A signal detection model is presented that combines a signal model and a noise model providing mathematical descriptions of the frequency of appearance of the signals, and of the signal-like features naturally occurring in the background. We derive expressions for the likelihood functions for the whole ensemble of observed suspicious locations, in various possible combinations of signals and fa...

Recently, there have been many case-control studies proposed to test for association between haplotypes and disease, which require the Hardy-Weinberg equilibrium (HWE) assumption of haplotype frequencies. As such, haplotype inference of unphased genotypes and development of haplotype-based HWE tests are crucial prior to fine mapping. The goodness-of-fit test is a frequently-used method to test ...

Receiver operating characteristic (ROC) analysis is widely used to describe the discriminatory power of a diagnostic test to differentiate between populations having or not having a specific disease, using a dichotomous threshold. In this way, positive and negative likelihood ratios (LR+ and LR-) can be calculated to be used in Bayes' way of estimating disease probabilities. Similarly, LRs can ...

A very popular form of hypothesis test is the likelihood ratio test, which is a generalization of the optimal test for simple null and alternative hypotheses that was developed by Neyman and Pearson (We skipped Neyman-Pearson lemma because we are short of time). The likelihood ratio test is based on the likelihood function fn(X−1, · · · , Xn|θ), and the intuition that the likelihood function te...

The essential role of the likelihood function in both Bayesian and non-Bayesian inference is described. Several topics related to the extension of likelihood-based methodology to more complex settings are reviewed, including modifications to profile likelihood, composite and pseudo-likelihoods, quasi-likelihood, semiparametric and non-parametric likelihoods, and empirical likelihood .  2010 Jo...

In this paper we discuss maximum likelihood estimation when some observations are missing in mixed graphical interaction models assuming a conditional Gaussian distribution as introduced by Lauritzen & Wermuth (1989). For the saturated case ML estimation with missing values via the EM algorithm has been proposed by Little & Schluchter (1985). We expand their results to the special restrictions ...

We study the critical points of monomial functions over an algebraic subset of the probability simplex. The number of critical points on the Zariski closure is a topological invariant of that embedded projective variety, known as its maximum likelihood degree. We present an introduction to this theory and its statistical motivations. Many favorite objects from combinatorial algebraic geometry a...

Maximum-likelihood methods have now been applied to most areas of macromolecular crystallography, including data reduction, molecular replacement, experimental phasing and refinement. However, students of macromolecular crystallography are predominantly taught only traditional crystallographic methods and therefore have little understanding of the methods underlying the modern software that the...

Although research indicates deer management cooperatives (DMCs) provide the needed means to influence large-scale resource changes, has yet identify which conservation initiatives DMC members find important and would likely implement. Therefore, we performed an Importance-Likelihood Analysis ascertain their likelihood of carrying out these initiatives. Results from our survey 459 across 5 U.S. ...