Quelques aspects actuels du travail statistique sont passes en revue sous trois rubriques generales: modeles de probabilite appliquee, plans experimentaux d'investigation, et analyse statistique et interpretation des donnees. L'accent est mis sur les applications au niveau des sciences et des technologies basees sur la science, bien que des commentaires soient aussi passes au sujet des statistiques en affaires publiques. Quoique aucun detail technique ne soit donne, on discute de domaines potentiels a developper. Le choix des sujects reflete les interets personels de l'auteur.

The Current Position of Statistics: A Personal View

We assume that allele frequency data have been extracted from several large DNA pools, each containing genetic material of up to hundreds of sampled individuals. Our goal is to estimate the haplotype frequencies among the sampled individuals by combining the pooled allele frequency data with prior knowledge about the set of possible haplotypes. Such prior information can be obtained, for example, from a database such as HapMap. We present a Bayesian haplotyping method for pooled DNA based on a continuous approximation of the multinomial distribution. The proposed method is applicable when the sizes of the DNA pools and/or the number of considered loci exceed the limits of several earlier methods. In the example analyses, the proposed model clearly outperforms a deterministic greedy algorithm on real data from the HapMap database. With a small number of loci, the performance of the proposed method is similar to that of an EM-algorithm, which uses a multinormal approximation for the pooled allele frequencies, but which does not utilize prior information about the haplotypes. The method has been implemented using Matlab and the code is available upon request from the authors.

Estimating Haplotype Frequencies by Combining Data from Large DNA Pools with Database Information

We build a mathematical model for the mutation process of microsatellites during polymerase chain reaction (PCR) using the theory of branching processes. Based on the model, we develop a method to estimate the mutation rate of microsatellites per PCR cycle and the probability of expansion by maximizing a quasi-likelihood of the observed data. We show by simulations that the proposed estimation method can accurately recover the relationship between the mutation rate and number of repeat units. The theoretical basis for the proposed method is also given. We apply the method to experimental data on poly-A and poly-CA repeats.

The Mutation Process of Microsatellites During the Polymerase Chain Reaction

Microsatellite mutations during the polymerase chain reaction: mean field approximations and their applications

On tests of independence based on minimum φ -divergence estimator with constraints: An application to modeling DNA

The polymerase chain reaction (PCR) makes possible rapid generation of a very large number of copies of a specific region of DNA. This enables the typing of quantities of DNA as small as a single molecule. PCR has led to the development of laboratory experiments which provide new approaches to many classic problems in genetics, such as estimation of linkage, marker ordering and genetic disease diagnosis. We describe some of these experiments and the statistical techniques that have been used to design them and to analyze the data they produce.

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N. Arnheim

Papers

Analysis of Genetic Data from the Polymerase Chain Reaction