Nearest Neighbor Classification Rule for Mixtures of Discrete and Continuous Random Variables

In this paper very simple nonparametric classification rule for mixtures of discrete and continuous random variables is described. It is based on the method of nearest neighbor proposed by Cover and Hart (1967). The bounds on the limit of the nearest neighbor rule risks are given. Both lower and upper bound depend on the Bayes risk and the loss function. Finally the method is compared with other existing methods on some practical data set.     

Progeny testing for recessive genes: procedures and interpretations

Summary Methods for calculating the probability of detecting a carrier of a recessive gene by utilizing matings among related individuals are presented for single and litter bearing species. The confidence level for detection of heterozygosity depends upon: (1) the genetic relationship between mates, (2) the number of mates per male and the number of offspring per mate, (3) whether an estimate of recessive gene frequency before selection is available and (4) the magnitude of that frequency. Methods of computing probability of heterozygosity vs homozygosity utilizing Bayes theorem also are presented. In the conventional progeny test method, a sire initially is assumed heterozygous before calculations are made, but no prior information concerning his probable genotype is utilized. In the method using Bayes theorem, prior sources of information from relatives or from estimates of population allele frequency are utilized. This method gives the exact probability that a sire is not a carrier, given prior information and that he produces all normal offspring. These methods could be used in any sexually reproducing species to identify not only detrimental genes but beneficial genes as well.     

Finding the maximum a posteriori probability (MAP) in a Bayesian taxonomic key is NP-hard

As an alternative to dichotomous keys, tabular keys are used for taxonomic identification. With the use of computers, keys based on the Bayes formula can also be made available more widely. For the development of a key, the maximum a posterior probability (MAP) for a taxon is important because it allows to evaluate the quality of a key. If it is low, the taxon is hard to distinguish from other taxa. In this paper, we show that finding MAP in a Bayesian key is NP-hard. Estimates for MAP or other measures have to be used for the estimation of the quality of a Bayesian key.     

Semiparametric estimation of the transformation model by leveraging external aggregate data in the presence of population heterogeneity

Leveraging information in aggregate data from external sources to improve estimation efficiency and prediction accuracy with smaller scale studies has drawn a great deal of attention in recent years. Yet, conventional methods often either ignore uncertainty in the external information or fail to account for the heterogeneity between internal and external studies. This article proposes an empirical likelihood-based framework to improve the estimation of the semiparametric transformation models by incorporating information about the t-year subgroup survival probability from external sources. The proposed estimation procedure incorporates an additional likelihood component to account for uncertainty in the external information and employs a density ratio model to characterize population heterogeneity. We establish the consistency and asymptotic normality of the proposed estimator and show that it is more efficient than the conventional pseudopartial likelihood estimator without combining information. Simulation studies show that the proposed estimator yields little bias and outperforms the conventional approach even in the presence of information uncertainty and heterogeneity. The proposed methodologies are illustrated with an analysis of a pancreatic cancer study.     

Marginal proportional hazards models for clustered interval-censored data with time-dependent covariates

The Botswana Combination Prevention Project was a cluster-randomized HIV prevention trial whose follow-up period coincided with Botswana's national adoption of a universal test and treat strategy for HIV management. Of interest is whether, and to what extent, this change in policy modified the preventative effects of the study intervention. To address such questions, we adopt a stratified proportional hazards model for clustered interval-censored data with time-dependent covariates and develop a composite expectation maximization algorithm that facilitates estimation of model parameters without placing parametric assumptions on either the baseline hazard functions or the within-cluster dependence structure. We show that the resulting estimators for the regression parameters are consistent and asymptotically normal. We also propose and provide theoretical justification for the use of the profile composite likelihood function to construct a robust sandwich estimator for the variance. We characterize the finite-sample performance and robustness of these estimators through extensive simulation studies. Finally, we conclude by applying this stratified proportional hazards model to a re-analysis of the Botswana Combination Prevention Project, with the national adoption of a universal test and treat strategy now modeled as a time-dependent covariate.     

Integrating sample similarities into latent class analysis: a tree-structured shrinkage approach

This paper is concerned with using multivariate binary observations to estimate the probabilities of unobserved classes with scientific meanings. We focus on the setting where additional information about sample similarities is available and represented by a rooted weighted tree. Every leaf in the given tree contains multiple samples. Shorter distances over the tree between the leaves indicate a priori higher similarity in class probability vectors. We propose a novel data integrative extension to classical latent class models with tree-structured shrinkage. The proposed approach enables (1) borrowing of information across leaves, (2) estimating data-driven leaf groups with distinct vectors of class probabilities, and (3) individual-level probabilistic class assignment given the observed multivariate binary measurements. We derive and implement a scalable posterior inference algorithm in a variational Bayes framework. Extensive simulations show more accurate estimation of class probabilities than alternatives that suboptimally use the additional sample similarity information. A zoonotic infectious disease application is used to illustrate the proposed approach. The paper concludes by a brief discussion on model limitations and extensions.