Related papers: A conjugate prior for the Dirichlet distribution

We study properties of popular near-uniform (Dirichlet) priors for learning undersampled probability distributions on discrete nonmetric spaces and show that they lead to disastrous results. However, an Occam-style phase space argument…

To understand biological diversification, it is important to account for large-scale processes that affect the evolutionary history of groups of co-distributed populations of organisms. Such events predict temporally clustered divergences…

The experimentally measured multiplicity distributions exhibit, after closer inspection, peculiarly enhanced void probability and oscillatory behavior of the modified combinants. We show that both these features can be used as additional…

Doubly intractable problems occur when both the likelihood and the posterior are available only in unnormalised form, with computationally intractable normalisation constants. Bayesian inference then typically requires direct approximation…

A new class of time-dependent Dirichlet priors is introduced as a generalisation of the Wright-Fisher diffusion, allowing discontinuities in the trajectories, as well as non-Markovian memory. This class is obtained as a simple stochastic…

An interesting line of research is the investigation of the laws of random variables known as Dirichlet means. However, there is not much information on interrelationships between different Dirichlet means. Here, we introduce two…

We adapt Thistlethwaite's alternating tangle decomposition of a knot diagram to identify the potential extreme terms in its bracket polynomial, and give a simple combinatorial calculation for their coefficients, based on the intersection…

We study the distribution of primes from a topological viewpoint. Certain conjecture is introduced, and we show that it is equivalent to the Riemann Hypothesis.

In this article we study the value distribution theory for the first derivative of the logarithmic derivative of Dirichlet $L$-functions, generalizing certain results of Ihara, Matsumoto et. al. related to ``$M$-functions" for $\sigma = $…

We study odd numbers through a straightforward indexing. We focus in particular on odd prime and composite numbers and their distribution. With a counting argument, we calculate the limit of two sums and compare their convergence rate.

In this research announcement we present a new q-analog of a classical formula for the exponential generating function of the Eulerian polynomials. The Eulerian polynomials enumerate permutations according to their number of descents or…

We present a new notion of distribution and derived distribution of rank $r \in \mathbb{N}$ for a global function field $K$ with a distinguished place $\infty$. It allows to describe the relations between division points, isogenies, and…

In this short note, we propose an unified method to derive formulas for derivations conjugated by exponential functions on an almost complex manifold. In v3, we corrected some mistakes in previous versions.

We describe two new classes of onto interpolating sequences for the Dirichlet space, in particular resolving a question of Bishop. We also give a complete description of the analogous sequences for a discrete model of the Dirichlet space.

The Bayesian approach to inference stands out for naturally allowing borrowing information across heterogeneous populations, with different samples possibly sharing the same distribution. A popular Bayesian nonparametric model for…

Dirichlet's theorem on arithmetic progressions called as Dirichlet prime number theorem is a classical result in number theory. Atle Selberg\cite{Selberg} gave an elementary proof of this theorem. In this article we give an alternative…

We demonstrate that the functional form of the likelihood contains a sufficient amount of information for constructing a prior for the unknown parameters. We develop a four-step algorithm by invoking the information entropy as the measure…

We investigate Newton series for truncated multiple $L$-values and thereby obtain a class of relations for multiple $L$-values. In addition, we give a formulation and a proof of extended derivation relations for multiple $L$-values.

Let $k$ be a number field and $O$ the ring of integers. In the previous paper [T06] we study the Dirichlet series counting discriminants of cubic algebras of $O$ and derive some density theorems on distributions of the discriminants by…

There is a well-known classification of conjugacy classes of involutions in finite Coxeter groups, in terms of subsets of nodes of their Coxeter graphs. In many cases, the product of an involution with the longest element is again an…