arXiv subjects

Benjamin Yakir

Publications and source records attributed to Benjamin Yakir.

4 recordsLinked to original sources

arXiv2014

Scanning a Poisson Random Field for Local Signals

The detection of local genomic signals using high-throughput DNA sequencing data can be cast as a problem of scanning a Poisson random field for local changes in the rate of the process. We propose a likelihood-based framework for for such scans, and derive formulas for false positive rate control and power calculations. The framework can also accommodate mixtures of Poisson processes to deal with over-dispersion. As a specific, detailed example, we consider the detection of insertions and deletions by paired-end DNA-sequencing. We propose several statistics for this problem, compare their power under current experimental designs, and illustrate their application on an Illumina Platinum Genomes data set.

stat.AP↗

arXiv2011

Detecting simultaneous variant intervals in aligned sequences

Given a set of aligned sequences of independent noisy observations, we are concerned with detecting intervals where the mean values of the observations change simultaneously in a subset of the sequences. The intervals of changed means are typically short relative to the length of the sequences, the subset where the change occurs, the "carriers," can be relatively small, and the sizes of the changes can vary from one sequence to another. This problem is motivated by the scientific problem of detecting inherited copy number variants in aligned DNA samples. We suggest a statistic based on the assumption that for any given interval of changed means there is a given fraction of samples that carry the change. We derive an analytic approximation for the false positive error probability of a scan, which is shown by simulations to be reasonably accurate. We show that the new method usually improves on methods that analyze a single sample at a time and on our earlier multi-sample method, which is most efficient when the carriers form a large fraction of the set of sequences. The proposed procedure is also shown to be robust with respect to the assumed fraction of carriers of the changes.

stat.AP↗

arXiv2008

The distribution of maxima of approximately Gaussian random fields

Motivated by the problem of testing for the existence of a signal of known parametric structure and unknown ``location'' (as explained below) against a noisy background, we obtain for the maximum of a centered, smooth random field an approximation for the tail of the distribution. For the motivating class of problems this gives approximately the significance level of the maximum score test. The method is based on an application of a likelihood-ratio-identity followed by approximations of local fields. Numerical examples illustrate the accuracy of the approximations.

math.ST↗

arXiv2004

An Urn Model of Diaconis

An urn model of Diaconis and some generalizations are discussed. A convergence theorem is proved that implies for Diaconis' model that the empirical distribution of balls in the urn converges with probability one to the uniform distribution.

math.PR↗