On Bayes' theorem and the inverse Bernoulli theorem

On the Inverse Function Theorem

The Rough Set View on Bayes' Theorem

MOTTO: " It is a capital mistake to theorise before one has data " Sherlock Holms In: A Scandal in Bohemia Abstract. Rough set theory offers new perspective on Bayes' theorem. The look on Bayes' theorem offered by rough set theory reveals that any data set (decision table) satisfies total probability theorem and Bayes' theorem. These properties can be used directly to draw conclusions from obje...

Bayes Theorem for the Clinician

pected disease is common or not, and whether the findings tend to support or discount this hypothesis. Such intuitive procedures may be, and often are, seriously biased1. It would be preferable to employ an open system where all the assumptions about diagnostic reasoning, and the way in which they are combined, are made quite explicit. Bayes theorem2 provides such a model. An understanding of h...

Brooks’ theorem for Bernoulli shifts

If Γ is an infinite group with finite symmetric generating set S, we consider the graph G(Γ, S) on [0, 1]Γ by relating two distinct points if an element of s sends one to the other via the shift action. We show that, aside from the cases Γ = Z and Γ = (Z/2Z) ∗ (Z/2Z), G(Γ, S) satisfies a measure-theoretic version of Brooks’ theorem: there is a G(Γ, S)-invariant conull Borel set B ⊆ [0, 1]Γ and ...

A rough set view on Bayes' theorem

Rough set theory offers new perspective on Bayes’ theorem. The look on Bayes’ theorem offered by rough set theory reveals that any data set (decision table) satisfies the total probability theorem and Bayes’ theorem. These properties can be used directly to draw conclusions from objective data without referring to subjective prior knowledge and its revision if new evidence is available. Thus, t...