Related papers: Lectures on Statistics in Theory: Prelude to Stati…
This introduction to Bayesian statistics presents the main concepts as well as the principal reasons advocated in favour of a Bayesian modelling. We cover the various approaches to prior determination as well as the basis asymptotic…
This chapter provides a overview of Bayesian inference, mostly emphasising that it is a universal method for summarising uncertainty and making estimates and predictions using probability statements conditional on observed data and an…
The traditional calculus-based introduction to statistical inference consists of a semester of probability followed by a semester of frequentist inference. Cobb (2015) challenges the statistical education community to rethink the…
A substantial school in the philosophy of science identifies Bayesian inference with inductive inference and even rationality as such, and seems to be strengthened by the rise and practical success of Bayesian statistics. We argue that the…
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…
The study of associations and their causal explanations is a central research activity whose methodology varies tremendously across fields. Even within specialized subfields, comparisons across textbooks and journals reveals that the basics…
Notes for a Course on Probability and Statistics: L1: Elements of Probability; L2: Bayesian Inference; L3: Monte Carlo Methods
Every scientific endeavour consists of (at least) two components: A hypothesis on the one hand and data on the other. There is always a more or less abstract level - some theory, a set of concepts, certain relations of ideas - and a…
We present a method of constructing statistical intervals that obtain a natural middle ground between Bayesian and frequentist statistical intervals, previously unexplored in literature: To a p% Bayesian credible interval we should assign a…
This textbook provides a systematic treatment of statistical machine learning for astronomical research through the lens of Bayesian inference, developing a unified framework that reveals connections between modern data analysis techniques…
These lecture notes were written with the aim to provide an accessible though technically solid introduction to the logic of systematical analyses of statistical data to both undergraduate and postgraduate students, in particular in the…
Statistics has made tremendous advances since the times of Fisher, Neyman, Jeffreys, and others, but the fundamental and practically relevant questions about probability and inference that puzzled our founding fathers remain unanswered. To…
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…
Bayesian probability theory is used as a framework to develop a formalism for the scientific method based on principles of inductive reasoning. The formalism allows for precise definitions of the key concepts in theories of physics and also…
Scientific knowledge expands by observing the world, hypothesizing some theories about it, and testing them against collected data. When those theories take the form of statistical models, statistical analyses are involved in the process of…
For many years, philosopher-of-statistics Deborah Mayo has been advocating the concept of severe testing as a key part of hypothesis testing. Her recent book, Statistical Inference as Severe Testing, is a comprehensive exposition of her…
The estimation of signal frequency count in the presence of background noise has had much discussion in the recent physics literature, and Mandelkern [1] brings the central issues to the statistical community, leading in turn to extensive…
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,…
Statistics comes in two main flavors: frequentist and Bayesian. For historical and technical reasons, frequentist statistics has dominated data analysis in the past; but Bayesian statistics is making a comeback at the forefront of science.…
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…