger size of N. The constructive results identify the source and structure of "adherent masses" in the limit of a sequence of finitely additive distributions. Appendices develop a novel geometrical representation of conditional probabilities which illuminate the analysis.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
10/16/2012

From imprecise probability assessments to conditional probabilities with quasi additive classes of conditioning events

In this paper, starting from a generalized coherent (i.e. avoiding unifo...
research
02/07/2023

Strictly Frequentist Imprecise Probability

Strict frequentism defines probability as the limiting relative frequenc...
research
01/24/2011

Projective Limit Random Probabilities on Polish Spaces

A pivotal problem in Bayesian nonparametrics is the construction of prio...
research
10/14/2019

Monitoring Event Frequencies

The monitoring of event frequencies can be used to recognize behavioral ...
research
01/16/2013

Marginalization in Composed Probabilistic Models

Composition of low-dimensional distributions, whose foundations were lai...
research
03/09/2022

A composite generalization of Ville's martingale theorem

We provide a composite version of Ville's theorem that an event has zero...
research
08/04/2017

Identification of Probabilities

Within psychology, neuroscience and artificial intelligence, there has b...

Please sign up or login with your details

Forgot password? Click here to reset