Related papers: On death processes and urn models

Using diffusion priors to solve inverse problems in imaging have significantly matured over the years. In this chapter, we review the various different approaches that were proposed over the years. We categorize the approaches into the more…

Models defined by moment conditions are at the center of structural econometric estimation, but economic theory is mostly agnostic about moment selection. While a large pool of valid moments can potentially improve estimation efficiency, in…

We investigate extended processes given by last-passage times in directed models defined using exponential variables with decaying mean. In certain cases we find the universal Airy process, but other cases lead to non-universal and trivial…

A classical P\'olya urn scheme is a Markov process whose evolution is encoded by a replacement matrix $(R_{i,j})_{1\leq i,j\leq d}$. At every discrete time-step, we draw a ball uniformly at random, denote its colour $c$, and replace it in…

In the 1958 paper "Shall we count the living or the dead?", Mindel C. Sheps proposed a principled solution to the familiar problem of asymmetry of the relative risk. We provide causal models to clarify the scope and limitations of Sheps'…

No matter the nature of the response and/or explanatory variables in a regression model, some basic issues such as the existence of an effect of the predictor on the response, or the assessment of a common shape across groups of…

We analyze general enough models of repeated indirect measurements in which a quantum system interacts repeatedly with randomly chosen probes on which Von Neumann direct measurements are performed. We prove, under suitable hypotheses, that…

We first propose and study a quantum toy model of black hole dynamics. The model is unitary, displays quantum thermalization, and the Hamiltonian couples every oscillator with every other, a feature intended to emulate the color sector…

We consider first the mixed discrete-continuous scheme of observation in multistate models; this is a classical pattern in epidemiology because very often clinical status is assessed at discrete visit times while times of death or other…

We study normal approximations for a class of discrete-time occupancy processes, namely, Markov chains with transition kernels of product Bernoulli form. This class encompasses numerous models which appear in the complex networks…

We impose the uniform probability measure on the set of all discrete Gelfand-Tsetlin patterns of depth $n$ with the particles on row $n$ in deterministic positions. These systems equivalently describe a broad class of random tilings models,…

Interacting urns with exponential reinforcement were introduced and studied in Launay (2011). As its parameter $\rho$ tends to $\iy$, this reinforcement mechanism converges to the "generalized" reinforcement, in which the probability of…

Simulating samples from arbitrary probability distributions is a major research program of statistical computing. Recent work has shown promise in an old idea, that sampling from a discrete distribution can be accomplished by perturbing and…

I introduce a generic method for inference on entire quantile and regression quantile processes in the presence of a finite number of large and arbitrarily heterogeneous clusters. The method asymptotically controls size by generating…

Renewal models are widely used in statistical epidemiology as semi-mechanistic models of disease transmission. While primarily used for estimating the instantaneous reproduction number, they can also be used for generating projections,…

We present an embedding of stochastic optimal control problems, of the so called path integral form, into reproducing kernel Hilbert spaces. Using consistent, sample based estimates of the embedding leads to a model free, non-parametric…

Cumulative probability models (CPMs) are a robust alternative to linear models for continuous outcomes. However, they are not feasible for very large datasets due to elevated running time and memory usage, which depend on the sample size,…

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…

We provide a general method to analyze the asymptotic properties of a variety of estimators of continuous time diffusion processes when the data are not only discretely sampled in time but the time separating successive observations may…

Consider a balanced non triangular two-color P\'olya-Eggenberger urn process, assumed to be large which means that the ratio sigma of the replacement matrix eigenvalues satisfies 1/2<sigma <1. The composition vector of both discrete time…