IDEAS home Printed from https://ideas.repec.org/a/bpj/sagmbi/v11y2012i4n14.html
   My bibliography  Save this article

Hessian Calculation for Phylogenetic Likelihood based on the Pruning Algorithm and its Applications

Author

Listed:
  • Kenney Toby

    (Dalhousie University)

  • Gu Hong

    (Dalhousie University)

Abstract

We analytically derive the first and second derivatives of the likelihood in maximum likelihood methods for phylogeny. These results enable the Newton-Raphson method to be used for maximising likelihood, which is important because there is a need for faster methods for optimisation of parameters in maximum likelihood methods. Furthermore, the calculation of the Hessian matrix also opens up possibilities for standard likelihood theory to be applied, for inference in phylogeny and for model selection problems. Another application of the Hessian matrix is local influence analysis, which can be used for detecting a number of biologically interesting phenomena. The pruning algorithm has been used to speed up computation of likelihoods for a tree. We explain how it can be used to speed up the computation for the first and second derivatives of the likelihood with respect to branch lengths and other parameters. The results in this paper apply not only to bifurcating trees, but also to general multifurcating trees. We demonstrate the use of our Hessian calculation for the three applications listed above, and compare with existing methods for those applications.

Suggested Citation

  • Kenney Toby & Gu Hong, 2012. "Hessian Calculation for Phylogenetic Likelihood based on the Pruning Algorithm and its Applications," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 11(4), pages 1-46, September.
    • Handle: RePEc:bpj:sagmbi:v:11:y:2012:i:4:n:14
    DOI: 10.1515/1544-6115.1779
    as

    Download full text from publisher

    File URL: https://doi.org/10.1515/1544-6115.1779
    Download Restriction: For access to full text, subscription to the journal or payment for the individual article is required.
    File URL: https://libkey.io/10.1515/1544-6115.1779?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Porter,Jack, 2002. "Efficiency of Covariance Matrix Estimators for Maximum Likelihood Estimation," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 431-440, July.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ivan Fernandez-Val, 2005. "Estimation of Structural Parameters and Marginal Effects in Binary Choice Panel Data Models with Fixed Effects," Boston University - Department of Economics - Working Papers Series WP2005-38, Boston University - Department of Economics.
    2. Fernández-Val, Iván & Vella, Francis, 2011. "Bias corrections for two-step fixed effects panel data estimators," Journal of Econometrics, Elsevier, vol. 163(2), pages 144-162, August.
    3. Fernández-Val, Iván, 2009. "Fixed effects estimation of structural parameters and marginal effects in panel probit models," Journal of Econometrics, Elsevier, vol. 150(1), pages 71-85, May.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bpj:sagmbi:v:11:y:2012:i:4:n:14. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Peter Golla (email available below). General contact details of provider: https://www.degruyter.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.