Related papers: High-dimensional ABC

Approximate Bayesian Computation (ABC) is a popular sampling method in applications involving intractable likelihood functions. Without evaluating the likelihood function, ABC approximates the posterior distribution by the set of accepted…

Designs of experiments for multivariate case are reviewed. Fast algorithm of construction of good Latin hypercube designs is developed.

We derive new formulas for the high dimensional biharmonic potential acting on Gaussians or Gaussians times special polynomials. These formulas can be used to construct accurate cubature formulas of an arbitrary high order which are fast…

This article surveys computational methods for posterior inference with intractable likelihoods, that is where the likelihood function is unavailable in closed form, or where evaluation of the likelihood is infeasible. We review recent…

A maximum likelihood methodology for a general class of models is presented, using an approximate Bayesian computation (ABC) approach. The typical target of ABC methods are models with intractable likelihoods, and we combine an ABC-MCMC…

Approximate Bayesian Computation (ABC) is a family of statistical inference techniques, which is increasingly used in biology and other scientific fields. Its main benefit is to be applicable to models for which the computation of the model…

We introduce an asymptotic notion of positivity in algebraic geometry that turns out to be related to some high-dimensional convex sets. The dimension of the convex sets grows with the number of birational operations. In the case of complex…

Mechanistic models are essential tools across ecology, epidemiology, and the life sciences, but parameter inference remains challenging when likelihood functions are intractable. Approximate Bayesian Computation with Sequential Monte Carlo…

We consider the path approximation of Bessel processes and develop a new and efficient algorithm. This study is based on a recent work by the authors, on the path approximation of the Brownian motion, and on the construction of specific own…

We present a growing dimension asymptotic formalism. The perspective in this paper is classification theory and we show that it can accommodate probabilistic networks classifiers, including naive Bayes model and its augmented version. When…

It is one of the most challenging problems in applied mathematics to approximatively solve high-dimensional partial differential equations (PDEs). Recently, several deep learning-based approximation algorithms for attacking this problem…

Traditional simulations on High-Performance Computing (HPC) systems typically involve modeling very large domains and/or very complex equations. HPC systems allow running large models, but limits in performance increase that have become…

This chapter will appear in the forthcoming Handbook of Approximate Bayesian Computation (2018). Indirect inference (II) is a classical likelihood-free approach that pre-dates the main developments of ABC and relies on simulation from a…

Conceptual Scaling is a useful standard tool in Formal Concept Analysis and beyond. Its mathematical theory, as elaborated in the last chapter of the FCA monograph, still has room for improvement. As it stands, even some of the basic…

This article appeared in the September 2024 issue (Vol. 31, No. 3) of the Bulletin of the International Society for Bayesian Analysis (ISBA).

The AAA algorithm, introduced in 2018, computes best or near-best rational approximations to functions or data on subsets of the real line or the complex plane. It is much faster and more robust than previous algorithms for such problems…

Selecting between different dependency structures of hidden Markov random field can be very challenging, due to the intractable normalizing constant in the likelihood. We answer this question with approximate Bayesian computation (ABC)…

The modern status of large extra dimensional (LED) approaches, highlights of their manifestation and short prehistory are discussed in this paper.

A detailed presentation of the results obtained during my Ph.D. research. The main investigations concern explicit descriptions of classes of finite dimensional pointed Hopf algebras and their quasi-isomorphism types.

This two-part comprehensive survey is devoted to a computing framework most commonly known under the names Hyperdimensional Computing and Vector Symbolic Architectures (HDC/VSA). Both names refer to a family of computational models that use…