Confidence intervals in molecular dating by maximum likelihood

Estimation of process performance index for the two-parameter exponential distribution with measurement error

Measurement errors are inevitable in practice, but they are not considered in the existing process performance index. Therefore, we propose an estimation method of process performance index for the two-parameter exponential distribution with measurement errors to fill this gap. In this paper, the relationship between the unobservable actual value and measurement value is considered as full error model, and the maximum likelihood estimation method is considered to obtain the unknown parameters. In addition, we also use the Bootstrap method to construct confidence intervals of process performance index. The performance of the proposed estimation is investigated in terms of bias, mean square error (MSE) and average interval length. Simulation results show that the proposed estimator outperforms other estimators. Finally, an example of the mileage data of the military personnel carrier is given to illustrate the implementation of the proposed estimation method.

Assessing the relative performance of fast molecular dating methods for phylogenomic data

Advances in genome sequencing techniques produced a significant growth of phylogenomic datasets. This massive amount of data represents a computational challenge for molecular dating with Bayesian approaches. Rapid molecular dating methods have been proposed over the last few decades to overcome these issues. However, a comparative evaluation of their relative performance on empirical data sets is lacking. We analyzed 23 empirical phylogenomic datasets to investigate the performance of two commonly employed fast dating methodologies: penalized likelihood (PL), implemented in treePL, and the relative rate framework (RRF), implemented in RelTime. They were compared to Bayesian analyses using the closest possible substitution models and calibration settings. We found that RRF was computationally faster and generally provided node age estimates statistically equivalent to Bayesian divergence times. PL time estimates consistently exhibited low levels of uncertainty. Overall, to approximate Bayesian approaches, RelTime is an efficient method with significantly lower computational demand, being more than 100 times faster than treePL. Thus, to alleviate the computational burden of Bayesian divergence time inference in the era of massive genomic data, molecular dating can be facilitated using the RRF, allowing evolutionary hypotheses to be tested more quickly and efficiently.