Step1: For each given gene g, fit all possible RIM (FEM) models that include at most two (0,1,or 2) clinical variables. In each model, calculate the p-values associated with the disease effect using likelihood ratio test (LRT) under the null hypothesis Ho:βg0 = 0 . Step2: Select the resulting RIM_minP (FEM_minP) model that has the smallest p-value among all models. Denote by the resulting minim...

The introduction of shape parameters into the statistical literature opened new areas of research and allowed statisticians to use models that produced better fits to experimental data. The Weibull and gamma families are prime examples wherein shape parameters produce more reliable statistical models than standard exponential models in lifetime studies. In the presence of many gamma-populations...

We implement an isolation with migration model for three species, with migration occurring between two closely related species while an out-group species is used to provide further information concerning gene trees and model parameters. The model is implemented in the likelihood framework for analyzing multilocus genomic sequence alignments, with one sequence sampled from each of the three spec...

For signalling alarms sooner when the dispersion of a multivariate process is “increased”, a multivariate control chart for Phase II process monitoring is proposed as a supplementary tool to the usual monitoring schemes designed for detecting general changes in the covariance matrix. The proposed chart is constructed based on the one-sided likelihood ratio test (LRT) for testing the hypothesis ...

Rare variant association studies are at a critical inflexion point with the increasing availability of exome-sequencing data. A popular test of association is the sequence kernel association test (SKAT). Weights are embedded within SKAT to reflect the hypothesized contribution of the variants to the trait variance. Correct weighting is expected to boost power, and yet the correct weights are ge...

For i = 1, ... ,p, let Xi!, ... ,Xini denote independent random samples from normal populations. The ith population has unknown mean Jli and unknown variance a;. We consider the sign testing problem of testing Ho : Jli :::; ai, for some i = 1, ... ,p, versus HI : Jli > ai, for all i = 1, ... ,p, where al,." ,ap are fixed constants. Here, HI might represent p different standards that a product m...

1 Likelihood Ratio Test Let X1, ..., Xn be a random sample from a distribution with pdf f(x|θ) where θ is some one dimensional (unknown) parameter. Suppose we want to test the null hypothesis, H0, that θ = θ0 against the alternative hypothesis, Ha, that θ = θ0. Assume the same regularity conditions hold as in the MLE theory. Then likelihood ratio test (LRT) statistic is λ(x) = L(θ0|x) L(θ̂ML|x) ...

The authors consider hidden Markov models (HMMs) with finite-valued latent process and statedependent distributions from a general one-parameter family. A test for m = 2 against m ≥ 3 states of the underlying Markov chain is proposed. So far, no satisfactory methods for this problem are available. The proposed test is an extension to HMMs of the modified likelihood ratio test (LRT) for two-stat...

We present a framework for the analysis of frame synchronization based on Synchronization Words (SWs), where the detection is based on the common sequential algorithm: the received samples are observed over a window of length equal to the SW; over this window a metric (e.g. correlation) is computed; a SW is declared if the computed metric is greater than a proper threshold, otherwise the observ...

Detection of stationary targets in urban sensing and through-the-wall radar images using likelihood ratio test (LRT) detectors has recently been considered in the literature. A shortcoming of the LRT detectors is that appropriate probability density functions of target and clutter images need to be predefined. In most practical scenarios, this information is not available a priori, and the mism...