Related papers: Reading Theorie Analytique des Probabilites
Philosophers now seem to agree that frequentism is an untenable strategy to explain the meaning of probabilities. Nevertheless, I want to revive frequentism, and I will do so by grounding probabilities on typicality in the same way as the…
The probabilistic interpretation of Laplace transforms is used to help to describe the Laplace Transform $L(s)$ of improper random variables. In particular, busy periods in queueing models are examined. The value of $L(0)$ is explained in…
An account of determinism and indeterminism in physics, addressed to non-physicist readers, leading up to proposals for how to understand statements about the future and single-event probability, motivated by quantum mechanics.
The notion of Laplace invariants is transferred to the lattices and discrete equations which are difference analogs of hyperbolic PDE's with two independent variables. The sequence of Laplace invariants satisfy the discrete analog of…
In this pedagogical text aimed at those wanting to start thinking about or brush up on probabilistic inference, I review the rules by which probability distribution functions can (and cannot) be combined. I connect these rules to the…
The classical Bayesian posterior arises naturally as the unique solution of several different optimization problems, without the necessity of interpreting data as conditional probabilities and then using Bayes' Theorem. For example, the…
This paper, which is dedicated to Alan Turing on the 50th anniversary of his death, gives an overview and discusses the philosophical implications of incompleteness, uncomputability and randomness.
To appear in Encyclopedia of Mathematical Physics, published by Elsevier in early 2006. Comments/corrections welcome. The article surveys topological aspects in gauge theories.
Comment on "Harold Jeffreys's Theory of Probability Revisited" [arXiv:0804.3173]
Comment on "Harold Jeffreys's Theory of Probability Revisited" [arXiv:0804.3173]
Comment on "Harold Jeffreys's Theory of Probability Revisited" [arXiv:0804.3173]
Comment on "Harold Jeffreys's Theory of Probability Revisited" [arXiv:0804.3173]
I present a proof of the quantum probability rule from decision-theoretic assumptions, in the context of the Everett interpretation. The basic ideas behind the proof are those presented in Deutsch's recent proof of the probability rule, but…
Statistics has moved beyond the frequentist-Bayesian controversies of the past. Where does this leave our ability to interpret results? I suggest that a philosophy compatible with statistical practice, labeled here statistical pragmatism,…
A Bayesian inference method for problems with small samples and sparse data is presented in this paper. A general type of prior ($\propto 1/\sigma^{q}$) is proposed to formulate the Bayesian posterior for inference problems under small…
This paper is a top down historical perspective on the several phases in the development of probability from its prehistoric origins to its modern day evolution, as one of the key methodologies in artificial intelligence, data science, and…
Preferences among acts are analyzed in the style of L. Savage, but as partially ordered. The rationality postulates considered are weaker than Savage's on three counts. The Sure Thing Principle is derived in this setting. The postulates are…
In this paper we provide a probabilistic representation of Lagrange's identity which we use to obtain Papathanasiou-type variance expansions of arbitrary order. Our expansions lead to generalized sequences of weights which depend on an…
This paper introduces a Laplace approximation to Bayesian inference in Dirichlet regression models, which can be used to analyze a set of variables on a simplex exhibiting skewness and heteroscedasticity, without having to transform the…
In recent years there has been a spate of papers describing systems for probabilisitic reasoning which do not use numerical probabilities. In some cases the simple set of values used by these systems make it impossible to predict how a…