Appropriate Likelihood Ratio Tests and Marginal Distributions for Evolutionary Tree Models with Constraints on Parameters

Appropriate likelihood ratio tests and marginal distributions for evolutionary tree models with constraints on parameters.

We show how to make appropriate likelihood ratio tests for evolutionary tree models when parameters such as edge (internodes or branches) lengths have nonnegativity constraints. In such cases, under the null model of an edge length being zero, the marginal distribution of this parameter is proven to be a "half-normal", that is, 50% zero values and 50% the positive half of a normal distribution....

Generalized Likelihood Ratio Tests for Additive Models

Likelihood-ratio tests for hidden Markov models.

We consider hidden Markov models as a versatile class of models for weakly dependent random phenomena. The topic of the present paper is likelihood-ratio testing for hidden Markov models, and we show that, under appropriate conditions, the standard asymptotic theory of likelihood-ratio tests is valid. Such tests are crucial in the specification of multivariate Gaussian hidden Markov models, whi...

On likelihood ratio tests

Likelihood ratio tests are intuitively appealing. Nevertheless, a number of examples are known in which they perform very poorly. The present paper discusses a large class of situations in which this is the case, and analyzes just how intuition misleads us; it also presents an alternative approach which in these situations is optimal. 1. The popularity of likelihood ratio tests Faced with a new...

Likelihood ratio tests for comparing several gamma distributions

Likelihood ratio tests (LRTs) for comparing several independent gamma distributions with respect to shape parameters, scale parameters, and means are derived. The LRT for testing homogeneity of several gamma distributions is also derived. Extensive simulation studies indicate that the null distributions of the LRT statistics for all four problems depend on the parameters only weakly, and for pr...