相关论文: Gaussian process priors with Markov properties for…

In the face of an infectious disease, a key epidemiological measure is the basic reproduction number, which quantifies the average secondary infections caused by a single case in a susceptible population. In practice, the effective…

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…

We find a representation of the integral of a Gauss-Markov process in the interval [0, t], in terms of Brownian motion. Moreover, some connections with first-passagetime problems are discussed, and some examples are reported.

We introduce a simulation-based, amortised Bayesian inference scheme to infer the parameters of random walks. Our approach learns the posterior distribution of the walks' parameters with a likelihood-free method. In the first step a graph…

Gaussian process regression is a powerful method for predicting states based on given data. It has been successfully applied for probabilistic predictions of structural systems to quantify, for example, the crack growth in mechanical…

The time-varying effective reproduction number $R_t$ is a widely used indicator of transmission dynamics during infectious disease outbreaks. Timely estimates of $R_t$ can be obtained from observations close to the original date of…

The COVID-19 pandemic provides new motivation for a classic problem in epidemiology: estimating the empirical rate of transmission during an outbreak (formally, the time-varying reproduction number) from case counts. While standard methods…

The effective reproduction number $R_t$ measures an infectious disease's transmissibility as the number of secondary infections in one reproduction time in a population having both susceptible and non-susceptible hosts. Current approaches…

The effective reproduction number is an important descriptor of an infectious disease epidemic. In small populations, ideally we would estimate the effective reproduction number using a Markov Jump Process (MJP) model of the spread of…

Epidemics are inherently stochastic, and stochastic models provide an appropriate way to describe and analyse such phenomena. Given temporal incidence data consisting of, for example, the number of new infections or removals in a given time…

In this paper, we introduce the notion of Gaussian processes indexed by probability density functions for extending the Mat\'ern family of covariance functions. We use some tools from information geometry to improve the efficiency and the…

The Bayesian analysis of infectious disease surveillance data from multiple locations typically involves building and fitting a spatio-temporal model of how the disease spreads in the structured population. Here we present new generally…

In this work we introduce correlated random walks on $\Z$. When picking suitably at random the coefficient of correlation, and taking the average over a large number of walks, we obtain a discrete Gaussian process, whose scaling limit is…

Gaussian process are a widely-used statistical tool for conducting non-parametric inference in applied sciences, with many computational packages available to fit to data and predict future observations. We study the use of the Greta…

Gaussian processes are a natural way of defining prior distributions over functions of one or more input variables. In a simple nonparametric regression problem, where such a function gives the mean of a Gaussian distribution for an…

It is considered the integrated process $X(t)= x + \int _0^t Y(s) ds ,$ where $Y(t)$ is a Gauss-Markov process starting from $y.$ The first-passage time (FPT) of $X$ through a constant boundary and the first-exit time of $X$ from an…

The main challenges that arise when adopting Gaussian Process priors in probabilistic modeling are how to carry out exact Bayesian inference and how to account for uncertainty on model parameters when making model-based predictions on…

We consider the accuracy of an approximate posterior distribution in nonparametric regression problems by combining posterior distributions computed on subsets of the data defined by the locations of the independent variables. We show that…

We consider a continuous-time Markov chain model of SIR disease dynamics with two levels of mixing. For this so-called stochastic households model, we provide two methods for inferring the model parameters---governing within-household…

This work is to popularize the method of computing the distribution of the excursion times for a Gaussian process that involves extended and multivariate Rice's formula. The approach was used in numerical implementations of the…