Related papers: A unified approach to Stein characterizations
We show by a surprisingly simple argument that the exchangeability condition, which is key to the exchangeable pair approach in Stein's method for distributional approximation, can be omitted in many standard settings. This is achieved by…
We consider the approximation of the stationary distribution of the finite inclusion process with the Poisson-Dirichlet distribution. Using Stein's method, we derive an explicit bound for the approximation error, which is of order 1/N in…
We consider estimation of the structural distribution function of the cell probabilities of a multinomial sample in situations where the number of cells is large. We review the performance of the natural estimator, an estimator based on…
This is an expository article on the Poisson binomial distribution. We review lesser known results and recent progress on this topic, including geometry of polynomials and distribution learning. We also provide examples to illustrate the…
In this paper, we quantify some known approximation to the Curie-Weiss model via applying the Stein method to the Markov chain whose stationary distribution coincides with Curie-Weiss model.
A class of probability distributions is characterized via equalities in law between two order statistics shifted by independent exponential variables. An explicit formula for the quintile function of the identified family of distributions…
Let $Z$ be a standard normal random variable and let $H_n$ denote the $n$-th Hermite polynomial. In this note, we obtain Stein equations for the random variables $H_3(Z)$ and $H_4(Z)$, which represents a first step towards developing…
Constructions in type-driven compositional distributional semantics associate large collections of matrices of size $D$ to linguistic corpora. We develop the proposal of analysing the statistical characteristics of this data in the…
Recently there have been increasing interests in learning and inference with implicit distributions (i.e., distributions without tractable densities). To this end, we develop a gradient estimator for implicit distributions based on Stein's…
Competing and Complementary risk (CCR) problems are often modelled using a class of distributions of the maximum, or minimum, of a random number of i.i.d. random variables; we call this class the CCR class of distributions. While the CCR…
The concept of Probability of Causation (PC) is critically important in legal contexts and can help in many other domains. While it has been around since 1986, current operationalizations can obtain only the minimum and maximum values of…
An important task in computational statistics and machine learning is to approximate a posterior distribution $p(x)$ with an empirical measure supported on a set of representative points $\{x_i\}_{i=1}^n$. This paper focuses on methods…
A new method for including systematic errors in the regression with Poisson data is reviewed in this contribution, with emphasis on applications to astronomical spectra. The method consists of generalizing the usual Poisson log-likelihood,…
Under mild assumptions the equivalence of the mixed Poisson process with mixing parameter a real-valued random variable to the one with mixing distribution as well as to the mixed Poisson process in the sense of Huang is obtained, and a…
Matrix-form Poisson probability distributions were recently introduced as one matrix generalization of Panjer distributions. We show in this paper that under the constraint that their representation is to be nonnegative, they have a…
Many problems in the geophysical sciences demand the ability to calibrate the parameters and predict the time evolution of complex dynamical models using sequentially-collected data. Here we introduce a general methodology for the joint…
We provide an overview of some recent techniques involving the Malliavin calculus of variations and the so-called ``Stein's method'' for the Gaussian approximations of probability distributions. Special attention is devoted to establishing…
In the context of survival analysis, Marshall and Olkin (1997) introduced families of distributions by adding a scalar parameter to a given survival function, parameterized or not. In that paper, we generalize their approach. We show how it…
We assess advantages of expressing tree-structured Ising models via their mean parameterization rather than their commonly chosen canonical parameterization. This includes fixedness of marginal distributions, often convenient for dependence…
A compound Poisson process whose parameters are all unknown is observed at finitely many equispaced times. Nonparametric estimators of the jump and L\'evy distributions are proposed and functional central limit theorems using the uniform…