Related papers: Methods of Retrieving Large-Variable Exponents
We consider method-of-quantiles estimators of unknown parameters, namely the analogue of method-of-moments estimators obtained by matching empirical and theoretical quantiles at some probability level lambda in (0,1). The aim is to present…
Many scientifically well-motivated statistical models in natural, engineering, and environmental sciences are specified through a generative process. However, in some cases, it may not be possible to write down the likelihood for these…
Starting from the orthogonal polynomial expansion of a function $F$ corresponding to a finite positive Borel measure with infinite compact support, we study the asymptotic behavior of certain associated rational functions…
This paper presents complexity analysis and variational methods for inference in probabilistic description logics featuring Boolean operators, quantification, qualified number restrictions, nominals, inverse roles and role hierarchies.…
An integer is said to be $y$-friable if its greatest prime factor is less than $y$. In this paper, we obtain estimates for exponential sums over $y$-friable numbers up to $x$ which are non-trivial when $y \geq \exp\{c \sqrt{\log x} \log…
Asymptotic analysis for related inference problems often involves similar steps and proofs. These intermediate results could be shared across problems if each of them is made self-contained and easily identified. However, asymptotic…
The asymptotic iteration method is applied, to calculate the angular spheroidal eigenvalues $\lambda^{m}_{\ell}(c)$ with arbitrary complex size parameter $c$. It is shown that, the obtained numerical results of $\lambda^{m}_{\ell}(c)$ are…
The event of large losses plays an important role in credit risk. As these large losses are typically rare, and portfolios usually consist of a large number of positions, large deviation theory is the natural tool to analyze the tail…
The method of extrapolating asymptotic series, based on the Self-Similar Approximation Theory, is developed. Several important questions are answered, which makes the foundation of the method unambiguous and its application straightforward.…
A new summation method is introduced to convert a relatively wide family of infinite sums and local expansions into integrals. The integral representations yield global information such as analytic continuability, position of singularities,…
Inference methods are often formulated as variational approximations: these approximations allow easy evaluation of statistics by marginalization or linear response, but these estimates can be inconsistent. We show that by introducing…
Generic Newton polygons for L-functions of exponential sums associated to Laurent polynomials in one variable are determined. The corresponding Hasse polynomials are also determined.
Given a truncated perturbation expansion of a physical quantity, one can, under certain circumstances, obtain lower or upper bounds (or both) to the sum of the full perturbation series by using the Borel transform and a variational…
A new approach to the problem of finding the asymptotical behaviour of large orders of semiclassical expansion is suggested. Asymptotics of high orders not only for eigenvalues, but also for eigenfunctions, are constructed. Thus, one can…
An approximation method is presented for probabilistic inference with continuous random variables. These problems can arise in many practical problems, in particular where there are "second order" probabilities. The approximation, based on…
We consider binomial and inverse binomial sums at infinity and rewrite them in terms of a small set of constants, such as powers of $\pi$ or $\log(2)$. In order to perform these simplifications, we view the series as specializations of…
We handle divergent {\epsilon} expansions in different universality classes derived from modified Landau-Wilson Hamiltonian. Landau-Wilson Hamiltonian can cater for describing critical phenomena on a wide range of physical systems which…
Multivariate extreme value statistical analysis is concerned with observations on several variables which are thought to possess some degree of tail-dependence. In areas such as the modeling of financial and insurance risks, or as the…
Variational inference methods for latent variable statistical models have gained popularity because they are relatively fast, can handle large data sets, and have deterministic convergence guarantees. However, in practice it is unclear…
We discuss several techniques for the evaluation of the generalised Lyapunov exponents which characterise the growth of products of random matrices in the large-deviation regime. A Monte Carlo algorithm that performs importance sampling…