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If the distribution P is considered random and distributed according to , as it is in Bayesian inference, then the posterior distribution is the conditional distribution of P given the observations. The prior is, of course, a measure on some σ-field on and we must assume that the expressions in the display are well defined. In particular, we assume that the… (More)

A Dirichlet mixture of normal densities is a useful choice for a prior distribution on densities in the problem of Bayesian density estimation. In the recent years, efficient Markov chain Monte Carlo method for the computation of the posterior distribution has been developed. The method has been applied to data arising from different fields of interest. The… (More)

- Malgorzata Bogdan, Jayanta K Ghosh, R W Doerge
- Genetics
- 2004

The problem of locating multiple interacting quantitative trait loci (QTL) can be addressed as a multiple regression problem, with marker genotypes being the regressor variables. An important and difficult part in fitting such a regression model is the estimation of the QTL number and respective interactions. Among the many model selection criteria that can… (More)

We review definitions and properties of reproducing kernel Hilbert spaces attached to Gaussian variables and processes, with a view to applications in nonparametric Bayesian statistics using Gaussian priors. The rate of contraction of posterior distributions based on Gaussian priors can be described through a concentration function that is expressed in the… (More)

We prove that the maximum of the sample importance weights in a high-dimensional Gaussian particle filter converges to unity unless the ensemble size grows exponentially in the system dimension. Our work is motivated by and parallels the derivations of Bengtsson, Bickel and Li (2007); however, we weaken their assumptions on the eigenvalues of the covariance… (More)

The antimicrobial activity of various naturally occurring microbicidal peptides was reported to result from their interaction with microbial membrane. In this study, we investigated the cytotoxicity of the hemolytic peptide dermaseptin S4 (DS4) and the nonhemolytic peptide dermaseptin S3 (DS3) toward human erythrocytes infected by the malaria parasite… (More)

The classical distribution theory of the log likelihood ratio test statistic does not hold for testing homogeneity (i.e., no mixture) against mixture alternatives. Asymptotic theory for this problem is developed. For some special cases, asymptotically locally minimax tests are also found. It is pointed out that the main problem is lack of identifiability of… (More)

In this article we investigate consistency of selection in regression models via the popular Lasso method. Here we depart from the traditional linear regression assumption and consider approximations of the regression function f with elements of a given dictionary of M functions. The target for consistency is the index set of those functions from this… (More)

In recent years, the literature in the area of Bayesian asymptotics has been rapidly growing. It is increasingly important to understand the concept of posterior consistency and validate specific Bayesian methods, in terms of consistency of posterior distributions. In this paper, we build up some conceptual issues in consistency of posterior distributions,… (More)

Mixture models have received considerable attention recently and Newton [Sankhyā Ser. A 64 (2002) 306–322] proposed a fast recursive algorithm for estimating a mixing distribution. We prove almost sure consistency of this recursive estimate in the weak topology under mild conditions on the family of densities being mixed. This recursive estimate depends on… (More)