MOTIVATION: Multi-strain infection is a common yet under-investigated phenomenon of many pathogens. Currently, biologists analyzing SNP information sometimes have to discard mixed infection samples as many downstream analyses require monogenomic inputs. Such a protocol impedes our understanding of the underlying genetic diversity, co-infection patterns, and genomic relatedness of pathogens. A scalable tool to learn and resolve the SNP-haplotypes from polygenomic data is an urgent need in molecular epidemiology. RESULTS: We develop a slice sampling Markov Chain Monte Carlo algorithm, named SNP-Slice, to learn not only the SNP-haplotypes of all strains in the populations but also which strains infect which hosts. Our method reconstructs SNP-haplotypes and individual heterozygosities accurately without reference panels and outperforms the state-of-the-art methods at estimating the multiplicity of infections and allele frequencies. Thus, SNP-Slice introduces a novel approach to address polygenomic data and opens a new avenue for resolving complex infection patterns in molecular surveillance. We illustrate the performance of SNP-Slice on empirical malaria and HIV datasets and provide recommendations for using our method on empirical datasets. AVAILABILITY AND IMPLEMENTATION: The implementation of the SNP-Slice algorithm, as well as scripts to analyze SNP-Slice outputs, are available at https://github.com/nianqiaoju/snp-slice.

Differentially private mechanisms protect privacy by introducing additional randomness into the data. Restricting access to only the privatized data makes it challenging to perform valid statistical inference on parameters underlying the confidential data. Specifically, the likelihood function of the privatized data requires integrating over the large space of confidential databases and is typically intractable. For Bayesian analysis, this results in a posterior distribution that is doubly intractable, rendering traditional MCMC techniques inapplicable. We propose an MCMC framework to perform Bayesian inference from the privatized data, which is applicable to a wide range of statistical models and privacy mechanisms. Our MCMC algorithm augments the model parameters with the unobserved confidential data, and alternately updates each one. For the potentially challenging step of updating the confidential data, we propose a generic approach that exploits the privacy guarantee of the mechanism to ensure efficiency. We give results on the computational complexity, acceptance rate, and mixing properties of our MCMC. We illustrate the efficacy and applicability of our methods on a naïve-Bayes log-linear model and on a linear regression model.

Online A/B tests play an instrumental role for Internet companies to improve products and technologies in a data-driven manner. An online A/B test, in its most straightforward form, can be treated as a static hypothesis test where traditional statistical tools such as p-values and power analysis might be applied to help decision makers determine which variant performs better. However, a static A/B test presents both time cost and the opportunity cost for rapid product iterations. For time cost, a fast-paced product evolution pushes its shareholders to consistently monitor results from online A/B experiments, which usually invites peeking and altering experimental designs as data collected. It is recognized that this flexibility might harm statistical guarantees if not introduced in the right way, especially when online tests are considered as static hypothesis tests. For opportunity cost, a static test usually entails a static allocation of users into different variants, which prevents an immediate roll-out of the better version to larger audience or risks of alienating users who may suffer from a bad experience. While some works try to tackle these challenges, no prior method focuses on a holistic solution to both issues. In this paper, we propose a unified framework utilizing sequential analysis and multi-armed bandit to address time cost and the opportunity cost of static online tests simultaneously. In particular, we present an imputed sequential Girshick test that accommodates online data and dynamic allocation of data. The unobserved potential outcomes are treated as missing data and are imputed using empirical averages. Focusing on the binomial model, we demonstrate that the proposed imputed Girshick test achieves Type-I error and power control with both a fixed allocation ratio and an adaptive allocation such as Thompson Sampling through extensive experiments. In addition, we also run experiments on historical Etsy.com A/B tests to show the reduction in opportunity cost when using the proposed method.