Related papers: Sampling Polya-Gamma random variates: alternate an…
Let $X$ and $Y$ be independent variance-gamma random variables with zero location parameter; then the exact probability density function of the ratio $X/Y$ is derived. Some basic distributional properties are also derived, including…
An algorithm for sampling exactly from the normal distribution is given. The algorithm reads some number of uniformly distributed random digits in a given base and generates an initial portion of the representation of a normal deviate in…
Survey sampling plays an important role in the efficient allocation and management of resources. The essence of survey sampling lies in acquiring a sample of data points from a population and subsequently using this sample to estimate the…
In this paper, we have developed a new class of sampling schemes for estimating parameters of binomial and Poisson distributions. Without any information of the unknown parameters, our sampling schemes rigorously guarantee prescribed levels…
We consider Bayesian inference from multiple time series described by a common state-space model (SSM) structure, but where different subsets of parameters are shared between different submodels. An important example is disease-dynamics,…
Random sampling is an essential tool in the processing and transmission of data. It is used to summarize data too large to store or manipulate and meet resource constraints on bandwidth or battery power. Estimators that are applied to the…
This paper is concerned with sampling from probability distributions $\pi$ on $\mathbb{R}^d$ admitting a density of the form $\pi(x) \propto e^{-U(x)}$, where $U(x)=F(x)+G(Kx)$ with $K$ being a linear operator and $G$ being…
The paper considers the classical Goodness of Fit test. It suggests to use the Gamma distribution for the approximation of the distribution of the Pearson statistics with unknown parameters estimated from raw data. The parameters of these…
We propose and analyze a generalized splitting method to sample approximately from a distribution conditional on the occurrence of a rare event. This has important applications in a variety of contexts in operations research, engineering,…
We provide an algorithm for properly learning mixtures of two single-dimensional Gaussians without any separability assumptions. Given $\tilde{O}(1/\varepsilon^2)$ samples from an unknown mixture, our algorithm outputs a mixture that is…
The break-by-one gamma distribution has a probability density function resembling the Schechter function, but with the small-argument behavior modified so it is normalizable in commonly arising cases where the Schechter function is not. Its…
We develop an algorithm for sampling from the unitary invariant random matrix ensembles. The algorithm is based on the representation of their eigenvalues as a determinantal point process whose kernel is given in terms of orthogonal…
We give an efficient algorithm to generate a graph from a distribution $\epsilon$-close to $G(n,p)$, in the sense of total variation distance. In particular, if $p$ is represented with $O(\log n)$-bit accuracy, then, with high probability,…
We study random string-duplication systems, which we call P\'olya string models. These are motivated by DNA storage in living organisms, and certain random mutation processes that affect their genome. Unlike previous works that study the…
We show that a distribution related to Gaussian Boson Sampling (GBS) on graphs can be sampled classically in polynomial time. Graphical applications of GBS typically sample from this distribution, and thus quantum algorithms do not provide…
We propose an approach to analyze the asymptotic behavior of P\'olya urns based on the contraction method. For this, a new combinatorial discrete time embedding of the evolution of the urn into random rooted trees is developed. A…
A new uniform asymptotic expansion for the incomplete gamma function $\Gamma(a,z)$ valid for large values of $z$ was given by the author in {\it J. Comput. Appl. Math.} {\bf 148} (2002) 323--339. This expansion contains a complementary…
Consider a graph on randomly scattered points in an arbitrary space, with two points $x,y$ connected with probability $\phi(x,y)$. Suppose the number of points is large but the mean number of isolated points is $O(1)$. We give general…
In the matter of selection of sample time points for the estimation of the power spectral density of a continuous time stationary stochastic process, irregular sampling schemes such as Poisson sampling are often preferred over regular…
A new class of dependent random measures which we call {\it compound random measures} are proposed and the use of normalized versions of these random measures as priors in Bayesian nonparametric mixture models is considered. Their…