The Poisson distribution has been widely studied and used for modeling univariate count-valued data. However, multivariate generalizations of the Poisson distribution that permit dependencies have been far less popular. Yet, real-world, high-dimensional, count-valued data found in word counts, genomics, and crime statistics, for example, exhibit rich dependencies and motivate the need for multivariate distributions that can appropriately model this data. We review multivariate distributions derived from the univariate Poisson, categorizing these models into three main classes: (1) where the marginal distributions are Poisson, (2) where the joint distribution is a mixture of independent multivariate Poisson distributions, and (3) where the node-conditional distributions are derived from the Poisson. We discuss the development of multiple instances of these classes and compare the models in terms of interpretability and theory. Then, we empirically compare multiple models from each class on three real-world datasets that have varying data characteristics from different domains, namely traffic accident data, biological next generation sequencing data, and text data. These empirical experiments develop intuition about the comparative advantages and disadvantages of each class of multivariate distribution that was derived from the Poisson. Finally, we suggest new research directions as explored in the subsequent Discussion section.

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This paper reviews and empirically compares multivariate models derived from the Poisson distribution which can be categorized into three model classes based on primary modeling assumptions.

The mean function is a central object of inquiry in the analysis of functional data. Typical questions related to the mean function include quantifying estimation uncertainty, testing parametric models, and making comparisons between populations. To make probabilistic statements about the mean function over its entire domain, rather than at a single location, it is necessary to infer all of its values simultaneously. Pointwise inference is not appropriate for this task and indeed produces anticonservative results, i.e., the coverage level of confidence regions is too low and the significance level of hypothesis tests too high. In contrast, simultaneous confidence bands (SCB) provide a flexible framework for conducting simultaneous inference on the mean function and other functional parameters. They also offer powerful visualization tools for communicating analytic results to interdisciplinary audiences. The construction of SCB in the context of functional data requires specific theory and methods. In particular, it is not addressed by the nonparametric regression literature. Although software is available to perform individual steps of an SCB procedure, resources that provide end-to-end computations are scarce. Applications of SCB to one- and two-sample inferences are illustrated here with the R package SCBmeanfd.

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Simultaneous confidence bands of level 95% for the average DNA copy number profile of patients with colorectal tumors. Chromosomal regions with significant gain/loss in DNA copy number are marked with black rectangles above the x-axis. These regions may contain cancer-causing genes.

Computer generation of experimental designs, for reasons including flexibility, speed, and ease of access, is the first line of approach for many experimentalists. The algorithms generating designs in many popular software packages employ optimality functions to measure design effectiveness. These optimality functions make implicit assumptions about the goals of the experiment that are not always considered and which may be inappropriate as the basis for design selection. General weighted optimality criteria address this problem by tailoring design selection to a practitioner's research questions. Implementation of weighted criteria in some popular design software is easily accomplished. The technique is demonstrated for factorial designs and for designing experiments with a control treatment. *WIREs Comput Stat* 2017, 9:e1393. doi: 10.1002/wics.1393

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Function-on-function regression refers to the situation where both independent and dependent variables in a regression model are of functional nature. Functional concurrent regression is a specific type of function-on-function regression that relates the response function at a specific point to the covariate value at that point and the point itself. Standard functional concurrent models are linear (a linear combination of the covariates is used), and often criticized due to their linearity assumption and lack of flexibility. This gives rise to nonparametric functional concurrent regression that models the response function at a specific point using a multivariate nonparametric function of both the point and the covariate value at that point. Such models allow for much more flexibility and predictive accuracy, especially when the underlying relationship is nonlinear. In the past decade, several methods have been proposed to perform estimation, prediction and inference in the nonparametric concurrent models using various methods such as spline smoothing, Gaussian process regression and local polynomial kernel regression. Such models have been shown to be useful tools in functional regression as well as stepping stone for further development. *WIREs Comput Stat* 2017, 9:e1394. doi: 10.1002/wics.1394

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Spline based fit of a nonparametric functional concurrent regression model for the Gait dataset using knee and hip angles (measured over time) as response and covariate, respectively.