###
3rd International Symposium
on

Imprecise
Probabilities and Their Applications

ISIPTA '03

#####
University of Lugano

Lugano, Switzerland

14-17 July 2003

####
ELECTRONIC PROCEEDINGS

# Towards a Chaotic Probability Model for Frequentist Probability: The Univariate Case

### Abstract

We adopt the same mathematical model of a set M of probability measures as
is central to the theory of coherent imprecise probability.
However, we endow this model with an objective, frequentist
interpretation in place of a behavioral subjective one. We seek to use M
to model stable physical sources of time series data that have
highly irregular behavior and not to model states of belief or knowledge
that are assuredly imprecise. The approach we present in this paper is
to understand a set of measures model M not as a traditional compound
hypothesis, in which one of the measures in M is a true description,
but rather as one in which none of the individual measures in M provides
an adequate description of the potential behavior of the physical source
as actualized in the form of a long time series.
We provide an instrumental construction of random process measures
consistent with M and the highly irregular physical phenomena we
intend to model by M. This construction provides us with the basic
tools for simulation of our models.
We present a method to estimate M from data which studies any given
data sequence by analyzing it into subsequences selected by a set of
computable rules. We prove results that help us to choose an adequate
set of rules and evaluate the performance of the estimator.

** Keywords. ** Imprecise probability, sets of measures, objective, frequentist interpretation.

**Paper Download **

The paper is availabe in the following formats:

** Authors addresses: **

Pablo Ignacio Fierens

Rhodes Hall 376

Cornell University

Ithaca, New York 14853

Terrence Fine

Professor Terrence L. Fine

Center for Applied Mathematics

Rhodes Hall 612

Cornell University

Ithaca, NY 14853, USA

** E-mail addresses: **

** Related Web Sites **

[ back
to the Proceedings of ISIPTA '03 home page ]

Send any remarks to the following address:
smc@decsai.ugr.es