Related papers: Estimating the Missing Mass, Partition Function or…
We consider the situation where the observed sample contains some observations whose class of origin is known (that is, they are classified with respect to the g underlying classes of interest), and where the remaining observations in the…
Estimating a Gibbs density function given a sample is an important problem in computational statistics and statistical learning. Although the well established maximum likelihood method is commonly used, it requires the computation of the…
Nested error regression models are useful tools for analysis of grouped data, especially in the case of small area estimation. This paper suggests a nested error regression model using uncertain random effects in which the random effect in…
In various practical situations, we encounter data from stochastic processes which can be efficiently modelled by an appropriate parametric model for subsequent statistical analyses. Unfortunately, the most common estimation and inference…
The problem of estimating the missing mass or total probability of unseen elements in a sequence of $n$ random samples is considered under the squared error loss function. The worst-case risk of the popular Good-Turing estimator is shown to…
Suppose some random resource (energy, mass or space) $\chi \geq 0$ is to be shared at random between (possibly infinitely many) species (atoms or fragments). Assume ${\Bbb E}\chi =\theta <\infty $ and suppose the amount of the individual…
In this paper, we are concerned with obtaining distribution-free concentration inequalities for mixture of independent Bernoulli variables that incorporate a notion of variance. Missing mass is the total probability mass associated to the…
Implicit sampling is a weighted sampling method that is used in data assimilation, where one sequentially updates estimates of the state of a stochastic model based on a stream of noisy or incomplete data. Here we describe how to use…
Probabilistic graphical models have emerged as a powerful modeling tool for several real-world scenarios where one needs to reason under uncertainty. A graphical model's partition function is a central quantity of interest, and its…
Computing the marginal likelihood or evidence is one of the core challenges in Bayesian analysis. While there are many established methods for estimating this quantity, they predominantly rely on using a large number of posterior samples…
Missing data is an important challenge when dealing with high dimensional data arranged in the form of an array. In this paper, we propose methods for estimation of the parameters of array variate normal probability model from partially…
We consider a semiparametric mixture of two univariate density functions where one of them is known while the weight and the other function are unknown. Such mixtures have a history of application to the problem of detecting differentially…
This paper is devoted to the multivariate estimation of a vector of Poisson means. A novel loss function that penalises bad estimates of each of the parameters and the sum (or equivalently the mean) of the parameters is introduced. Under…
This paper considers an empirical likelihood inference for parameters defined by general estimating equations, when data are missing at random. The efficiency of existing estimators depends critically on correctly specifying the conditional…
In this paper, we propose a maximum smoothed likelihood method to estimate the component density functions of mixture models, in which the mixing proportions are known and may differ among observations. The proposed estimates maximize a…
Estimations of physical parameters using data usually involve non-uniform experimental efficiencies. In this article, a method of maximum likelihood fit is introduced using the efficiency as a weight, while the probability distribution…
This paper concerns the use of the expectation-maximisation (EM) algorithm for inference in partially observed diffusion processes. In this context, a well known problem is that all except a few diffusion processes lack closed-form…
We study the problem of estimating a distribution over a finite alphabet from an i.i.d. sample, with accuracy measured in relative entropy (Kullback-Leibler divergence). While optimal bounds on the expected risk are known, high-probability…
We consider a two-component mixture model with one known component. We develop methods for estimating the mixing proportion and the unknown distribution nonparametrically, given i.i.d.~data from the mixture model, using ideas from shape…
The marginal likelihood is a central tool for drawing Bayesian inference about the number of components in mixture models. It is often approximated since the exact form is unavailable. A bias in the approximation may be due to an incomplete…