Related papers: Stationary 1-dependent Counting Processes: from Ru…
Working with generating functions, the combinatorics of a recurrence relation can be expressed in a way that allows for more efficient calculation of the quantity. This is true of the Catalan numbers for an ordered binary tree…
The paper considers functional linear regression, where scalar responses $Y_1,\ldots,Y_n$ are modeled in dependence of i.i.d. random functions $X_1,\ldots,X_n$. We study a generalization of the classical functional linear regression model.…
Using the theory of exponential Riordan arrays and orthogonal polynomials, we demonstrate that the "descending power" Eulerian polynomials, and their once shifted sequence, are moment sequences for simple families of orthogonal polynomials,…
We consider a measurable stationary Gaussian stochastic process. A criterion for testing hypotheses about the covariance function of such a process using estimates for its norm in the space $L_p(\mathbb {T}),\,p\geq1$, is constructed.
We have presented a multivariate polynomial function termed as factor elimination function,by which, we can generate prime numbers. This function's mapping behavior can explain the irregularities in the occurrence of prime numbers on the…
We consider a polling system: a queueing system of $N\ge 1$ queues with Poisson arrivals $Q_1,...,Q_N$ visited in a cyclic order (with or without switchover times) by a single server. For this system we derive the probability generating…
Many spatial processes exhibit nonstationary features. We estimate a variance function from a single process observation where the errors are nonstationary and correlated. We propose a difference-based approach for a one-dimensional…
We present a novel extension of multi-output Gaussian processes for handling heterogeneous outputs. We assume that each output has its own likelihood function and use a vector-valued Gaussian process prior to jointly model the parameters in…
We apply Bayesian statistics to the estimation of correlation functions. We give the probability distributions of auto- and cross-correlations as functions of the data. Our procedure uses the measured data optimally and informs about the…
We apply symbolic method to deduce functional equation which generating function of counting sequence of dependency trees must satisfy. Then we use Lagrange inversion theorem to obtain concrete expression of the counting sequence. We apply…
We compute the generating function of random planar quadrangulations with three marked vertices at prescribed pairwise distances. In the scaling limit of large quadrangulations, this discrete three-point function converges to a simple…
Stationary points embedded in the derivatives are often critical for a model to be interpretable and may be considered as key features of interest in many applications. We propose a semiparametric Bayesian model to efficiently infer the…
Sequences are often conveniently encoded in the form of a generating function depending on a formal variable. This note presents two observations that allow one to draw conclusions about the generated sequence from the generating function.…
The study of the singularities and zeros of the generating functions of multiplicity distributions is advocated. Some hints from well known probability distributions and experimental data are given. The statistical mechanics analogies…
We present a probabilistic generative model for inferring a description of coordinated, recursively structured group activities at multiple levels of temporal granularity based on observations of individuals' trajectories. The model…
We propose a formalism to analyze discrete stochastic processes with finite-state-level N. By using an (N+1)-dimensional representation of su(2) Lie algebra, we re-express the master equation to a time-evolution equation for the state…
Seemingly unrelated regressions are statistical regression models based on the Gaussian distribution. They are popular in econometrics but also arise in graphical modeling of multivariate dependencies. In maximum likelihood estimation, the…
In this work we present a model for computation of random processes in digital computers which solves the problem of periodic sequences and hidden errors produced by correlations. We show that systems with non-invertible non-linearities can…
The limit Gaussian distribution of multivariate weighted functionals of nonlinear transformations of Gaussian stationary processes, having multiple singular spectra, is derived, under very general conditions on the weight function. This…
The paper deals with a certain class of random evolutions. We develop a construction that yields an invariant measure for a continuous-time Markov process with random transitions. The approach is based on a particular way of constructing…