arXiv subjects

Riccardo Gatto

Publications and source records attributed to Riccardo Gatto.

4 recordsLinked to original sources

arXiv2024

Analytic and Monte Carlo Approximations to the Distribution of the First Passage Time of the Drifted Diffusion with Stochastic Resetting and Mixed Boundary Conditions

This article introduces two techniques for computing the distribution of the absorption or first passage time of the drifted Wiener diffusion subject to Poisson resetting times, to an upper hard wall barrier and to a lower absorbing barrier. The first method, which we call ``Padé-partial fraction'' approximation, starts with the Padé approximation to the Laplace transform of the first passage time distribution, which is then exactly inverted by means of the partial fraction decomposition. The second method, which we call "multiresolution algorithm", is a Monte Carlo technique that exploits the properties of the Wiener process in order to generate Brownian bridges at increasing levels of resolution. Our numerical study reveals that the multiresolution algorithm has higher efficiency than standard Monte Carlo, whereas the faster Padé-partial fraction method is accurate in various circumstances and provides an analytical formula. Also, a closed-form exact expression for the expected first passage time is derived.

physics.comp-ph↗

arXiv2024

A unified perspective on exponential tilt and bridge algorithms for rare trajectories of discrete Markov processes

This article analyzes and compares two general techniques of rare event simulation for generating paths of Markov processes over fixed time horizons: exponential tilting and stochastic bridge. These two methods allow to accurately compute the probability that a Markov process ends within a rare region, which is unlikely to be attained. Exponential tilting is a general technique for obtaining an alternative or tilted sampling probability measure, under which the Markov process becomes likely to hit the rare region at terminal time. The stochastic bridge technique involves conditioning paths towards two endpoints: the terminal point and the initial one. The terminal point is generated from some appropriately chosen probability distribution that covers well the rare region. We show that both methods belong to the class of importance sampling procedures, by providing a common mathematical framework of these two conceptually different methods of sampling rare trajectories. We also conduct a numerical comparison of these two methods, revealing distinct areas of application for each Monte Carlo method, where they exhibit superior efficiency. Detailed simulation algorithms are provided.

cond-mat.stat-mech↗

arXiv2021

Bayesian tests of symmetry for the generalized von Mises distribution

Bayesian tests on the symmetry of the generalized von Mises model for planar directions (Gatto and Jammalamadaka, 2007) are introduced. The generalized von Mises distribution is a flexible model that can be axially symmetric or asymmetric, unimodal or bimodal. A characterization of axial symmetry is provided and taken as null hypothesis for one of the proposed Bayesian tests. The Bayesian tests are obtained by the technique of probability perturbation. The prior probability measure is perturbed so to give a positive prior probability to the null hypothesis, which would be null otherwise. This allows for the derivation of simple computational formulae for the Bayes factors. Numerical results reveal that, whenever the simulation scheme of the samples supports the null hypothesis, the null posterior probabilities appear systematically larger than their prior counterpart.

math.ST↗

arXiv2021

Information theoretic results for stationary time series and the Gaussian-generalized von Mises time series

This chapter presents some novel information theoretic results for the analysis of stationary time series in the frequency domain. In particular, the spectral distribution that corresponds to the most uncertain or unpredictable time series with some values of the autocovariance function fixed, is the generalized von Mises spectral distribution. It is thus a maximum entropy spectral distribution and the corresponding stationary time series is called the generalized von Mises time series. The generalized von Mises distribution is used in directional statistics for modelling planar directions that follow a multimodal distribution. Furthermore, the Gaussian-generalized von Mises times series is presented as the stationary time series that maximizes entropies in frequency and time domains, respectively referred to as spectral and temporal entropies. Parameter estimation and some computational aspects with this time series are briefly analyzed.

math.ST↗