Related papers: Three Lectures on Probability and Statistics
These are the lecture notes for quantum and statistical mechanics courses that are given by DC at Ben-Gurion University. They are complementary to "Lecture Notes in Quantum Mechanics" [arXiv: quant-ph/0605180]. Some additional topics are…
This article introduces three invariance principles under which P is different from NP. In the second part a theorem of convergence is proven. This theorem states that for any language L there exists an infinite sequence of languages from…
Accelerators and detectors are expensive, both in terms of money and human effort. It is thus important to invest effort in performing a good statistical analysis of the data, in order to extract the best information from it. This series of…
This is the logical foundation for for Relativity Theory, Probability Theory, and for Quantum Theory. Contents is the following: 1 Introduction. 2 Classical logic. 3 Time and space. 3.1 Recorders. 3.2 Time. 3.3 Space. 3.4 Relativity. 4.…
This paper deals with the probabilistic behaviours of distributed systems described by a process calculus considering both probabilistic internal choices and nondeterministic external choices. For this calculus we define and study a typing…
We highlight the different uses of the word 'likelihood' that have arisen in statistics and meteorology, and make the recommendation that one of these uses should be dropped to prevent confusion and misunderstanding.
Bayesian predictive probabilities are commonly used for interim monitoring of clinical trials through efficacy and futility stopping rules. Despite their usefulness, calculation of predictive probabilities, particularly in pre-experiment…
We develop a technique for generalising from data in which models are samplers represented as program text. We establish encouraging empirical results that suggest that Markov chain Monte Carlo probabilistic programming inference techniques…
We propose and analyze a method for computing failure probabilities of systems modeled as numerical deterministic models (e.g., PDEs) with uncertain input data. A failure occurs when a functional of the solution to the model is below (or…
In this chapter, we will first present the most standard computational challenges met in Bayesian Statistics, focussing primarily on mixture estimation and on model choice issues, and then relate these problems with computational solutions.…
A core problem in statistics and probabilistic machine learning is to compute probability distributions and expectations. This is the fundamental problem of Bayesian statistics and machine learning, which frames all inference as…
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…
These lectures concern two topics that are becoming increasingly important in the analysis of High Energy Physics (HEP) data: Bayesian statistics and multivariate methods. In the Bayesian approach we extend the interpretation of probability…
This book is a graduate-level introduction to probabilistic programming. It not only provides a thorough background for anyone wishing to use a probabilistic programming system, but also introduces the techniques needed to design and build…
Unlike the Probability Theory based on additivity, Statistical Inference seems to hesitate between "Additivity" and a so-called "Maxitivity" approach. After a brief overview of three types of principles for any (parametric) statistical…
The recent progresses in Machine Learning opened the door to actual applications of learning algorithms but also to new research directions both in the field of Machine Learning directly and, at the edges with other disciplines. The case…
We present a few techniques for proving $L^p$ estimates for martingales. Basic applications to It\^o integration and rough paths are included.
I review the classical theory of likelihood based inference and consider how it is being extended and developed for use in complex models and sampling schemes.
We present 18 Introductory Lectures on K-Theory covering its basic three branches, namely topological, analytic (K-Homology) and Higher Algebraic K-Theory, 6 lectures on each branch. The skeleton of these notes was provided by the author's…
We present a symbolic machinery that admits both probabilistic and causal information about a given domain and produces probabilistic statements about the effect of actions and the impact of observations. The calculus admits two types of…