arXiv subjects

Barak Brill

Publications and source records attributed to Barak Brill.

3 recordsLinked to original sources

arXiv2023

Exact confidence intervals for the mixing distribution from binomial mixture distribution samples

We present methodology for constructing pointwise confidence intervals for the cumulative distribution function and the quantiles of mixing distributions on the unit interval from binomial mixture distribution samples. No assumptions are made on the shape of the mixing distribution. The confidence intervals are constructed by inverting exact tests of composite null hypotheses regarding the mixing distribution. Our method may be applied to any deconvolution approach that produces test statistics whose distribution is stochastically monotone for stochastic increase of the mixing distribution. We propose a hierarchical Bayes approach, which uses finite Polya Trees for modelling the mixing distribution, that provides stable and accurate deconvolution estimates without the need for additional tuning parameters. Our main technical result establishes the stochastic monotonicity property of the test statistics produced by the hierarchical Bayes approach. Leveraging the need for the stochastic monotonicity property, we explicitly derive the smallest asymptotic confidence intervals that may be constructed using our methodology. Raising the question whether it is possible to construct smaller confidence intervals for the mixing distribution without making parametric assumptions on its shape.

stat.ME↗

arXiv2020

Testing for differential abundance in compositional counts data, with application to microbiome studies

Identifying which taxa in our microbiota are associated with traits of interest is important for advancing science and health. However, the identification is challenging because the measured vector of taxa counts (by amplicon sequencing) is compositional, so a change in the abundance of one taxon in the microbiota induces a change in the number of sequenced counts across all taxa. The data is typically sparse, with zero counts present either due to biological variance or limited sequencing depth (technical zeros). For low abundance taxa, the chance for technical zeros is non-negligible. We show that existing methods designed to identify differential abundance for compositional data may have an inflated number of false positives due to improper handling of the zero counts. We introduce a novel non-parametric approach which provides valid inference even when the fraction of zero counts is substantial. Our approach uses a set of reference taxa that are non-differentially abundant, which can be estimated from the data or from outside information. We show the usefulness of our approach via simulations, as well as on three different data sets: a Crohn's disease study, the Human Microbiome Project, and an experiment with 'spiked-in' bacteria.

q-bio.GN↗

arXiv2015

Consistent distribution-free $K$-sample and independence tests for univariate random variables

A popular approach for testing if two univariate random variables are statistically independent consists of partitioning the sample space into bins, and evaluating a test statistic on the binned data. The partition size matters, and the optimal partition size is data dependent. While for detecting simple relationships coarse partitions may be best, for detecting complex relationships a great gain in power can be achieved by considering finer partitions. We suggest novel consistent distribution-free tests that are based on summation or maximization aggregation of scores over all partitions of a fixed size. We show that our test statistics based on summation can serve as good estimators of the mutual information. Moreover, we suggest regularized tests that aggregate over all partition sizes, and prove those are consistent too. We provide polynomial-time algorithms, which are critical for computing the suggested test statistics efficiently. We show that the power of the regularized tests is excellent compared to existing tests, and almost as powerful as the tests based on the optimal (yet unknown in practice) partition size, in simulations as well as on a real data example.

stat.ME↗