Related papers: Towards understanding the central limit theorem by…
LLMs promise to democratize technical work in complex domains like programmatic data analysis, but not everyone benefits equally. We study how students with varied experiences use LLMs to complete Python-based data analysis in computational…
Many automated system analysis techniques (e.g., model checking, model-based testing) rely on first obtaining a model of the system under analysis. System modeling is often done manually, which is often considered as a hindrance to adopt…
What factors impact the comprehensibility of code? Previous research suggests that expectation-congruent programs should take less time to understand and be less prone to errors. We present an experiment in which participants with…
Recently, the National Research Council's framework for next generation science standards highlighted "computational thinking" as one of its "fundamental practices". 9th Grade students taking a physics course that employed the Modeling…
Risk control has become one of the major concern of financial institutions. The need for adequate statistical tools to measure and anticipate the amplitude of the potential moves of financial markets is clearly expressed, in particular for…
This project report attempts to evaluate the educational properties of the Python computer language, in practice. This is done by examining computer language evolution history, related scientific background work, the existing educational…
Probability Theory and Statistics are two of the most useful mathematical fields, and also two of the most difficult to learn. In other science fields, as Physics, experimentation is an useful tool to develop students intuition, but the…
Understanding program code is a complicated endeavor. As such, myriad different factors can influence the outcome. Investigations of program comprehension, and in particular those using controlled experiments, have to take these factors…
The ability to make decisions based on data, with its inherent uncertainties and variability, is a complex and vital skill in the modern world. The need for such quantitative critical thinking occurs in many different contexts, and while it…
Probabilistic logic programs are logic programs where some facts hold with a specified probability. Here, we investigate these programs with a causal framework that allows counterfactual queries. Learning the program structure from…
These lecture notes give an introduction to the theory of interacting particle systems. The main subjects are the construction using generators and graphical representations, the mean field limit, stochastic order, duality, and the relation…
In this pedagogical text aimed at those wanting to start thinking about or brush up on probabilistic inference, I review the rules by which probability distribution functions can (and cannot) be combined. I connect these rules to the…
Unifying probabilistic and logical learning is a key challenge in AI. We introduce a Bayesian inductive logic programming approach that learns minimum message length hypotheses from noisy data. Our approach balances hypothesis complexity…
As predictive algorithms grow in popularity, using the same dataset to both train and test a new model has become routine across research, policy, and industry. Sample-splitting attains valid inference on model properties by using separate…
This is a joint introduction to classical and free probability, which are twin sisters. We first review the foundations of classical probability, notably with the main limiting theorems (CLT, CCLT, PLT, CPLT), and with a look into examples…
Proof Blocks is a software tool that provides students with a scaffolded proof-writing experience, allowing them to drag and drop prewritten proof lines into the correct order instead of starting from scratch. In this paper we describe a…
Python is known to be a versatile language, well suited both for beginners and advanced users. Some elements of the language are easier to understand than others: some are found in any kind of code, while some others are used only by…
This note tries to show that a re-examination of a first course in analysis, using the more sophisticated tools and approaches obtained in later stages, can be a real fun for experts, advanced students, etc. We start by going to the…
It is well known that a binomial $(n,p)$ can be approximated by a Poisson distribution with parameter $np$. The typical approach in undergraduate probability texts is to show a convergence result for the distribution of the binomial as $n$…
The functional programming paradigm has a long and storied history, with its beginnings in the Lambda Calculus. In recent decades, pure functional languages such as Haskell have been shown to be highly effective in producing robust software…