Mixed Poisson Regression Models with Varying Dispersion Arising from Non-Conjugate Mixing Distributions

In this article we present a class of mixed Poisson regression models with varying dispersion arising from non-conjugate to the Poisson mixing distributions for modelling overdispersed claim counts in non-life insurance. The proposed family of models combined with the adopted modelling framework can provide sufficient flexibility for dealing with different levels of overdispersion. For illustrative purposes, the Poisson-lognormal regression model with regression structures on both its mean and dispersion parameters is employed for modelling claim count data from a motor insurance portfolio. Maximum likelihood estimation is carried out via an expectation-maximization type algorithm, which is developed for the proposed family of models and is demonstrated to perform satisfactorily.

On a Multivariate Analog of the Zolotarev Problem

A generalized multivariate problem due to V. M. Zolotarev is considered. Some related results on geometric random sums and (multivariate) geometric stable distributions are extended to a more general case of “anisotropic” random summation where sums of independent random vectors with multivariate random index having a special multivariate geometric distribution are considered. Anisotropic-geometric stable distributions are introduced. It is demonstrated that these distributions are coordinate-wise scale mixtures of elliptically contoured stable distributions with the Marshall–Olkin mixing distributions. The corresponding “anisotropic” analogs of multivariate Laplace, Linnik and Mittag–Leffler distributions are introduced. Some relations between these distributions are presented.

MixTwice: large-scale hypothesis testing for peptide arrays by variance mixing

Summary Peptide microarrays have emerged as a powerful technology in immunoproteomics as they provide a tool to measure the abundance of different antibodies in patient serum samples. The high dimensionality and small sample size of many experiments challenge conventional statistical approaches, including those aiming to control the false discovery rate (FDR). Motivated by limitations in reproducibility and power of current methods, we advance an empirical Bayesian tool that computes local FDR statistics and local false sign rate statistics when provided with data on estimated effects and estimated standard errors from all the measured peptides. As the name suggests, the MixTwice tool involves the estimation of two mixing distributions, one on underlying effects and one on underlying variance parameters. Constrained optimization techniques provide for model fitting of mixing distributions under weak shape constraints (unimodality of the effect distribution). Numerical experiments show that MixTwice can accurately estimate generative parameters and powerfully identify non-null peptides. In a peptide array study of rheumatoid arthritis, MixTwice recovers meaningful peptide markers in one case where the signal is weak, and has strong reproducibility properties in one case where the signal is strong. Availabilityand implementation MixTwice is available as an R software package https://cran.r-project.org/web/packages/MixTwice/. Supplementary information Supplementary data are available at Bioinformatics online.

iMAP: integration of multiple single-cell datasets by adversarial paired transfer networks

The integration of single-cell RNA-sequencing datasets from multiple sources is critical for deciphering cell-to-cell heterogeneities and interactions in complex biological systems. We present a novel unsupervised batch effect removal framework, called iMAP, based on both deep autoencoders and generative adversarial networks. Compared with current methods, iMAP shows superior, robust, and scalable performance in terms of both reliably detecting the batch-specific cells and effectively mixing distributions of the batch-shared cell types. Applying iMAP to tumor microenvironment datasets from two platforms, Smart-seq2 and 10x Genomics, we find that iMAP can leverage the powers of both platforms to discover novel cell-cell interactions.

Testing the consistency of preferences in discrete choice experiments: an eye tracking study

A within-subjects experiment with eye tracking was implemented to test the consistency of preferences over three repeated choice experiments. The empirical results indicate that after changing the position of the same alternatives in the choice set, participants were consistent with their choices 69 per cent of the time. Moreover, after reverting back to the identical original positions of the alternatives but randomising the order of the choice sets, individuals’ choices were consistent 67 per cent of the time. Eye tracking data revealed that subjects’ visual attention towards the product attributes was also consistent over the sequence of choices. The robustness of these results was further demonstrated by using random parameters models with flexible mixing distributions to calculate willingness-to-pay for the product attributes and compare its consistency across choice experiments.

Grouped Normal Variance Mixtures

Grouped normal variance mixtures are a class of multivariate distributions that generalize classical normal variance mixtures such as the multivariate t distribution, by allowing different groups to have different (comonotone) mixing distributions. This allows one to better model risk factors where components within a group are of similar type, but where different groups have components of quite different type. This paper provides an encompassing body of algorithms to address the computational challenges when working with this class of distributions. In particular, the distribution function and copula are estimated efficiently using randomized quasi-Monte Carlo (RQMC) algorithms. We propose to estimate the log-density function, which is in general not available in closed form, using an adaptive RQMC scheme. This, in turn, gives rise to a likelihood-based fitting procedure to jointly estimate the parameters of a grouped normal mixture copula jointly. We also provide mathematical expressions and methods to compute Kendall’s tau, Spearman’s rho and the tail dependence coefficient λ. All algorithms presented are available in the R package nvmix (version ≥ 0.0.5).

Sensitivity Analysis and Simulation of a Multiserver Queueing System with Mixed Service Time Distribution

The motivation of mixing distributions in communication/queueing systems modeling is that some input data (e.g., service time in queueing models) may follow several distinct distributions in a single input flow. In this paper, we study the sensitivity of performance measures on proximity of the service time distributions of a multiserver system model with two-component Pareto mixture distribution of service times. The theoretical results are illustrated by numerical simulation of the M/G/c systems while using the perfect sampling approach.

A Conditional Gradient Approach for Nonparametric Estimation of Mixing Distributions

Mixture models are versatile tools that are used extensively in many fields, including operations, marketing, and econometrics. The main challenge in estimating mixture models is that the mixing distribution is often unknown, and imposing a priori parametric assumptions can lead to model misspecification issues. In this paper, we propose a new methodology for nonparametric estimation of the mixing distribution of a mixture of logit models. We formulate the likelihood-based estimation problem as a constrained convex program and apply the conditional gradient (also known as Frank–Wolfe) algorithm to solve this convex program. We show that our method iteratively generates the support of the mixing distribution and the mixing proportions. Theoretically, we establish the sublinear convergence rate of our estimator and characterize the structure of the recovered mixing distribution. Empirically, we test our approach on real-world datasets. We show that it outperforms the standard expectation-maximization (EM) benchmark on speed (16 times faster), in-sample fit (up to 24% reduction in the log-likelihood loss), and predictive (average 28% reduction in standard error metrics) and decision accuracies (extracts around 23% more revenue). On synthetic data, we show that our estimator is robust to different ground-truth mixing distributions and can also account for endogeneity. This paper was accepted by Serguei Netessine, operations management.