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A statistical language model assigns probability to strings of arbitrary length. Unfortunately, it is not possible to gather reliable statistics on strings of arbitrary length from a finite corpus. Therefore, a statistical language model…
Recently, Forr\'e (arXiv:2104.11547, 2021) introduced transitional conditional independence, a notion of conditional independence that provides a unified framework for both random and non-stochastic variables. The original paper establishes…
The jump behavior of an infinitely active It\^o semimartingale can be conveniently characterized by a jump activity index of Blumenthal-Getoor type, typically assumed to be constant in time. We study Markovian semimartingales with a…
Piecewise-deterministic Markov processes combine continuous in time dynamics with jump events, the rates of which generally depend on the continuous variables and thus are not constants. This leads to a problem in a Monte-Carlo simulation…
In this paper, we develop a general method to estimate the instantaneous frequencies of the modes making up a multicomponent signal when the former exhibit interference in the time-frequency plane. In particular, studying the representation…
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…
We consider the nonparametric robust estimation problem for regression models in continuous time with semi-Markov noises. An adaptive model selection procedure is proposed. Under general moment conditions on the noise distribution a sharp…
We propose and investigate a method for identifying timescales of dissipation in nonequilibrium steady states modeled as discrete-state Markov jump processes. The method is based on how the irreversibility-measured by the statistical…
In this paper we study time-inhomogeneous affine processes beyond the common assumption of stochastic continuity. In this setting times of jumps can be both inaccessible and predictable. To this end we develop a general theory of finite…
Previous approaches to modelling interval-censored data have often relied on assumptions of homogeneity in the sense that the censoring mechanism, the underlying distribution of occurrence times, or both, are assumed to be time-invariant.…
We present the mathematical basis of a new approach to the analysis of temporal coding. The foundation of the approach is the construction of several families of novel distances (metrics) between neuronal impulse trains. In contrast to most…
We study efficiency of non-parametric estimation of diffusions (stochastic differential equations driven by Brownian motion) from long stationary trajectories. First, we introduce estimators based on conditional expectation which is…
We consider the problem of estimating the asymptotic variance of a function defined on a Markov chain, an important step for statistical inference of the stationary mean. We design a novel recursive estimator that requires $O(1)$…
Interspike intervals describe the output of neurons. Signal transmission in a neuronal network implies that the output of some neurons becomes the input of others. The output should reproduce the main features of the input to avoid a…
In this paper, we study the problem of estimating a Markov chain $X$(signal) from its noisy partial information $Y$, when the transition probability kernel depends on some unknown parameters. Our goal is to compute the conditional…
Neuroscientists have worked on the problem of estimating synaptic properties, such as connectivity and strength, from simultaneously recorded spike trains since the 1960s. Recent years have seen renewed interest in the problem, coinciding…
This paper is concerned with tests for changes in the jump behaviour of a time-continuous process. Based on results on weak convergence of a sequential empirical tail integral process, asymptotics of certain tests statistics for breaks in…
Equilibrium rate theories play a crucial role in understanding rare, reactive events. However, they are inapplicable to a range of irreversible processes in systems driven far from thermodynamic equilibrium like active and biological…
It can be argued that optimal prediction should take into account all available data. Therefore, to evaluate a prediction interval's performance one should employ conditional coverage probability, conditioning on all available observations.…
Statistical inference for stochastic processes based on high-frequency observations has been an active research area for more than two decades. One of the most well-known and widely studied problems has been the estimation of the quadratic…