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We first review existing sequential methods for estimating a binomial proportion. Afterward, we propose a new family of group sequential sampling schemes for estimating a binomial proportion with prescribed margin of error and confidence…
Parametric unfolding of a true distribution distorted due to finite resolution and limited efficiency for the registration of individual events is discussed. Details of the computational algorithm of the unfolding procedure are presented.
A method is described, which computes from an observed sample of events upper limits for production rates of particles, or, in case of appearance of a signal, the probability for an upwards fluctuation of the background. For any candidate,…
Symmetry is a cornerstone of much of mathematics, and many probability distributions possess symmetries characterized by their invariance to a collection of group actions. Thus, many mathematical and statistical methods rely on such…
We consider the problem of parametric statistical inference when likelihood computations are prohibitively expensive but sampling from the model is possible. Several so-called likelihood-free methods have been developed to perform inference…
In this article we provide initial findings regarding the problem of solving likelihood equations by means of a maximum entropy approach. Unlike standard procedures that require equating at zero the score function of the maximum-likelihood…
Methods for quantifying the similarity of datasets are relevant in applications where two or more datasets, or their underlying distributions, need to be compared, ranging from two- and k-sample testing to applications in machine learning…
We commonly encounter the problem of identifying an optimally weight adjusted version of the empirical distribution of observed data, adhering to predefined constraints on the weights. Such constraints often manifest as restrictions on the…
A general Bayesian framework for model selection on random network models regarding their features is considered. The goal is to develop a principle Bayesian model selection approach to compare different fittable, not necessarily nested,…
Given a large set $U$ where each item $a\in U$ has weight $w(a)$, we want to estimate the total weight $W=\sum_{a\in U} w(a)$ to within factor of $1\pm\varepsilon$ with some constant probability $>1/2$. Since $n=|U|$ is large, we want to do…
The abundance of models of complex networks and the current insufficient validation standards make it difficult to judge which models are strongly supported by data and which are not. We focus here on likelihood maximization methods for…
An exact mapping is established between sequence alignment, one of the most commonly used tools of computational biology, and the asymmetric exclusion process, one of the few exactly solvable models of nonequilibrium physics. The…
Tuning parameters are parameters involved in an estimating procedure for the purpose of reducing the risk of some other estimator. Examples include the degree of penalization in penalized regression and likelihood problems, as well as the…
In studies of exoplanet atmospheres using transmission spectroscopy, Bayesian retrievals are the most popular form of analysis. In these procedures it is common to adopt a Gaussian likelihood. However, this implicitly assumes that the upper…
Several methods are available in the literature to stochastically compare random variables and random vectors. We introduce the notion of asymptotic stochastic order for random processes and define four such orders. Various properties and…
For high volume data streams and large data warehouses, sampling is used for efficient approximate answers to aggregate queries over selected subsets. Mathematically, we are dealing with a set of weighted items and want to support queries…
We are living in the big data era, as current technologies and networks allow for the easy and routine collection of data sets in different disciplines. Bayesian Statistics offers a flexible modeling approach which is attractive for…
Expectation Maximization (EM) is among the most popular algorithms for estimating parameters of statistical models. However, EM, which is an iterative algorithm based on the maximum likelihood principle, is generally only guaranteed to find…
Due to lack of scientific understanding, some mechanisms may be missing in mathematical modeling of complex phenomena in science and engineering. These mathematical models thus contain some uncertainties such as uncertain parameters. One…
We consider approximate maximum likelihood parameter estimation in nonlinear state-space models. We discuss both direct optimization of the likelihood and expectation--maximization (EM). For EM, we also give closed-form expressions for the…