相关论文: New Dirichlet Mean Identities

Many popular Bayesian nonparametric priors can be characterized in terms of exchangeable species sampling sequences. However, in some applications, exchangeability may not be appropriate. We introduce a {novel and probabilistically coherent…

In general, while obtaining the probability density function of sums and products of shifted random variables, ordinary analytical methods such as Fourier and Mellin transforms tend to provide integrals which cannot be expressed in terms of…

We formulate dynamical rate equations for physical processes driven by a combination of diffusive growth, size fragmentation and fragment coagulation. Initially, we consider processes where coagulation is absent. In this case we solve the…

We study diffusion processes and stochastic flows which are time-changed random perturbations of a deterministic flow on a manifold. Using non-symmetric Dirichlet forms and their convergence in a sense close to the Mosco-convergence, we…

Within Bayesian nonparametrics, dependent Dirichlet process mixture models provide a highly flexible approach for conducting inference about the conditional density function. However, several formulations of this class make either rather…

We study the distribution of large (and small) values of several families of $L$-functions on a line $\text{Re(s)}=\sigma$ where $1/2<\sigma<1$. We consider the Riemann zeta function $\zeta(s)$ in the $t$-aspect, Dirichlet $L$-functions in…

Graphical models are used to describe the conditional independence relations in multivariate data. They have been used for a variety of problems, including log-linear models (Liu and Massam, 2006), network analysis (Holland and Leinhardt,…

This thesis describes work on two applications of probabilistic programming: the learning of probabilistic program code given specifications, in particular program code of one-dimensional samplers; and the facilitation of sequential Monte…

We first introduce and derive some basic properties of a two-parameters family of one-sided Levy processes. Their Laplace exponents are given in terms of the Pochhammer symbol. This family includes, in a limit case, the family of Brownian…

The purpose of this work is to describe a duality between a fragmentation associated to certain Dirichlet distributions and a natural random coagulation. The dual fragmentation and coalescent chains arising in this setting appear in the…

Simplex-valued data appear throughout statistics and machine learning, for example in the context of transfer learning and compression of deep networks. Existing models for this class of data rely on the Dirichlet distribution or other…

Parameter estimation in HEP experiments often involves Monte-Carlo simulation to model the experimental response function. A typical application are forward-folding likelihood analyses with re-weighting, or time-consuming minimization…

We show that an almost trivial inequality for the first and second mean of a random variable can be used to give non-trivial improvements on deep results. As applications we improve on results on lower bounds for the Riemann zeta-function…

A sharp, distribution free, non-asymptotic result is proved for the concentration of a random function around the mean function, when the randomization is generated by a finite sequence of independent data and the random functions satisfy…

We consider a random variable $Y$ and approximations $Y\_n$, defined on the same probability space with values in the same measurable space as $Y$. We are interested in situations where the approximations $Y\_n$ allow to define a Dirichlet…

``Orderly divergence'' deals with limit theorems for weighted stochastic Gamma integrals of otherwise nonintegrable functions. Although for monotonic functions this category usually coincides with the classical notion of weighted limit…

It is shown that a simple Dirichlet process mixture of multivariate normals offers Bayesian density estimation with adaptive posterior convergence rates. Toward this, a novel sieve for non-parametric mixture densities is explored, and its…

Training machine learning and statistical models often involves optimizing a data-driven risk criterion. The risk is usually computed with respect to the empirical data distribution, but this may result in poor and unstable out-of-sample…

In this paper we shall consider some famous means such as arithmetic, harmonic, geometric, root square mean, etc. Considering the difference of these means, we can establish. some inequalities among them. Interestingly, the difference of…

The two-parameter Poisson--Dirichlet distribution is a probability distribution on the totality of positive decreasing sequences with sum 1 and hence considered to govern masses of a random discrete distribution. A characterization of the…