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Statistical analysis is an important tool to distinguish systematic from chance findings. Current statistical analyses rely on distributional assumptions reflecting the structure of some underlying model, which if not met lead to problems…
In many scientific experiments, the data annotating cost constraints the pace for testing novel hypotheses. Yet, modern machine learning pipelines offer a promising solution, provided their predictions yield correct conclusions. We focus on…
The rapid evolution of artificial intelligence has led to expectations of transformative impact on science, yet current systems remain fundamentally limited in enabling genuine scientific discovery. This perspective contends that progress…
Causal inference is central to scientific discovery, yet choosing appropriate methods remains challenging because of the complexity of both statistical methodology and real-world data. Inspired by the success of artificial intelligence in…
Shape analysis is of great importance for the verification of the correctness and memory-safety of heap-manipulating programs, yet such analyses have been shown to be highly difficult problems. The integration of separation logic into shape…
A discovery system for detecting correspondences in data is described, based on the familiar induction methods of J. S. Mill. Given a set of observations, the system induces the ``causally'' related facts in these observations. Its…
The integration of the history and philosophy of statistics was initiated at least by Hacking (1975) and advanced by Hacking (1990), Mayo (1996), and Zabell (2005), but it has not received sustained follow-up. Yet such integration is more…
Abductive reasoning is inference to the most plausible explanation. For example, if Jenny finds her house in a mess when she returns from work, and remembers that she left a window open, she can hypothesize that a thief broke into her house…
Explanatory inference is the creation and evaluation of hypotheses that provide explanations, and is sometimes known as abduction or abductive inference. Generative AI is a new set of artificial intelligence models based on novel algorithms…
Indirect inference (II) is a methodology for estimating the parameters of an intractable (generative) model on the basis of an alternative parametric (auxiliary) model that is both analytically and computationally easier to deal with. Such…
Learning about cause and effect is arguably the main goal in applied econometrics. In practice, the validity of these causal inferences is contingent on a number of critical assumptions regarding the type of data that has been collected and…
Predictive inference is a fundamental task in statistics, traditionally addressed using parametric assumptions about the data distribution and detailed analyses of how models learn from data. In recent years, conformal prediction has…
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…
These lecture notes aim at a post-Bachelor audience with a background at an introductory level in Applied Mathematics and Applied Statistics. They discuss the logic and methodology of the Bayes-Laplace approach to inductive statistical…
Motivated by the search for a counterexample to the Poincar\'e conjecture in three and four dimensions, the Andrews-Curtis conjecture was proposed in 1965. It is now generally suspected that the Andrews-Curtis conjecture is false, but small…
Active inference is an ambitious theory that treats perception, inference and action selection of autonomous agents under the heading of a single principle. It suggests biologically plausible explanations for many cognitive phenomena,…
One can argue that one of the main roles of the subject of statistics is to characterize what the evidence in collected data says about questions of scientific interest. There are two broad questions that we will refer to as the estimation…
Reacting against the limitation of statistics to decision procedures, R. A. Fisher proposed for inductive reasoning the use of the fiducial distribution, a parameter-space distribution of epistemological probability transferred directly…
Many scientifically well-motivated statistical models in natural, engineering and environmental sciences are specified through a generative process, but in some cases it may not be possible to write down a likelihood for these models…
(l) I have enough evidence to render the sentence S probable. (la) So, relative to what I know, it is rational of me to believe S. (2) Now that I have more evidence, S may no longer be probable. (2a) So now, relative to what I know, it is…