Related papers: Conditional probabilities and van Lambalgen theore…
Algorithmic statistics considers the following problem: given a binary string $x$ (e.g., some experimental data), find a "good" explanation of this data. It uses algorithmic information theory to define formally what is a good explanation.…
In this paper, we introduce and develop the concept of conditional quantization for Borel probability measures on $\mathbb{R}^k,$ considering both constrained and unconstrained frameworks. For each setting, we define the associated…
Given a finite collection of probability measures defined on subsets of a measurable space, how can we determine if they are compatible, in the sense that they can be realized as conditional distributions of a single probability measure on…
In 1933 Kolmogorov constructed a general theory that defines the modern concept of conditional probability. In 1955 Renyi fomulated a new axiomatic theory for probability motivated by the need to include unbounded measures. This note…
Kolmogorov's axioms of probability theory are extended to conditional probabilities among distinct (and sometimes intertwining) contexts. Formally, this amounts to row stochastic matrices whose entries characterize the conditional…
We describe a Groebner basis of relations among conditional probabilities in a discrete probability space, with any set of conditioned-upon events. They may be specialized to the partially-observed random variable case, the purely…
We are now witnessing a rapid growth of a new part of group theory which has become known as "statistical group theory". A typical result in this area would say something like ``a random element (or a tuple of elements) of a group G has a…
Predicting the future is an important component of decision making. In most situations, however, there is not enough information to make accurate predictions. In this paper, we develop a theory of causal reasoning for predictive inference…
This text presents an unified approach of probability and statistics in the pursuit of understanding and computation of randomness in engineering or physical or social system with prediction with generalizability. Starting from elementary…
We consider the problem of defining conditional objects (a|b), which would allow one to regard the conditional probability Pr(a|b) as a probability of a well-defined event rather than as a shorthand for Pr(ab)/Pr(b). The next issue is to…
We discuss conditionalisation for Accept-Desirability models in an abstract decision-making framework, where uncertain rewards live in a general linear space, and events are special projection operators on that linear space. This abstract…
The need to condition distributional properties such as expectation, variance, and entropy arises in algorithmic fairness, model simplification, robustness and many other areas. At face value however, distributional properties are not…
In this paper, we propose some algorithms for the simulation of the distribution of certain diffusions conditioned on terminal point. We prove that the conditional distribution is absolutely continuous with respect to the distribution of…
The concept of typicality refers to properties holding for the "overwhelming majority" of cases and is a fundamental idea of the qualitative approach to dynamical problems. We argue that measure-theoretical typicality would be the adequate…
We propose that a quantum particle in a potential in one space dimension can be described by a probabilistic cellular automaton. While the simple updating rule of the automaton is deterministic, the probabilistic description is introduced…
This expository paper advocates an approach to physics in which ``typicality" is identified with a suitable form of algorithmic randomness. To this end various theorems from mathematics and physics are reviewed. Their original versions…
We study a new framework for property testing of probability distributions, by considering distribution testing algorithms that have access to a conditional sampling oracle.* This is an oracle that takes as input a subset $S \subseteq [N]$…
This paper presents an investigation on the structure of conditional events and on the probability measures which arise naturally in this context. In particular we introduce a construction which defines a (finite) {\em Boolean algebra of…
We present a semantics for adding uncertainty to conditional logics for default reasoning and belief revision. We are able to treat conditional sentences as statements of conditional probability, and express rules for revision such as "If A…
The language of probability is used to define several different types of conditional statements. There are four principal types: subjunctive, material, existential, and feasibility. Two further types of conditionals are defined using the…