Related papers: A Bayesian Redesign of the First Probability/Stati…
Education in statistics, the application of statistics in scientific research, and statistics itself as a scientific discipline are in crisis. Within science, the main cause of the crisis is the insufficiently clarified concept of…
Sufficiency, Conditionality and Invariance are basic principles of statistical inference. Current mathematical statistics courses do not devote much teaching time to these classical principles, and even ignore the latter two, in order to…
The two statistical methods, namely the frequentist and the Bayesian methods, are both commonly used for probabilistic inference in many scientific situations. However, it is not straightforward to interpret the result of one approach in…
Many have argued that statistics students need additional facility to express statistical computations. By introducing students to commonplace tools for data management, visualization, and reproducible analysis in data science and applying…
As inductive inference and machine learning methods in computer science see continued success, researchers are aiming to describe ever more complex probabilistic models and inference algorithms. It is natural to ask whether there is a…
We present a basis for studying questions of cause and effect in statistics which subsumes and reconciles the models proposed by Pearl, Robins, Rubin and others, and which, as far as mathematical notions and notation are concerned, is…
These lectures deal with the problem of inductive inference, that is, the problem of reasoning under conditions of incomplete information. Is there a general method for handling uncertainty? Or, at least, are there rules that could in…
It is argued that the nature of probability is essentially informational rather than physical and that quantum mechanical predictions should be viewed as logical inferences made on the basis of the information content of a given…
In the realm of statistical learning, the increasing volume of accessible data and increasing model complexity necessitate robust methodologies. This paper explores two branches of robust Bayesian methods in response to this trend. The…
Approximate Bayesian computation (ABC) methods perform inference on model-specific parameters of mechanistically motivated parametric statistical models when evaluating likelihoods is difficult. Central to the success of ABC methods is…
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…
Usually the first course in mathematics is calculus. Its a core course in the curriculum of the Business, Engineering and the Sciences. However many students face difficulties to learn calculus. These difficulties are often caused by the…
Within the Kolmogorov theory of probability, Bayes' rule allows one to perform statistical inference by relating conditional probabilities to unconditional probabilities. As we show here, however, there is a continuous set of alternative…
Course notes about an introduction to Bayesian Statistics. First, an explanation of the bayesian paradigm is motivated and explained in detail (first three chapters). Then, a brief introduction to the basics about Decision Theory in chapter…
Quantitative methods and mathematical modeling are playing an increasingly important role across disciplines. As a result, interdisciplinary mathematics courses are increasing in popularity. However, teaching such courses at an advanced…
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…
The emergent field of probabilistic numerics has thus far lacked clear statistical principals. This paper establishes Bayesian probabilistic numerical methods as those which can be cast as solutions to certain inverse problems within the…
As a result of the increased emphasis on mis- and over-use of $p$-values in scientific research and the rise in popularity of Bayesian statistics, Bayesian education is becoming more important at the undergraduate level. With the advances…
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…
Cognitive transfer is the ability to apply learned skills and knowledge to new applications and contexts. This investigation evaluates cognitive transfer outcomes for a tertiary-level introductory statistics course using the CATALST…