Journal of Statistical Sciences

A Bidirectional Hidden Markov Model in Linear Memory

Hamid Pezeshk

Hidden Markov models are widely used in Bioinformatics. They are applied to protein sequence alignment, protein family annotation and gene-finding.The Baum-Welch training is an expectation-maximization algorithm for training the emission and transition probabilities of hidden Markov models. For very long training sequence, even the most efficient algorithms are memory-consuming. In this paper we discuss different approaches to decrease the memory use and compare the performance of different algorithms. In addition, we propose a bidirection algorithm with linear memory. We apply this algorithm to simulated data of protein profile to analyze the strength and weakness of the algorithm.

Post-Stage Search Property of the 12-run Plackett-Burman Design

Hooshang Talebi

So far, the Plackett-Burman (PB) designs have been considered as saturated non-regular fractional factorial designs for screening purposes. Since introduction of the hidden projection of PB's by Wang and Wu (1995), the estimation capability of such projections onto a subset of factors has been investigated by many researchers. In this paper, by considering the search and estimation capability of a design, we introduce the post-stage search designs, using sparsity principle of factorial effects. That is, by the post-stage property of a design, we mean the capability of such a design in searching and estimating possible nonzero 3-factorial interactions along with estimation of the general mean, main effects and active 2-factor interaction effects, identified in the pre-stage. We show that a 12-runs PB projections onto 4 and 5 factors are post-stage search designs.

Kernel Smoothing for ROC Curve and Estimation of its Area for Thyroid Stimulating Hormone

Mehdi Tazhibi

Receiver Operating Characteristic (ROC) curves are frequently used in biomedical informatics research to evaluate classification and prediction models to support decision, diagnosis, and prognosis. ROC analysis investigates the accuracy of models and ability to separate positive from negative cases. It is especially useful in evaluating predictive models and in comparing with other tests which produce output values in a continuous range. Empirical ROC curve is jagged but a true ROC curve is smooth. For this purpose kernel smoothing is used. The Area Under ROC Curve (AUC) is frequently used as a measure of the effectiveness of diagnostic markers. In this study we compare estimation of this area based on normal assumptions and kernel smoothing. This study used measurements of TSH from patients and non-patients in congenital hypothyroidism screening in Isfahan province. Using this method, TSH ROC curves from infants in Isfahan were fitted. For evaluating of accuracy of this test, AUC and its standard error calculated. Also effectiveness of the kernel methods in comparison with other methods are showed.

Normality and Exponentiality Tests Based on New Entropy Estimators

Ehsan Zamanzadeh

In this paper, we first introduce two new entropy estimators. These estimators are obtained by correcting Corea(1995)'s estimator in the extreme points and also assigning different weights to the end points.We then make a comparison among our proposed new entropy estimators and the entropy estimators proposed by Vasicek (1976), Ebrahimi, et al. (1994) and Corea(1995). We also introduce goodness of fit tests for exponentiality and normality based on our proposed entropy estimators. Results of a simulation study show that the proposed estimators and goodness of fit tests have good performances in comparison with the leading competitors.

Comparison of Different Entropy Estimators and Power of Exponentiality Tests Based on Entropy Estimators

Maliheh Abbasnejad

In this paper, we establish a goodness of fit test for exponentiality based on the estimated Renyi information. We use an estimator for Renyi distance in manner of Correa entropy estimate. Critical values of the test are computed by Monte Carlo simulation. Also we compute the power of the test under different alternatives and show that it compares favorably with the leading competitor.

Bayesian Estimation of Penalty Function in Homogeneity Test of Mixture Models

Rahman Farnoosh

The modified likelihood ratio test, which is based on penalized likelihood function, is usually used for testing homogeneity of the mixture models. The efficiency of this test is seriously affected by the shape of penalty function that is used in penalized likelihood function. The selection of penalty function is usually based on avoiding of complexity and increasing tractability, hence the results may be far from optimality. In this paper, we consider a more general form of penalty function that depends on a shape parameter. Then this shape parameter and the parameters of mixture models are estimated by using Bayesian paradigm. It is shown that the proposed Bayesian approach is more efficient in comparison to modified likelihood test. The proposed Bayesian approach is clearly more efficient, specially in nonidentifiability situation, where frequentist approaches are almost failed.