Related papers: Jeffreys priors for mixture estimation: properties…

A number of distributions that arise in statistical applications can be expressed in the form of a weighted density: the product of a base density and a nonnegative weight function. Generating variates from such a distribution may be…

In the present article, a new method for the evaluation of fractional derivatives of arbitrary real order is proposed. Numerous but inequivalent formulations have been given in the past. Some of them exhibit unsatisfactory properties such…

Given a random sample from a distribution with density function that depends on an unknown parameter $\theta$, we are interested in accurately estimating the true parametric density function at a future observation from the same…

Expected Fisher information can be found a priori and as a result its inverse is the primary variance approximation used in the design of experiments. This is in contrast to the common claim that the inverse of observed Fisher information…

We consider estimating the parameters of a Gaussian mixture density with a given number of components best representing a given set of weighted samples. We adopt a density interpretation of the samples by viewing them as a discrete Dirac…

The use of {\it Mathematica} in deriving mean likelihood estimators is discussed. Comparisons between the maximum likelihood estimator, the mean likelihood estimator and the Bayes estimate based on a Jeffrey's noninformative prior using the…

The prior distribution for the unknown model parameters plays a crucial role in the process of statistical inference based on Bayesian methods. However, specifying suitable priors is often difficult even when detailed prior knowledge is…

In this paper, we consider objective Bayesian inference of the generalized exponential distribution using the independence Jeffreys prior and validate the propriety of the posterior distribution under a family of structured priors. We…

Fitted probabilities from widely used Bayesian multinomial probit models can depend strongly on the choice of a base category, which is used to uniquely identify the parameters of the model. This paper proposes a novel identification…

In nonlinear regression models the Fisher information depends on the parameters of the model. Consequently, optimal designs maximizing some functional of the information matrix cannot be implemented directly but require some preliminary…

Consider the problem of joint parameter estimation and prediction in a Markov random field: i.e., the model parameters are estimated on the basis of an initial set of data, and then the fitted model is used to perform prediction (e.g.,…

The use of objective prior in Bayesian applications has become a common practice to analyze data without subjective information. Formal rules usually obtain these priors distributions, and the data provide the dominant information in the…

The task of mixture proportion estimation (MPE) is to estimate the weight of a component distribution in a mixture, given observations from both the component and mixture. Previous work on MPE adopts the irreducibility assumption, which…

Confidence sequences are collections of confidence regions that simultaneously cover the true parameter for every sample size at a prescribed confidence level. Tightening these sequences is of practical interest and can be achieved by…

In this note, we consider the problem of estimating multinomial cell probabilities under the entropy loss when side information in aggregated data is available. We use the Jeffreys prior to obtain Bayes estimators. It is shown that by…

We propose a flexible class of models based on scale mixture of uniform distributions to construct shrinkage priors for covariance matrix estimation. This new class of priors enjoys a number of advantages over the traditional scale mixture…

Although Bayesian inference is an immensely popular paradigm among a large segment of scientists including statisticians, most applications consider objective priors and need critical investigations (Efron, 2013, Science). While it has…

Nowadays in density estimation, posterior rates of convergence for location and location-scale mixtures of Gaussians are only known under light-tail assumptions; with better rates achieved by location mixtures. It is conjectured, but not…

In multiple importance sampling we combine samples from a finite list of proposal distributions. When those proposal distributions are used to create control variates, it is possible (Owen and Zhou, 2000) to bound the ratio of the resulting…

A mixture preorder is a preorder on a mixture space (such as a convex set) that is compatible with the mixing operation. In decision theoretic terms, it satisfies the central expected utility axiom of strong independence. We consider when a…