DeepAI AI Chat
Log In Sign Up

Constriction for sets of probabilities

by   Michele Caprio, et al.
University of Pennsylvania
Carnegie Mellon University

Given a set of probability measures 𝒫 representing an agent's knowledge on the elements of a sigma-algebra β„±, we can compute upper and lower bounds for the probability of any event Aβˆˆβ„± of interest. A procedure generating a new assessment of beliefs is said to constrict A if the bounds on the probability of A after the procedure are contained in those before the procedure. It is well documented that (generalized) Bayes' updating does not allow for constriction, for all Aβˆˆβ„± <cit.>. In this work, we show that constriction can take place with and without evidence being observed, and we characterize these possibilities.


page 1

page 2

page 3

page 4

βˆ™ 10/08/2021

Dynamic Precise and Imprecise Probability Kinematics

We introduce a new method for updating subjective beliefs based on Jeffr...
βˆ™ 07/22/2019

Learning Probabilities: Towards a Logic of Statistical Learning

We propose a new model for forming beliefs and learning about unknown pr...
βˆ™ 05/21/2021

Certification of Iterative Predictions in Bayesian Neural Networks

We consider the problem of computing reach-avoid probabilities for itera...
βˆ™ 02/13/2013

Independence with Lower and Upper Probabilities

It is shown that the ability of the interval probability representation ...
βˆ™ 09/21/2014

Oblivious Bounds on the Probability of Boolean Functions

This paper develops upper and lower bounds for the probability of Boolea...
βˆ™ 11/01/2021

Extended probabilities in Statistics

We propose a new, more general definition of extended probability measur...
βˆ™ 01/16/2014

Making Decisions Using Sets of Probabilities: Updating, Time Consistency, and Calibration

We consider how an agent should update her beliefs when her beliefs are ...