Related papers: Strong approximation of Bessel processes
We study the strong approximation of a Backward SDE with finite stopping time horizon, namely the first exit time of a forward SDE from a cylindrical domain. We use the Euler scheme approach of Bouchard and Touzi, Zhang 04}. When the domain…
Performing inference in Bayesian models requires sampling algorithms to draw samples from the posterior. This becomes prohibitively expensive as the size of data sets increase. Constructing approximations to the posterior which are cheap to…
The computation of (i) $\varepsilon$-kernels, (ii) approximate diameter, and (iii) approximate bichromatic closest pair are fundamental problems in geometric approximation. In this paper, we describe new algorithms that offer significant…
Approximate Bayesian computation (ABC) is a popular likelihood-free inference method for models with intractable likelihood functions. As ABC methods usually rely on comparing summary statistics of observed and simulated data, the choice of…
We study the asymptotic behaviour of partial sums of long range dependent random variables and that of their counting process, together with an appropriately normalized integral process of the sum of these two processes, the so-called…
Motivated by the goal of improving the efficiency of small sample design, we propose a novel Bayesian stochastic approximation method to estimate the root of a regression function. The method features adaptive local modelling and…
We consider the problem of inference for the states and parameters of a continuous-time multitype branching process from partially observed time series data. Exact inference for this class of models, typically using sequential Monte Carlo,…
With larger data at their disposal, scientists are emboldened to tackle complex questions that require sophisticated statistical models. It is not unusual for the latter to have likelihood functions that elude analytical formulations. Even…
The use of approximation is fundamental in computational science. Almost all computational methods adopt approximations in some form in order to obtain a favourable cost/accuracy trade-off and there are usually many approximations that…
Gaussian processes are a powerful framework for quantifying uncertainty and for sequential decision-making but are limited by the requirement of solving linear systems. In general, this has a cubic cost in dataset size and is sensitive to…
We define a time dependent empirical process based on $n$ i.i.d.~fractional Brownian motions and establish Gaussian couplings and strong approximations to it by Gaussian processes. They lead to functional laws of the iterated logarithm for…
In this paper we present a fast and accurate numerical algorithm for the computation of hyperspherical Bessel functions of large order and real arguments. For the hyperspherical Bessel functions of closed type, no stable algorithm existed…
Approximate Bayesian computation performs approximate inference for models where likelihood computations are expensive or impossible. Instead simulations from the model are performed for various parameter values and accepted if they are…
Inference for mechanistic models is challenging because of nonlinear interactions between model parameters and a lack of identifiability. Here we focus on a specific class of mechanistic models, which we term stable differential equations.…
Approximate Bayesian computation (ABC) is a family of computational techniques in Bayesian statistics. These techniques allow to fi t a model to data without relying on the computation of the model likelihood. They instead require to…
Approximate Bayesian computation (ABC) is an approach for sampling from an approximate posterior distribution in the presence of a computationally intractable likelihood function. A common implementation is based on simulating model,…
Deciding what to sense is a crucial task, made harder by dependencies and by a nonadditive utility function. We develop approximation algorithms for selecting an optimal set of measurements, under a dependency structure modeled by a…
The generation of decision-theoretic Bayesian optimal designs is complicated by the significant computational challenge of minimising an analytically intractable expected loss function over a, potentially, high-dimensional design space. A…
The Markov Chain Monte Carlo method is the dominant paradigm for posterior computation in Bayesian analysis. It is common to control computation time by making approximations to the Markov transition kernel. Comparatively little attention…
This paper proposes a new methodology to perform Bayesian inference for a class of multidimensional Cox processes in which the intensity function is piecewise constant. Poisson processes with piecewise constant intensity functions are…