Related papers: Martingale marginals do not always determine conve…
Estimation of finite mixture models when the mixing distribution support is unknown is an important problem. This paper gives a new approach based on a marginal likelihood for the unknown support. Motivated by a Bayesian Dirichlet prior…
In this article, we discuss a bivariate distribution whose conditionals are univariate binomial distributions and the marginals are not binomial that exhibits negative correlation. Some useful structural properties of this distribution…
This paper develops techniques to study the number of descents in random permutations via martingales. We relax an assumption in the Berry-Esseen theorem of Bolthausen (1982) to extend the theorem's scope to martingale differences of…
An equivalent condition for the product of elements of an independent random sample on a compact algebraic group converging in distribution to some random variable as the sample size increases is obtained. Namely, a limit distribution…
It will be recalled that the classical bivariate normal distributions have normal marginals and normal conditionals. It is natural to ask whether a similar phenomenon can be encountered involving Poisson marginals and conditionals.…
In this note we introduce a new kind of augmentation of filtrations along a sequence of stopping times. This augmentation is suitable for the construction of new probability measures associated to a positive strict local martingale as done…
There is a growing interest in the so-called Bayesian Predictive Inference approach, which allows to perform Bayesian inference without specifying the likelihood and prior of the model, or the need of any MCMC. Instead, only a sequence of…
Marginal models involve restrictions on the conditional and marginal association structure of a set of categorical variables. They generalize log-linear models for contingency tables, which are the fundamental tools for modelling the…
Bayesian inference for models that have an intractable partition function is known as a doubly intractable problem, where standard Monte Carlo methods are not applicable. The past decade has seen the development of auxiliary variable Monte…
In this paper, we give rates of convergence, for minimal distances and for the uniform distance, between the law of partial sums of martingale differences and thelimiting Gaussian distribution. More precisely, denoting by $P_{X}$ the law of…
Given a random sample from a random variable $T$ which is bounded from above, $T\le\tau$ a.s., we define processes that are positive supermartingales if $E(T)\ge\mu$. Such processes are called test martingales. Tests of the supermartingale…
We use the abstract method of (local) martingale problems in order to give criteria for convergence of stochastic processes. Extending previous notions, the formulation we use is neither restricted to Markov processes (or semimartingales),…
We illustrate a process that constructs martingales from raw material that arises naturally from the theory of sampling without replacement.The usefulness of the new martingales is illustrated by the development of maximal inequalities for…
In the propositional setting, the marginal problem is to find a (maximum-entropy) distribution that has some given marginals. We study this problem in a relational setting and make the following contributions. First, we compare two…
We give concentration bounds for martingales that are uniform over finite times and extend classical Hoeffding and Bernstein inequalities. We also demonstrate our concentration bounds to be optimal with a matching anti-concentration…
Hoeffding has shown that tail bounds on the distribution for sampling from a finite population with replacement also apply to the corresponding cases of sampling without replacement. (A special case of this result is that binomial tail…
We give optimal convergence rates in the central limit theorem for a large class of martingale difference sequences with bounded third moments. The rates depend on the behaviour of the conditional variances and for stationary sequences the…
We introduce a new non-linear optimal transport formulation for a pair of probability measures on $\mathbb{R}^d$ sharing a common barycentre, in which admissible transference plans satisfy two martingale-type constraints. This bi-martingale…
To take sample biases and skewness in the observations into account, practitioners frequently weight their observations according to some marginal distribution. The present paper demonstrates that such weighting can indeed improve the…
A theory of martingales for censoring is developed. The Doob-Meyer martingale is shown to be inadequate in general, and a repaired martingale is proposed with a non-predictable centering term. Associated martingale transforms, variation…