Several phylogenetic approaches have been developed to estimate species trees from collections of gene trees. However, maximum likelihood approaches for estimating species trees under the coalescent model are limited. Although the likelihood of a species tree under the multispecies coalescent model has already been derived by Rannala and Yang, it can be shown that the maximum likelihood estimate (MLE) of the species tree (topology, branch lengths, and population sizes) from gene trees under this formula does not exist. In this paper, we develop a pseudo-likelihood function of the species tree to obtain maximum pseudo-likelihood estimates (MPE) of species trees, with branch lengths of the species tree in coalescent units.

The estimation of species trees (phylogenies) is one of the most important problems in evolutionary biology, and recently, there has been greater appreciation of the need to estimate species trees directly rather than using gene trees as a surrogate. A Bayesian method constructed under the multispecies coalescent model can consistently estimate species trees but involves intensive computation, which can hinder its application to the phylogenetic analysis of large-scale genomic data. Many summary statistics–based approaches, such as shallowest coalescences (SC) and Global LAteSt Split (GLASS), have been developed to infer species phylogenies for multilocus data sets. In this paper, we propose 2 methods, species tree estimation using average ranks of coalescences (STAR) and species tree estimation using average coalescence times (STEAC), based on the summary statistics of coalescence times. It can be shown that the 2 methods are statistically consistent under the multispecies coalescent model. STAR uses the ranks of coalescences and is thus resistant to variable substitution rates along the branches in gene trees. A simulation study suggests that STAR consistently outperforms STEAC, SC, and GLASS when the substitution rates among lineages are highly variable. Two real genomic data sets were analyzed by the 2 methods and produced species trees that are consistent with previous results.

Iterative multiple imputation is a popular technique for missing data analysis. It updates the parameter estimators iteratively using multiple imputation method. This technique is convenient and flexible. However, the parameter estimators do not converge point-wise and are not efficient for finite imputation size m. In this paper, we propose a regression multiple imputation method. It uses the parameter estimators obtained from multiple imputation method to estimate the parameter estimators based on expectation maximization algorithm. We show that the resulting estimators are asymptotically efficient and converge point-wise for small m values, when the iteration k of the iterative multiple imputation goes to infinity. We evaluate the performance of the new proposed methods through simulation studies. A real data analysis is also conducted to illustrate the new method.

A birth and death process is frequently used for modeling the size of a gene family that may vary along the branches of a phylogenetic tree. Under the birth and death model, maximum likelihood methods have been developed to estimate the birth and death rate and the sizes of ancient gene families (numbers of gene copies at the internodes of the phylogenetic tree). This paper aims to provide a Bayesian approach for estimating parameters in the birth and death model.

Measurement error is pervasive in statistics due to the non-availability of authentic data. The reasons for measurement error mainly relate to cost, convenience, and human error. Measurement error can result in non-negligible bias due to attenuated estimates, reduced power of statistical tests, and lower coverage probabilities of the coefficient estimators in a regression model. Several methods have been proposed to correct for measurement error, all of which can be grouped into two broad categories based on the underlying model—functional and structural. Functional models provide flexibility and robustness to estimators by placing minimal or no assumptions on the distribution of the mismeasured covariate or by treating them as a fixed entity, as opposed to a structural model which treats the underlying mismeasured covariates as random with a specified structure. The simulation extrapolation method is one method that is used for the partial correction of measurement error in both structural and functional models. Reviews of measurement error correction techniques are available in the literature. However, none of the previously conducted reviews has exclusively focused on simulation extrapolation and its application in continuous measurement error models, despite its widespread use and ease of application. We attempt to close this gap in the literature by highlighting its development over the past two and a half decades.