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Humans and other animals behave as if we perform fast Bayesian inference underlying decisions and movement control given uncertain sense data. Here we show that a biophysically realistic model of the subthreshold membrane potential of a…
Poisson processes and one-dimensional Poisson point processes satisfy three main properties: superposition, thinning, and conditioning. The proof of the first two relies on basic estimates involving the Poisson distribution that are also…
We consider the model selection problem for a large class of time series models, including, multivariate count processes, causal processes with exogenous covariates. A procedure based on a general penalized contrast is proposed. Some…
In this paper, we consider Bayesian point estimation and predictive density estimation in the binomial case. After presenting preliminary results on these problems, we compare the risk functions of the Bayes estimators based on the…
High-dimensional self-exciting point processes have been widely used in many application areas to model discrete event data in which past and current events affect the likelihood of future events. In this paper, we are concerned with…
We propose a multivariate framework for modeling dependent default times that extends the classical Cox process by incorporating both common and idiosyncratic shocks. Our construction uses c\`adl\`ag, increasing processes to model…
The problem of disorder seeks to determine a stopping time which is as close as possible to the unknown time of ``disorder'' when the observed process changes its probability characteristics. We give a partial answer to this question for…
Restricted mean survival time (RMST) is an intuitive summary statistic for time-to-event random variables, and can be used for measuring treatment effects. Compared to hazard ratio, its estimation procedure is robust against the…
The statistics of the first-encounter time of diffusing particles changes drastically when they are placed under confinement. In the present work, we make use of Monte Carlo simulations to study the behavior of a two-particle system in two-…
We consider a single Leaky integrate-and-fire neuron stimulated with Poisson process. We develop a method, which allows one to obtain the first passage time probability density function without any additional approximations.
A mixture of multivariate contaminated normal distributions is developed for model-based clustering. In addition to the parameters of the classical normal mixture, our contaminated mixture has, for each cluster, a parameter controlling the…
A model for the phenomenological description of tick-by-tick share prices in a stock exchange is introduced. It is based on mixtures of compound Poisson processes. Preliminary results based on Monte Carlo simulation show that this model can…
We consider a system of asymmetric independent random walks on $\mathbb{Z}^d$, denoted by $\{\eta_t,t\in{\mathbb{R}}\}$, stationary under the product Poisson measure $\nu_{\rho}$ of marginal density $\rho>0$. We fix a pattern $\mathcal{A}$,…
Probabilistic model checking for systems with large or unbounded state space is a challenging computational problem in formal modelling and its applications. Numerical algorithms require an explicit representation of the state space, while…
Targeted maximum likelihood estimation is a general methodology combining flexible ensemble learning and semiparametric efficiency theory in a two-step procedure for estimation of causal parameters. Proposed targeted maximum likelihood…
We consider parameter estimation, hypothesis testing and variable selection for partially time-varying coefficient models. Our asymptotic theory has the useful feature that it can allow dependent, nonstationary error and covariate…
Several key metrics in public health convey the probability that a primary event will lead to a more serious secondary event in the future. These "severity rates" can change over the course of an epidemic in response to shifting conditions…
We consider the problem of computing first-passage time distributions for reaction processes modelled by master equations. We show that this generally intractable class of problems is equivalent to a sequential Bayesian inference problem…
We address the common problem of calculating intervals in the presence of systematic uncertainties. We aim to investigate several approaches, but here describe just a Bayesian technique for setting upper limits. The particular example we…
In this work we consider time series with a finite number of discrete point changes. We assume that the data in each segment follows a different probability density functions (pdf). We focus on the case where the data in all segments are…