Related papers: Real-number Computability from the Perspective of …
Making good predictions of a physical system using a computer code requires the inputs to be carefully specified. Some of these inputs called control variables have to reproduce physical conditions whereas other inputs, called parameters,…
For nearly any challenging scientific problem evaluation of the likelihood is problematic if not impossible. Approximate Bayesian computation (ABC) allows us to employ the whole Bayesian formalism to problems where we can use simulations…
The real numbers are important in both mathematics and computation theory. Computationally, real numbers can be represented in several ways; most commonly using inexact floating-point data-types, but also using exact arbitrary-precision…
In this paper we examine the potential of computer-assisted proof methods to be applied much more broadly than commonly recognized. More specifically, we contend that there are vast opportunities to derive useful mathematical results and…
How can complexity theory and algorithms benefit from practical advances in computing? We give a short overview of some prior work using practical computing to attack problems in computational complexity and algorithms, informally describe…
Verification of C++ programs has seen considerable progress in several areas, but not for programs that use these languages' mathematical libraries. The reason is that all libraries in widespread use come with no guarantees about the…
In this short note we report on results on a computational search for a counterexample to the strong coincidence conjecture. In particular, we discuss the method used so that further searches can be conducted.
Probably we have observed a new simple phenomena dealing with approximations to two real numbers.
In the rapidly growing literature on explanation algorithms, it often remains unclear what precisely these algorithms are for and how they should be used. In this position paper, we argue for a novel and pragmatic perspective: Explainable…
Let $p$ be a prime. We discuss methods of solution of congruences modulo $p^n$ using $p$-adic numbers; these methods are similar to computations with real numbers (local methods). Examples of relations between local and global methods are…
Quantifying errors and losses due to the use of Floating-Point (FP) calculations in industrial scientific computing codes is an important part of the Verification, Validation and Uncertainty Quantification (VVUQ) process. Stochastic…
In this paper a new mathematical procedure is presented for combining different pieces of evidence which are represented in the interval form to reflect our knowledge about the truth of a hypothesis. Evidences may be correlated to each…
Designing scalable estimation algorithms is a core challenge in modern statistics. Here we introduce a framework to address this challenge based on parallel approximants, which yields estimators with provable properties that operate on the…
A method for the multifidelity Monte Carlo (MFMC) estimation of statistical quantities is proposed which is applicable to computational budgets of any size. Based on a sequence of optimization problems each with a globally minimizing…
Security risk assessment is essential in establishing the trustworthiness and reliability of modern systems. While various security risk assessment approaches exist, prevalent applications are "pen and paper" implementations that -- even if…
While concepts and tools from Theoretical Computer Science are regularly applied to, and significantly support, software development for discrete problems, Numerical Engineering largely employs recipes and methods whose correctness and…
There has been a great deal of recent interest in methods for performing lifted inference; however, most of this work assumes that the first-order model is given as input to the system. Here, we describe lifted inference algorithms that…
Approximate Bayesian computation (ABC) has advanced in two decades from a seminal idea to a practically applicable inference tool for simulator-based statistical models, which are becoming increasingly popular in many research domains. The…
We analyze different types of simulations that applied researchers can use to assess whether their inference methods reliably control false-positive rates. We show that different assessments involve trade-offs, varying in the types of…
This thesis examines a modern concept for machine numbers based on interval arithmetic called 'Unums' and compares it to IEEE 754 floating-point arithmetic, evaluating possible uses of this format where floating-point numbers are…