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Related Concept Videos

Harmonic Mean01:09

Harmonic Mean

The arithmetic mean is usually skewed towards the larger values in the data set. Therefore, to avoid this inherent bias towards smaller values, the harmonic mean is used.
Take the example of the speed of a car, which is the measure of the rate of distance traveled. If the vehicle traverses the same distance back-and-forth, its average speed equals the total distance traveled divided by the total time taken. However, if the car moves with varying speeds, then the arithmetic mean is more skewed...
Microbial Phylogeny01:28

Microbial Phylogeny

Understanding the evolutionary relationships among microorganisms is fundamental to microbial ecology and taxonomy. Phylogenetic trees are essential tools for inferring these relationships, relying primarily on comparative analyses of molecular sequences such as DNA, RNA, or proteins. In microbial studies, these trees typically depict the evolutionary paths of diverse bacterial and archaeal species by mapping genetic differences accumulated over time.Phylogenetic trees are composed of tips,...
Evolutionary Relationships through Genome Comparisons02:54

Evolutionary Relationships through Genome Comparisons

Genome comparison is one of the excellent ways to interpret the evolutionary relationships between organisms. The basic principle of genome comparison is that if two species share a common feature, it is likely encoded by the DNA sequence conserved between both species. The advent of genome sequencing technologies in the late 20th century enabled scientists to understand the concept of conservation of domains between species and helped them to deduce evolutionary relationships across diverse...
Phylogenetic Trees03:21

Phylogenetic Trees

Phylogenetic trees come in many forms. It matters in which sequence the organisms are arranged from the bottom to the top of the tree, but the branches can rotate at their nodes without altering the information. The lines connecting individual nodes can be straight, angled, or even curved.
Phylogenetic Trees03:21

Phylogenetic Trees

Phylogenetic trees come in many forms. It matters in which sequence the organisms are arranged from the bottom to the top of the tree, but the branches can rotate at their nodes without altering the information. The lines connecting individual nodes can be straight, angled, or even curved.
Trimmed Mean01:10

Trimmed Mean

While measuring the mean of a data set, care needs to be taken when associating the mean to its central tendency. The same goes for the arithmetic mean, the geometric mean, or the harmonic mean. This is because the presence of a single outlier data value can significantly affect the mean. That is, the mean is sensitive to fluctuations in the data set.
Although certain measures of central tendency are not sensitive to outliers, there are alternative versions of the mean that get around the...

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Updated: May 24, 2026

A Practical Guide to Phylogenetics for Nonexperts
12:00

A Practical Guide to Phylogenetics for Nonexperts

Published on: February 5, 2014

Improved harmonic mean estimator for phylogenetic model evidence.

Serena Arima1, Luca Tardella

  • 1Dipartimento di Metodi e Modelli per l'Economia, il Territorio e la Finanza, Sapienza Università di Roma, Rome, Italy. serena.arima@uniroma1.it

Journal of Computational Biology : a Journal of Computational Molecular Cell Biology
|March 15, 2012
PubMed
Summary

Bayesian model selection in phylogenetics is improved by new harmonic mean estimators. These methods offer reliable and computationally efficient alternatives to existing techniques for estimating marginal likelihoods.

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Area of Science:

  • Molecular Systematics
  • Computational Biology
  • Statistical Phylogenetics

Background:

  • Bayesian phylogenetic methods are increasingly popular for molecular systematics.
  • Bayesian model selection relies on comparing models using Bayes factors, which require accurate marginal likelihood estimation.
  • Existing methods for marginal likelihood computation present trade-offs between implementation simplicity, computational cost, and accuracy.

Purpose of the Study:

  • To introduce and evaluate improved harmonic mean (HM) estimators for marginal likelihoods in Bayesian phylogenetics.
  • To address the known biases and potential infinite variance issues associated with the standard HM estimator.
  • To compare the performance of these novel estimators against established techniques like thermodynamic integration.

Main Methods:

  • Development of generalized harmonic mean (GHM) estimators that leverage posterior simulations from Markov Chain Monte Carlo (MCMC).
  • Focus on estimators that maintain computational simplicity while resolving the infinite variance problem.
  • Comparative analysis against thermodynamic integration variants for assessing reliability and performance.

Main Results:

  • The proposed improved harmonic mean estimators demonstrate reliability in practice.
  • These new methods overcome the infinite variance issue inherent in the basic harmonic mean estimator.
  • Comparative performance indicates these estimators are competitive with more complex methods.

Conclusions:

  • Improved harmonic mean estimators offer a practical and reliable solution for marginal likelihood estimation in Bayesian phylogenetics.
  • These methods provide a valuable alternative for researchers seeking accurate and computationally feasible model selection.
  • The findings suggest a shift towards more robust and efficient Bayesian phylogenetic analyses.