Related papers: Computation of the Marcum Q-function

Probabilistic submeasures generalizing the classical (numerical) submeasures are introduced and discussed in connection with some classes of aggregation functions. A special attention is paid to triangular norm-based probabilistic…

When applying the quasi-Monte Carlo (QMC) method of numerical integration of univariate functions, Koksma's inequality provides a basic estimate of the error in terms of the discrepancy of the used evaluation points and the total variation…

Doubly intractable distributions arise in many settings, for example in Markov models for point processes and exponential random graph models for networks. Bayesian inference for these models is challenging because they involve intractable…

Learning parity functions, more general modular addition, is a challenging machine learning task due to its input sensitivity. A recent study substantially scaled modular addition learning in both the number of summands and the modulus. Its…

We present an efficient quantum algorithm for estimating Gauss sums over finite fields and finite rings. This is a natural problem as the description of a Gauss sum can be done without reference to a black box function. With a reduction…

In this paper, we use some standard numerical techniques to approximate the hypergeometric function $$ {}_2F_1[a,b;c;x]=1+\frac{ab}{c}x+\frac{a(a+1)b(b+1)}{c(c+1)}\frac{x^2}{2!}+\cdots $$ for a range of parameter triples $(a,b,c)$ on the…

Mossinghoff, Trudgian, and the first author~\cite{MMT23} recently introduced a family of arithmetic functions called ``fake $\mu$'s'', which are multiplicative functions for which there is a $\{-1,0,1\}$-valued sequence…

Fundamental matrix operations and solving linear systems of equations are ubiquitous in scientific investigations. Using the "Sender-Receiver" model, we propose quantum algorithms for matrix operations such as matrix-vector product,…

The expectation-maximization (EM) algorithm is a powerful computational technique for finding the maximum likelihood estimates for parametric models when the data are not fully observed. The EM is best suited for situations where the…

We explore the behavior and establish new properties of the cumulative-sum process (CUSUM) and its running maximum. The study includes precise expressions for CUSUM's moment generating function and moments, fast recursive computing…

This paper concerns the use of sequential Monte Carlo methods (SMC) for smoothing in general state space models. A well-known problem when applying the standard SMC technique in the smoothing mode is that the resampling mechanism introduces…

We study from a theoretical viewpoint the fundamental problem of efficiently computing the stationary distribution of general classes of structured Markov processes. In strong contrast with previous work, we consider this fundamental…

The prevalence of spatially referenced multivariate data has impelled researchers to develop a procedure for the joint modeling of multiple spatial processes. This ordinarily involves modeling marginal and cross-process dependence for any…

We consider distributed estimation of the inverse covariance matrix, also called the concentration or precision matrix, in Gaussian graphical models. Traditional centralized estimation often requires global inference of the covariance…

Sequential Monte Carlo (SMC) methods are a widely used set of computational tools for inference in non-linear non-Gaussian state-space models. We propose a new SMC algorithm to compute the expectation of additive functionals recursively.…

We introduce efficient numerical methods for generic HJM equations of interest rate theory by means of high-order weak approximation schemes. These schemes allow for QMC implementations due to the relatively low dimensional integration…

We study signal processing tasks in which the signal is mapped via some generalized time-frequency transform to a higher dimensional time-frequency space, processed there, and synthesized to an output signal. We show how to approximate such…

We cover some useful techniques in computational aspects of analytic number theory, with specific emphasis on ideas relevant to the evaluation of L-functions. These techniques overlap considerably with basic methods from analytic number…

Numerically estimating the integral of functions in high dimensional spaces is a non-trivial task. A oft-encountered example is the calculation of the marginal likelihood in Bayesian inference, in a context where a sampling algorithm such…

Several applied problems are characterized by the need to numerically solve equations with an operator function (matrix function). In particular, in the last decade, mathematical models with a fractional power of an elliptic operator and…