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.     

On Testing Equality of Means of Correlated Variates with Incomplete Data

A statistic is proposed for testing the hypothesis of equality of the means of a bivariate normal distribution with unknown common variance and correlation coefficient when observations are missing on one of the variates. Expressions for the second and fourth central moments of the statistic are obtained. These moments are used to approximate the distribution of the statistic by a Student's t distribution under the null hypothesis. The powers of the test are computed and compared with those of the conventional paired t and the other known statistics.     

On Comparing Correlated Means in the Presence of Incomplete Data

Two statistics are proposed for testing the hypothesis of equality of the means of a bivariate normal distribution with unknown common variance and correlation coefficient when observations are missing on both variates. One of the statistics reduces to the one proposed by Bhoj (1978, 1984) when the unpaired observations on the variates are equal. The distributions of the statistics are approximated by well known distributions under the null hypothesis. The empirical powers of the tests are computed and compared with those of some known statistics. The comparison supports the use of one of the statistics proposed in this paper.     

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.