Related papers: Parameter estimation of a two-colored urn model cl…
The P\'olya urn scheme is a discrete-time process concerning the addition and removal of colored balls. There is a known embedding of it in continuous-time, called the P\'olya process. We deal with a generalization of this stochastic model,…
We present a multiple colour generalisation of the model of graph interacting urns studied by Benaim et. al., Random Struct. Alg., 46: 614-634, 2015. We show that for complete graphs and for a broad class of reinforcement functions…
We consider multicolor urn models with multiple drawings. An urn model is called linear if the conditional expected value of the urn composition at time $n$ is a linear function of the composition at time $n-1$. For four different sampling…
Ordinary Differential Equations are widespread tools to model chemical, physical, biological process but they usually rely on parameters which are of critical importance in terms of dynamic and need to be estimated directly from the data.…
Parameter inference and uncertainty quantification are important steps when relating mathematical models to real-world observations, and when estimating uncertainty in model predictions. However, methods for doing this can be…
In this paper, we study the linear transformation model in the most general setup. This model includes many important and popular models in statistics and econometrics as special cases. Although it has been studied for many years, the…
We consider a model of a discrete time "interacting particle system" on the integer line where infinitely many changes are allowed at each instance of time. We describe the model using chameleons of two different colours, {\it viz}., red…
An algorithm observes the trajectories of random walks over an unknown graph $G$, starting from the same vertex $x$, as well as the degrees along the trajectories. For all finite connected graphs, one can estimate the number of edges $m$ up…
We study random graphs with latent geometric structure, where the probability of each edge depends on the underlying random positions corresponding to the two endpoints. We focus on the setting where this conditional probability is a…
Various indicators and measures of the real life procedures rise up as functionals of the quantile process of a parent random variable Z. However, Z can be observed only through a response in a linear model whose covariates are not under…
We study the joint asymptotics of forward and backward processes of numbers of non-empty urns in an infinite urn scheme. The probabilities of balls hitting the urns are assumed to satisfy the conditions of regular decrease. We prove weak…
Estimating the parameters of a probabilistic directed graphical model from incomplete data is a long-standing challenge. This is because, in the presence of latent variables, both the likelihood function and posterior distribution are…
Graphs are widely used for describing systems made up of many interacting components and for understanding the structure of their interactions. Various statistical models exist, which describe this structure as the result of a combination…
An urn containing specified numbers of balls of distinct ordered colors is considered. A multiple q-Polya urn model is introduced by assuming that the probability of q-drawing a ball of a specific color from the urn varies geometrically,…
We construct an independent increments Gaussian process associated to a class of multicolor urn models. The construction uses random variables from the urn model which are different from the random variables for which central limit theorems…
Stochastic differential equations such as the Ornstein-Uhlenbeck process have long been used to model realworld probablistic events such as stock prices and temperature fluctuations. While statistical methods such as Maximum Likelihood…
Many causal parameters depend on a moment of the joint distribution of potential outcomes. Such parameters are especially relevant in policy evaluation settings, where noncompliance is common and accommodated through the model of Imbens &…
In this paper, we address the identification problem for the systems characterized by linear time-invariant dynamics with bilinear observation models. More precisely, we consider a suitable parametric description of the system and formulate…
In this work we generalize Polya urn schemes with possibly infinitely many colors and extend the earlier models described in [4, 5, 7]. We provide a novel and unique approach of representing the observed sequence of colors in terms a…
Level set estimation (LSE), the problem of identifying the set of input points where a function takes value above (or below) a given threshold, is important in practical applications. When the function is expensive-to-evaluate and…