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A one - dimensional iterative map with two control parameters, i.e. the Kim - Kong map, is proposed. Our purpose is to investigate the characteristic properties of this map, and to discuss numerically the multifractal behavior of the…
Markov processes serve as a universal model for many real-world random processes. This paper presents a data-driven approach for learning these models through the spectral decomposition of the infinitesimal generator (IG) of the Markov…
The particle Gibbs sampler is a Markov chain Monte Carlo (MCMC) algorithm to sample from the full posterior distribution of a state-space model. It does so by executing Gibbs sampling steps on an extended target distribution defined on the…
Recursive stochastic algorithms have gained significant attention in the recent past due to data driven applications. Examples include stochastic gradient descent for solving large-scale optimization problems and empirical dynamic…
We introduce and study a fractional version of the Skellam process of order $k$ by time-changing it with an independent inverse stable subordinator. We call it the fractional Skellam process of order $k$ (FSPoK). An integral representation…
We define two new classes of stochastic processes, called tempered fractional L\'{e}vy process of the first and second kinds (TFLP and TFLP $I\!I$, respectively). TFLP and TFLP $I\!I$ make up very broad finite-variance, generally…
Discrete state spaces represent a major computational challenge to statistical inference, since the computation of normalisation constants requires summation over large or possibly infinite sets, which can be impractical. This paper…
We explore the concept of a consistent exchangeable survival process - a joint distribution of survival times in which the risk set evolves as a continuous-time Markov process with homogeneous transition rates. We show a correspondence with…
By expressing prior distributions as general stochastic processes, nonparametric Bayesian methods provide a flexible way to incorporate prior knowledge and constrain the latent structure in statistical inference. The Indian buffet process…
Continuous time random walks are non-Markovian stochastic processes, which are only partly characterized by single-time probability distributions. We derive a closed evolution equation for joint two-point probability density functions of a…
As the amount and complexity of available data increases, the need for robust statistical learning becomes more pressing. To enhance resilience against model misspecification, the generalized posterior inference method adjusts the…
In this paper we introduce a new probability distribution on (0,1), associated with the I-function, namely, the I-function distribution. This distribution generalizes several known distributions with positive support. It is also shown that…
This paper is devoted to the structure of the complete asymptotic expansion of the probability that a large combinatorial object is irreducible or consists of a given number of irreducible parts, where irreducibility is understood in terms…
We propose an iterative estimating equations procedure for analysis of longitudinal data. We show that, under very mild conditions, the probability that the procedure converges at an exponential rate tends to one as the sample size…
Given a stochastic structure with a filtration $\mathbb{F}$, the class of all random times whose conditional distribution functions are differentiable with respect to some $\mathbb{F}$ adapted non decreasing processes is considered. The…
We study time-changed Markov processes to speed up the convergence of Markov chain Monte Carlo (MCMC) algorithms. The time-changed process is defined by adjusting the speed of time of a base process via a user-chosen, state-dependent…
The Collective Graphical Model (CGM) models a population of independent and identically distributed individuals when only collective statistics (i.e., counts of individuals) are observed. Exact inference in CGMs is intractable, and previous…
Stochastic processes are a flexible and widely used family of models for statistical modeling. While stochastic processes offer attractive properties such as inclusion of uncertainty properties, their inference is typically intractable,…
Clustered multistate process data are commonly encountered in multicenter observational studies and clinical trials. A clinically important estimand with such data is the marginal probability of being in a particular transient state as a…
We develop a predictive inference procedure that combines conformal prediction (CP) with unconditional quantile regression (QR) -- a commonly used tool in econometrics that involves regressing the recentered influence function (RIF) of the…