A martingale approach to scan statistics

Translocation detection from Hi-C data via scan statistics

Recent Hi-C technology enables more comprehensive chromosomal conformation research, including the detection of structural variations, especially translocations. In this paper, we formulate the inter-chromosomal translocation detection as a problem of scan clustering in a spatial point process. We then develop TranScan, a new translocation detection method through scan statistics with the control of false discovery. The simulation shows that TranScan is more powerful than an existing sophisticated scan clustering method, especially under strong signal situations. Evaluation of TranScan against current translocation detection methods on realistic breakpoint simulations generated from real data suggests better discriminative power under the receiver operating characteristic curve. Power analysis also highlights TranScan's consistent outperformance when sequencing depth and heterozygosity rate is varied. Comparatively, Type I error rate is lowest when evaluated using a karyotypically normal cell line. Both the simulation and real data analysis indicate that TranScan has great potentials in inter-chromosomal translocation detection using Hi-C data. This article is protected by copyright. All rights reserved.

New maximal inequalities for N-demimartingales with scan statistic applications

In the present work, some new maximal inequalities for nonnegative N-demi(super)martingales are first developed. As an application, new bounds for the cumulative distribution function of the waiting time for the first occurrence of a scan statistic in a sequence of independent and identically distributed (i.i.d.) binary trials are obtained. A numerical study is also carried out for investigating the behavior of the new bounds.

Gambling Teams and Waiting Times for Patterns in Two-State Markov Chains

Methods using gambling teams and martingales are developed and applied to find formulae for the expected value and the generating function of the waiting time to observation of an element of a finite collection of patterns in a sequence generated by a two-state Markov chain of first, or higher, order.

Gambling Teams and Waiting Times for Patterns in Two-State Markov Chains

Methods using gambling teams and martingales are developed and applied to find formulae for the expected value and the generating function of the waiting time to observation of an element of a finite collection of patterns in a sequence generated by a two-state Markov chain of first, or higher, order.