Rates of molecular evolution vary over time and, hence, among lineages. In contrast, widely used methods for estimating divergence times from molecular sequence data assume constancy of rates. Therefore, methods for estimation of divergence times that incorporate rate variation are attractive. Improvements on a previously proposed Bayesian technique for divergence time estimation are described....

Density ratio estimation has gathered a great deal of attention recently since it can be used for various data processing tasks. In this paper, we consider three methods of density ratio estimation: (A) the numerator and denominator densities are separately estimated and then the ratio of the estimated densities is computed, (B) a logistic regression classifier discriminating denominator sample...

Set-membership algorithms, including the conventional optimal bounding ellipsoid (OBE) algorithm, require a priori knowledge of exact error bounds which is unknown in most applications. Conservative (over-estimated) error bounds used in practice lead to inconsistent parameter estimation. The novel OBE algorithm with automatic bound estimation (OBE-ABE) is shown to be consistently convergent wit...

Bayesian inference of species divergence times is an unusual statistical problem, because the divergence time parameters are not identifiable unless both fossil calibrations and sequence data are available. Commonly used marginal priors on divergence times derived from fossil calibrations may conflict with node order on the phylogenetic tree causing a change in the prior on divergence times for...

Variable selection via penalized estimation is appealing for dimension reduction. For penalized linear regression, Efron, et al. (2004) introduced the LARS algorithm. Recently, the coordinate descent (CD) algorithm was developed by Friedman, et al. (2007) for penalized linear regression and penalized logistic regression and was shown to gain computational superiority. This paper explores...

Estimating branch lengths in proportion to time is confounded by the fact that the rate of evolution and time are intrinsically linked when inferring genetic differences between species. A model of lineage-specific substitution rate variation must be applied to tease apart rate and time. When applied in methods for divergence time estimation, the resulting trees have branch lengths that are pro...