Related papers: Hypothesis Formalization: Empirical Findings, Soft…
As the frontiers of applied statistics progress through increasingly complex experiments we must exploit increasingly sophisticated inferential models to analyze the observations we make. In order to avoid misleading or outright erroneous…
The utilization of statistical methods an their applications within the new field of study known as Topological Data Analysis has has tremendous potential for broadening our exploration and understanding of complex, high-dimensional data…
This set of theories presents a formalisation in Isabelle/HOL+Isar of data dependencies between components. The approach allows to analyse system structure oriented towards efficient checking of system: it aims at elaborating for a concrete…
In computational materials science, mechanical properties are typically extracted from simulations by means of analysis routines that seek to mimic their experimental counterparts. However, simulated data often exhibit uncertainties that…
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…
Autoformalization, the process of transforming informal mathematical propositions into verifiable formal representations, is a foundational task in automated theorem proving, offering a new perspective on the use of mathematics in both…
Sequential hypothesis testing asks for decision rules that update as data arrive. A natural goal is \emph{eventual correctness}: the rule may change its mind early on, but it should make only finitely many wrong decisions almost surely.…
A machine that learns a task from observations must encounter and process uncertainty and novelty, especially when it is to maintain performance when observing new information and to select the hypothesis that best fits the current…
This paper explores algorithms for processing probabilistic and deterministic information when the former is represented as a belief network and the latter as a set of boolean clauses. The motivating tasks are 1. evaluating beliefs networks…
Insightful interdisciplinary collaboration is essential to the principled governance of technology. When such efforts address the interaction between computation and society, they often focus on modeling, the process by which computer…
Stochastic processes offer a flexible mathematical formalism to model and reason about systems. Most analysis tools, however, start from the premises that models are fully specified, so that any parameters controlling the system's dynamics…
Data analysis is a powerful tool in all experimental sciences. Statistical methods, such as sampling theory, computer technologies necessary for handling large amounts of data, skill in analysing information contained in different types of…
The effort invested in a software project is probably one of the most important and most analyzed variables in recent years in the process of project management. The limitation of algorithmic effort prediction models is their inability to…
Our decision-making processes are becoming more data driven, based on data from multiple sources, of different types, processed by a variety of technologies. As technology becomes more relevant for decision processes, the more likely they…
The steadily increasing size of scientific Monte Carlo simulations and the desire for robust, correct, and reproducible results necessitates rigorous testing procedures for scientific simulations in order to detect numerical problems and…
Note: Published now as a chapter in "Handbook of the History and Philosophy of Mathematical Practice" (Springer Nature, editor B. Sriraman, https://doi.org/10.1007/978-3-030-19071-2_105-1). The application of mathematical probability theory…
The data science revolution has led to an increased interest in the practice of data analysis. While much has been written about statistical thinking, a complementary form of thinking that appears in the practice of data analysis is design…
Statistical practice does not automatically follow methodological innovation. Regularization methods, widely advocated to reduce overfitting and stabilize inference, are readily available in modern software, but are not consistently used by…
In view of the paradigm shift that makes science ever more data-driven, in this paper we consider deterministic scientific hypotheses as uncertain data. In the form of mathematical equations, hypotheses symmetrically relate aspects of the…
Verifying mathematical proofs is difficult, but can be automated with the assistance of a computer. Autoformalization is the task of automatically translating natural language mathematics into a formal language that can be verified by a…