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This report introduces general ideas and some basic methods of the Bayesian probability theory applied to physics measurements. Our aim is to make the reader familiar, through examples rather than rigorous formalism, with concepts such as:…
Data visualization is a core part of statistical practice and is ubiquitous in many fields. Although there are numerous books on data visualization, instructors in statistics and data science may be unsure how to teach data visualization,…
As data have become more prevalent in academia, industry, and daily life, it is imperative that undergraduate students are equipped with the skills needed to analyze data in the modern environment. In recent years there has been a lot of…
A research frontier has emerged in scientific computation, wherein numerical error is regarded as a source of epistemic uncertainty that can be modelled. This raises several statistical challenges, including the design of statistical…
Statistical thinking partially depends upon an iterative process by which essential features of a problem setting are identified and mapped onto an abstract model or archetype, and then translated back into the context of the original…
This work contains the mathematical exploration of a few prototypical games in which central concepts from statistics and probability theory naturally emerge. The first two kinds of games are termed Fisher and Bayesian games, which are…
Statistical Inference is the process of determining a probability distribution over the space of parameters of a model given a data set. As more data becomes available this probability distribution becomes updated via the application of…
The past decades have seen enormous improvements in computational inference based on statistical models, with continual enhancement in a wide range of computational tools, in competition. In Bayesian inference, first and foremost, MCMC…
The traditional theoretical statistics course which develops the theoretical underpinnings of the discipline (usually following a probability course) is undergoing near-continuous revision in the statistics community. In particular, recent…
In social sciences and economics, causal inference traditionally focuses on assessing the impact of predefined treatments (or interventions) on predefined outcomes, such as the effect of education programs on earnings. Causal discovery, in…
Approximate Bayesian computation (ABC) is a set of techniques for Bayesian inference when the likelihood is intractable but sampling from the model is possible. This work presents a simple yet effective ABC algorithm based on the…
Statistical inference as a formal scientific method to covert experience to knowledge has proven to be elusively difficult. While frequentist and Bayesian methodologies have been accepted in the contemporary era as two dominant schools of…
This paper is about how we study statistical methods. As an example, it uses the random regressions model, in which the intercept and slope of cluster-specific regression lines are modeled as a bivariate random effect. Maximizing this…
A common concern with Bayesian methodology in scientific contexts is that inferences can be heavily influenced by subjective biases. As presented here, there are two types of bias for some quantity of interest: bias against and bias in…
A growing number of students are completing undergraduate degrees in statistics and entering the workforce as data analysts. In these positions, they are expected to understand how to utilize databases and other data warehouses, scrape data…
Bayesian inference requires specification of a single, precise prior distribution, whereas frequentist inference only accommodates a vacuous prior. Since virtually every real-world application falls somewhere in between these two extremes,…
There are three principle paradigms of statistical inference: (i) Bayesian, (ii) information-based and (iii) frequentist inference. We describe an objective prior (the weighting or $w$-prior) which unifies objective Bayes and…
The widely claimed replicability crisis in science may lead to revised standards of significance. The customary frequentist confidence intervals, calibrated through hypothetical repetitions of the experiment that is supposed to have…
Demand for data science education is surging and traditional courses offered by statistics departments are not meeting the needs of those seeking training. This has led to a number of opinion pieces advocating for an update to the…
Introducing the Boltzmann distribution very early in a statistical thermodynamics course (in the spirit of Feynmann) has many didactic advantages, in particular that of easily deriving the Gibbs entropy formula. In this note, a short…