The Topology of Statistical Verifiability

07/27/2017
by   Konstantin Genin, et al.
0

Topological models of empirical and formal inquiry are increasingly prevalent. They have emerged in such diverse fields as domain theory [1, 16], formal learning theory [18], epistemology and philosophy of science [10, 15, 8, 9, 2], statistics [6, 7] and modal logic [17, 4]. In those applications, open sets are typically interpreted as hypotheses deductively verifiable by true propositional information that rules out relevant possibilities. However, in statistical data analysis, one routinely receives random samples logically compatible with every statistical hypothesis. We bridge the gap between propositional and statistical data by solving for the unique topology on probability measures in which the open sets are exactly the statistically verifiable hypotheses. Furthermore, we extend that result to a topological characterization of learnability in the limit from statistical data.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
09/16/2019

Extending and Automating Basic Probability Theory with Propositional Computability Logic

Classical probability theory is formulated using sets. In this paper, we...
research
12/21/2019

Foundations of Structural Statistics: Topological Statistical Theory

Topological Statistical Theory, provides the foundation for a new unders...
research
11/23/2011

Falsification and future performance

We information-theoretically reformulate two measures of capacity from s...
research
08/11/2014

In principle determination of generic priors

Probability theory as extended logic is completed such that essentially ...
research
04/06/2021

Hypothesis Formalization: Empirical Findings, Software Limitations, and Design Implications

Data analysis requires translating higher level questions and hypotheses...
research
01/11/2022

Topology-based goodness-of-fit tests for sliced spatial data

In materials science and many other application domains, 3D information ...
research
03/20/2019

Topological Data Analysis in Information Space

Various kinds of data are routinely represented as discrete probability ...

Please sign up or login with your details

Forgot password? Click here to reset