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We introduce a few of the key ideas of statistical analysis using two real-world examples to illustrate how these ideas are used in practice.
Causal multiteam semantics is a framework where probabilistic dependencies arising from data and causation between variables can be together formalized and studied logically. We consider several logics in the setting of causal multiteam…
Probabilistic programming is becoming increasingly popular thanks to its ability to specify problems with a certain degree of uncertainty. In this work, we focus on term rewriting, a well-known computational formalism. In particular, we…
Expectation is a central notion in probability theory. The notion of expectation also makes sense for other notions of uncertainty. We introduce a propositional logic for reasoning about expectation, where the semantics depends on the…
We examine three probabilistic concepts related to the sentence "two variables have no bearing on each other". We explore the relationships between these three concepts and establish their relevance to the process of constructing similarity…
The purpose of this paper is twofold. First, the definition of new statistical convergence with Fibonacci sequence is given and some fundamental properties of statistical convergence are examined. Second, approximation theory worked as a…
The features of a logically sound approach to a theory of statistical reasoning are discussed. A particular approach that satisfies these criteria is reviewed. This is seen to involve selection of a model, model checking, elicitation of a…
Causality is a non-obvious concept that is often considered to be related to temporality. In this paper we present a number of past and present approaches to the definition of temporality and causality from philosophical, physical, and…
Large probabilistic models are often shaped by a pool of known individuals (a universe) and relations between them. Lifted inference algorithms handle sets of known individuals for tractable inference. Universes may not always be known,…
These lectures introduce key concepts in probability and statistical inference at a level suitable for graduate students in particle physics. Our goal is to paint as vivid a picture as possible of the concepts covered.
The paper is a survey of notions and results related to classical and new generalizations of the notion of a periodic sequence. The topics related to almost periodicity in combinatorics on words, symbolic dynamics, expressibility in logical…
Probabilities in the multiverse can be calculated by assuming that we are typical representatives in a given reference class. But is this class well defined? What should be included in the ensemble in which we are supposed to be typical?…
Complete sets of commutation relations for arbitrary pairs of quantum minors are computed, with explicit coefficients in closed form.
Relational probabilistic models have the challenge of aggregation, where one variable depends on a population of other variables. Consider the problem of predicting gender from movie ratings; this is challenging because the number of movies…
Polynomials are common algebraic structures, which are often used to approximate functions including probability distributions. This paper proposes to directly define polynomial distributions in order to describe stochastic properties of…
We consider the contextual fraction as a quantitative measure of contextuality of empirical models, i.e. tables of probabilities of measurement outcomes in an experimental scenario. It provides a general way to compare the degree of…
These lecture notes are an informal introduction to the theory of computational complexity and its links to quantum computing and statistical mechanics.
Abstraction is a powerful idea widely used in science, to model, reason and explain the behavior of systems in a more tractable search space, by omitting irrelevant details. While notions of abstraction have matured for deterministic…
We present a versatile inequality of uncertainty relations which are useful when one approximates an observable and/or estimates a physical parameter based on the measurement of another observable. It is shown that the optimal choice for…
We survey a collective achievement of a group of researchers: the PCP Theorems. They give new definitions of the class \np, and imply that computing approximate solutions to many \np-hard problems is itself \np-hard. Techniques developed to…