相关论文: Probability and Statistical Inference

These are lecture notes on the subject defined in the title. As such, they do not pretend to be really new, probably except for the only section about Poisson equations with potentials. Yet, the hope of the author is that they may serve as…

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,…

These notes aim at presenting an overview of Bayesian statistics, the underlying concepts and application methodology that will be useful to astronomers seeking to analyse and interpret a wide variety of data about the Universe. The level…

In the last two decades, Bayesian inference has become commonplace in astronomy. At the same time, the choice of algorithms, terminology, notation, and interpretation of Bayesian inference varies from one sub-field of astronomy to the next,…

We analyze the notion that physical theories are quantitative and testable by observations in experiments. This leads us to propose a new, Bayesian, interpretation of probabilities in physics that unifies their current use in classical…

Despite the huge amount of literature on h-index, few papers have been devoted to the statistical analysis of h-index when a probabilistic distribution is assumed for citation counts. The present contribution relies on showing the available…

The goal of this thesis is twofold; introduce the fundamentals of Bayesian inference and computation focusing on astronomical and cosmological applications, and present recent advances in probabilistic computational methods developed by the…

The aim of these lectures is to provide (experimental particle physics Ph.D.) students with an introduction to some of the core concepts and methods of QCD that are relevant in an LHC context.

Bayesian statistics is based on the subjective definition of probability as {\it ``degree of belief''} and on Bayes' theorem, the basic tool for assigning probabilities to hypotheses combining {\it a priori} judgements and experimental…

We give a survey of the foundations of statistical queries and their many applications to other areas. We introduce the model, give the main definitions, and we explore the fundamental theory statistical queries and how how it connects to…

Predictive inference is a fundamental task in statistics, traditionally addressed using parametric assumptions about the data distribution and detailed analyses of how models learn from data. In recent years, conformal prediction has…

In this article the idea of random variables over the set theoretic universe is investigated. We explore what it can mean for a random set to have a specific probability of belonging to an antecedently given class of sets.

This mini-course gives an introduction to the techniques used in experimental particle physics with an emphasis on the impact of technological advances. The basic detector types and particle accelerator facilities will be briefly covered…

This study has the purpose of addressing four questions that lie at the base of the probability theory and statistics, and includes two main steps. As first, we conduct the textual analysis of the most significant works written by eminent…

Statistical learning theory provides the theoretical basis for many of today's machine learning algorithms. In this article we attempt to give a gentle, non-technical overview over the key ideas and insights of statistical learning theory.…

I developed the lecture notes based on my ``Causal Inference'' course at the University of California Berkeley over the past seven years. Since half of the students were undergraduates, my lecture notes only required basic knowledge of…

The main goal of these lectures -- introduction to Quantum Mechanics for mathematically-minded readers. The second goal is to discuss the mathematical interpretation of the main quantum postulates: transitions between quantum stationary…

These lecture notes on Generalised Parton Distributions aim at providing a general picture of the field on the theoretical and phenomenological sides to master and Ph.D. students. They go along with the lecture given at the Baryon…

Invitation to the statistical study of language: The topic of this presentation is the interdisciplinary nexus between linguistics and statistics. It targets linguists, for whom it may have a theoretical interest, or professionals that work…

We report on the development of students' ideas of probability and probability density in a University of Maine laboratory-based general education physics course called Intuitive Quantum Physics. Students in the course are generally math…