A randomness test for functional panels

Functional panels are collections of functional time series, and arise often in the study of high frequency multivariate data. We develop a portmanteau style test to determine if the cross-sections of such a panel are independent and identically distributed. Our framework allows the number of functional projections and/or the number of time series to grow with the sample size. A large sample justification is based on a new central limit theorem for random vectors of increasing dimension. With a proper normalization, the limit is standard normal, potentially making this result easily applicable in other FDA context in which projections on a subspace of increasing dimension are used. The test is shown to have correct size and excellent power using simulated panels whose random structure mimics the realistic dependence encountered in real panel data. It is expected to find application in climatology, finance, ecology, economics, and geophysics. We apply it to Southern Pacific sea surface temperature data, precipitation patterns in the South-West United States, and temperature curves in Germany.Comment: Supplemental material from the authors' homepage or upon reques

Panel Assignment in the Federal Courts of Appeals

It is common knowledge that the federal courts of appeals typically hear cases in panels of three judges and that the composition of the panel can have significant consequences for case outcomes and for legal doctrine more generally. Yet neither legal scholars nor social scientists have focused on the question of how judges are selected for their panels. Instead, a substantial body of scholarship simply assumes that panel assignment is random. This Article provides what, up until this point, has been a missing account of panel assignment. Drawing on a multiyear qualitative study of five circuit courts, including in-depth interviews with thirty-five judges and senior administrators, I show that strictly random selection is a myth, and an improbable one at that—in many instances, it would have been impossible as a practical matter for the courts studied here to create their panels by random draw. Although the courts generally tried to “mix up” the judges, the chief judges and clerks responsible for setting the calendar also took into account various other factors, from collegiality to efficiency-based considerations. Notably, those factors differed from one court to the next; no two courts approached the challenge of panel assignment in precisely the same way. These findings pose an important challenge to the widespread assumption of panel randomness and reveal key normative questions that have been largely ignored in the literature. Although randomness is regarded as the default selection method across much of judicial administration, there is little exposition of why it is valuable. What, exactly, is desirable about having judges brought together randomly in the first place? What, if anything, is problematic about nonrandom methods of selection? This Article sets out to clarify both the costs and benefits of randomness, arguing that there can be valid reasons to depart from it. As such, it provides a framework for assessing different panel assignment practices and the myriad other court practices that rely, to some extent, on randomness

Panel Assignment in the Federal Courts of Appeals

It is common knowledge that the federal courts of appeals typically hear cases in panels of three judges and that the composition of the panel can have significant consequences for case outcomes and for legal doctrine more generally. Yet neither legal scholars nor social scientists have focused on the question of how judges are selected for their panels. Instead, a substantial body of scholarship simply assumes that panel assignment is random. This Article provides what, up until this point, has been a missing account of panel assignment. Drawing on a multiyear qualitative study of five circuit courts, including in-depth interviews with thirty-five judges and senior administrators, I show that strictly random selection is a myth, and an improbable one at that—in many instances, it would have been impossible as a practical matter for the courts studied here to create their panels by random draw. Although the courts generally tried to “mix up” the judges, the chief judges and clerks responsible for setting the calendar also took into account various other factors, from collegiality to efficiency-based considerations. Notably, those factors differed from one court to the next; no two courts approached the challenge of panel assignment in precisely the same way. These findings pose an important challenge to the widespread assumption of panel randomness and reveal key normative questions that have been largely ignored in the literature. Although randomness is regarded as the default selection method across much of judicial administration, there is little exposition of why it is valuable. What, exactly, is desirable about having judges brought together randomly in the first place? What, if anything, is problematic about nonrandom methods of selection? This Article sets out to clarify both the costs and benefits of randomness, arguing that there can be valid reasons to depart from it. As such, it provides a framework for assessing different panel assignment practices and the myriad other court practices that rely, to some extent, on randomness

Perturbation Detection Through Modeling of Gene Expression on a Latent Biological Pathway Network: A Bayesian hierarchical approach

Cellular response to a perturbation is the result of a dynamic system of biological variables linked in a complex network. A major challenge in drug and disease studies is identifying the key factors of a biological network that are essential in determining the cell's fate. Here our goal is the identification of perturbed pathways from high-throughput gene expression data. We develop a three-level hierarchical model, where (i) the first level captures the relationship between gene expression and biological pathways using confirmatory factor analysis, (ii) the second level models the behavior within an underlying network of pathways induced by an unknown perturbation using a conditional autoregressive model, and (iii) the third level is a spike-and-slab prior on the perturbations. We then identify perturbations through posterior-based variable selection. We illustrate our approach using gene transcription drug perturbation profiles from the DREAM7 drug sensitivity predication challenge data set. Our proposed method identified regulatory pathways that are known to play a causative role and that were not readily resolved using gene set enrichment analysis or exploratory factor models. Simulation results are presented assessing the performance of this model relative to a network-free variant and its robustness to inaccuracies in biological databases

The Computational Structure of Spike Trains

Neurons perform computations, and convey the results of those computations through the statistical structure of their output spike trains. Here we present a practical method, grounded in the information-theoretic analysis of prediction, for inferring a minimal representation of that structure and for characterizing its complexity. Starting from spike trains, our approach finds their causal state models (CSMs), the minimal hidden Markov models or stochastic automata capable of generating statistically identical time series. We then use these CSMs to objectively quantify both the generalizable structure and the idiosyncratic randomness of the spike train. Specifically, we show that the expected algorithmic information content (the information needed to describe the spike train exactly) can be split into three parts describing (1) the time-invariant structure (complexity) of the minimal spike-generating process, which describes the spike train statistically; (2) the randomness (internal entropy rate) of the minimal spike-generating process; and (3) a residual pure noise term not described by the minimal spike-generating process. We use CSMs to approximate each of these quantities. The CSMs are inferred nonparametrically from the data, making only mild regularity assumptions, via the causal state splitting reconstruction algorithm. The methods presented here complement more traditional spike train analyses by describing not only spiking probability and spike train entropy, but also the complexity of a spike train's structure. We demonstrate our approach using both simulated spike trains and experimental data recorded in rat barrel cortex during vibrissa stimulation.Comment: Somewhat different format from journal version but same conten

Universal flux-fluctuation law in small systems

We thank Dr. DeMenezes for providing the microchip data. This work was partially supported by the NSF of China under Grant Nos. 11135001, 11275003. Y.C.L. was supported by ARO under Grant No. W911NF-14-1-0504.Peer reviewedPublisher PD

Training-free Measures Based on Algorithmic Probability Identify High Nucleosome Occupancy in DNA Sequences

We introduce and study a set of training-free methods of information-theoretic and algorithmic complexity nature applied to DNA sequences to identify their potential capabilities to determine nucleosomal binding sites. We test our measures on well-studied genomic sequences of different sizes drawn from different sources. The measures reveal the known in vivo versus in vitro predictive discrepancies and uncover their potential to pinpoint (high) nucleosome occupancy. We explore different possible signals within and beyond the nucleosome length and find that complexity indices are informative of nucleosome occupancy. We compare against the gold standard (Kaplan model) and find similar and complementary results with the main difference that our sequence complexity approach. For example, for high occupancy, complexity-based scores outperform the Kaplan model for predicting binding representing a significant advancement in predicting the highest nucleosome occupancy following a training-free approach.Comment: 8 pages main text (4 figures), 12 total with Supplementary (1 figure