Maximum Likelihood Estimation of Parameters in Linkage. Numerical Iterative Methods
Abstract
Taking into account the advantages of Maximum Likelihood Method (most precise estimation), the statistical properties of MLEs (unbiasedness, consistency, efficiency, invariance, asymptotic normality) this paper aim is to present MLE in the context of estimate the recombination fraction r in linkage analysis. Maximum Likelihood Method follows some steps: specifies the likelihood function; takes derivatives of likelihood with respect to the parameters; sets the derivatives equal to zero and finally generates a likelihood equation, that maximized provides the most precise estimation of the recombination fraction. Generally, it is solved by iterative procedures, if no, closed form solution exists for likelihood equation. In this work we discuss comparatively two iterative optimization methods useful in computing MLE of the recombination fraction: Newton-Raphson method and Fisher`s Method of Scoring. We implemented these two methods in Maple application and we illustrated them by an example: the estimation of the recombination fraction in the case of the Morgan (1909) experiment on fruit flies. The Maple code for these two methods connected with the Morgan example is given in the appendix. We can not guarantee which of the two presented methods give us an optimal maximum.
Â
Authors who publish with this journal agree to the following terms:
a) Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
b) Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
c) Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
