Related papers: A conjugate prior for the Dirichlet distribution

Let G be a simple algebraic group over an algebraically closed field k. We classify the spherical conjugacy classes of G.

We define the derivative of an integer to be the map sending every prime to 1 and satisfying the Leibniz rule. The aim of this article is to calculate the Dirichlet product of this map with a function arithmetic multiplicative.

We present a comprehensive insight into counting distributions from the perspective of the combinants extracted from them. In particular, we focus on cases where these combinants exhibit oscillatory behavior that can provide an invaluable…

In the present work we show that the Dirichlet series with the Euler product having analytical continuation to the critical strip without singularities, in some natural conditions, can be approximated by partial products of Euler type in…

As a continuation of the authors and Wakatsuki's previous paper [5], we study relations among Dirichlet series whose coefficients are class numbers of binary cubic forms. We show that for any integral models of the space of binary cubic…

The distribution of descents in a fixed conjugacy class of $S_n$ is studied, and it is shown that its moments have an interesting property. A particular conjugacy class that is of interest is the class of matchings (also known as fixed…

In this note we prove an explicit binomial formula for Jack polynomials and discuss some applications of it.

We construct families of finitely presented groups exhibiting new divergence behavior; we obtain divergence functions of the form $r^\alpha$ for a dense set of exponents $\alpha \in [2,\infty)$ and $r^n\log(r)$ for integers $n \geq 2$. The…

In this paper we prove an existence theorem concerning linear forms of a given Diophantine type and apply it to study the structure of the spectrum of lattice exponents.

We describe singular diffusion in bounded subsets $\Omega$ of $\mathbb{R}^n$ by form methods and characterize the associated operator. We also prove positivity and contractivity of the corresponding semigroup. This results in a description…

Using the Dirichlet integrals, which are employed in the theory of Fourier series, this paper develops a useful method for the summation of series and the evaluation of integrals.

This article is written for pedagogical purposes aiming at practitioners trying to estimate the finite support of continuous probability distributions, i.e., the minimum and the maximum of a distribution defined on a finite domain.…

We extend classic characterisations of posterior distributions under Dirichlet process and gamma random measures priors to a dynamic framework. We consider the problem of learning, from indirect observations, two families of time-dependent…

In this paper, We use the Fourier series expansion of real variables function, We give a formula to calculate the Dirichlet character sum, and four special examples are given.

We consider a sum of the derivatives of Dirichlet $L$-functions over the zeros of Dirichlet $L$-functions. We give an asymptotic formula for the sum.

Let G be a connected reductive group. We define a map from the set of unipotent classes in G to the set of conjugacy classes in the Weyl group (assuming that the characteristic is not bad). This map is a one sided inverse of a map in the…

Although discrete mixture modeling has formed the backbone of the literature on Bayesian density estimation, there are some well known disadvantages. We propose an alternative class of priors based on random nonlinear functions of a uniform…

Bayesian models that mix multiple Dirichlet prior parameters, called Multi-Dirichlet priors (MD) in this paper, are gaining popularity. Inferring mixing weights and parameters of mixed prior distributions seems tricky, as sums over…

We study a new parametric family of distributions on the ordered simplex $\nabla^{d-1} = \{y \in \mathbb{R}^d: y_1 \geq \dots \geq y_d \geq 0, \sum_{k=1}^d y_k = 1\}$, which we call Generalized Rank Dirichlet (GRD) distributions. Their…

This paper presents a number of identities for Dirichlet series and series with Stirling numbers of the first kind. As coefficients for the Dirichlet series we use Cauchy numbers of the first and second kinds, hyperharmonic numbers,…