Exactly Computing the Tail of the Poisson-Binomial Distribution

We present ShiftConvolvePoibin, a fast exact method to compute the tail of a Poisson-binomial distribution (PBD). Our method employs an exponential shift to retain its accuracy when computing a tail probability, and in practice we find that it is immune to the significant relative errors that other methods, exact or approximate, can suffer from when computing very small tail probabilities of the PBD. The accompanying R package is also competitive with the fastest implementations for computing the entire PBD.

Efficient Mining of Frequent Item Sets on Large Uncertain Databases

In applications like location-based services, sensor monitoring systems and data integration diligence the data manipulated is highly ambiguous. mining manifold itemsets from generous ambiguous database illustrated under possible world semantics is a crucial dispute. Mining manifold Itemsets is technically brave because the ambiguous database can accommodate a fractional number of possible worlds. The mining process can be formed as a Poisson binomial distribution, by noticing that an Approximated algorithm is established to ascertain manifold Itemsets from generous ambiguous database exceedingly. Preserving the mining result of scaling a database is a substantial dispute when a new dataset is inserted in an existing database. In this paper, an incremental mining algorithm is adduced to retain the mining consequence. The cost and time are reduced by renovating the mining result rather than revising the whole algorithm on the new database from the scrap. We criticize the support for incremental mining and ascertainment of manifold Itemsets. Two common ambiguity models in the mining process are Tuple and Attribute ambiguity. Our approach reinforced both the tuple and attribute uncertainty. Our accession is authorized by interpreting both real and synthetic datasets.

On moderate deviations in Poisson approximation

In this paper we first use the distribution of the number of records to demonstrate that the right tail probabilities of counts of rare events are generally better approximated by the right tail probabilities of a Poisson distribution than those of the normal distribution. We then show that the moderate deviations in Poisson approximation generally require an adjustment and, with suitable adjustment, we establish better error estimates of the moderate deviations in Poisson approximation than those in [18]. Our estimates contain no unspecified constants and are easy to apply. We illustrate the use of the theorems via six applications: Poisson-binomial distribution, the matching problem, the occupancy problem, the birthday problem, random graphs, and 2-runs. The paper complements the works [16], [8], and [18].

A new and intuitive test for zero modification

While there do exist several statistical tests for detecting zero modification in count data regression models, these rely on asymptotical results and do not transparently distinguish between zero inflation and zero deflation. In this manuscript, a novel non-asymptotic test is introduced which makes direct use of the fact that the distribution of the number of zeros under the null hypothesis of no zero modification can be described by a Poisson-binomial distribution. The computation of critical values from this distribution requires estimation of the mean parameter under the null hypothesis, for which a hybrid estimator involving a zero-truncated mean estimator is proposed. Power and nominal level attainment rates of the new test are studied, which turn out to be very competitive to those of the likelihood ratio test. Illustrative data examples are provided.

DiffTAD: Detecting Differential contact frequency in Topologically Associating Domains Hi-C experiments between conditions

MotivationIn recent years, the interest in analyzing chromosome conformation by Hi-C and related techniques has grown. It has been shown that contact frequency matrices obtained by these methods correlate with other methods of measurement of activity such as transcriptomics and histone modification assays. This brings a question of testing for differential contact frequency between experiments to the field.ResultsIn this work, we provide a freely available software that implements two statistical methods for testing the significance of differential contact frequency in topological domains between two experiments. One method follows an empirical, permutation based approach to computing p-values, while the other is a parametric test based on the Poisson-Binomial distribution.AvailabilityThe software is freely available on the GNU General Public License at https://bitbucket.org/rzaborowski/differential-analysisContact[r.zaborowski|bartek]@mimuw.edu.plSupplementary informationSupplementary data are available at Bioinformatics online.