Decision-Making with Heterogeneous Sensors - A Copula Based Approach

Statistical decision making has wide ranging applications, from communications and signal processing to econometrics and finance. In contrast to the classical one source-one receiver paradigm, several applications have been identified in the recent past that require acquiring data from multiple sources or sensors. Information from the multiple sensors are transmitted to a remotely located receiver known as the fusion center which makes a global decision. Past work has largely focused on fusion of information from homogeneous sensors. This dissertation extends the formulation to the case when the local sensors may possess disparate sensing modalities. Both the theoretical and practical aspects of multimodal signal processing are considered. The first and foremost challenge is to \u27adequately\u27 model the joint statistics of such heterogeneous sensors. We propose the use of copula theory for this purpose. Copula models are general descriptors of dependence. They provide a way to characterize the nonlinear functional relationships between the multiple modalities, which are otherwise difficult to formalize. The important problem of selecting the `best\u27 copula function from a given set of valid copula densities is addressed, especially in the context of binary hypothesis testing problems. Both, the training-testing paradigm, where a training set is assumed to be available for learning the copula models prior to system deployment, as well as generalized likelihood ratio test (GLRT) based fusion rule for the online selection and estimation of copula parameters are considered. The developed theory is corroborated with extensive computer simulations as well as results on real-world data. Sensor observations (or features extracted thereof) are most often quantized before their transmission to the fusion center for bandwidth and power conservation. A detection scheme is proposed for this problem assuming unifom scalar quantizers at each sensor. The designed rule is applicable for both binary and multibit local sensor decisions. An alternative suboptimal but computationally efficient fusion rule is also designed which involves injecting a deliberate disturbance to the local sensor decisions before fusion. The rule is based on Widrow\u27s statistical theory of quantization. Addition of controlled noise helps to \u27linearize\u27 the higly nonlinear quantization process thus resulting in computational savings. It is shown that although the introduction of external noise does cause a reduction in the received signal to noise ratio, the proposed approach can be highly accurate when the input signals have bandlimited characteristic functions, and the number of quantization levels is large. The problem of quantifying neural synchrony using copula functions is also investigated. It has been widely accepted that multiple simultaneously recorded electroencephalographic signals exhibit nonlinear and non-Gaussian statistics. While the existing and popular measures such as correlation coefficient, corr-entropy coefficient, coh-entropy and mutual information are limited to being bivariate and hence applicable only to pairs of channels, measures such as Granger causality, even though multivariate, fail to account for any nonlinear inter-channel dependence. The application of copula theory helps alleviate both these limitations. The problem of distinguishing patients with mild cognitive impairment from the age-matched control subjects is also considered. Results show that the copula derived synchrony measures when used in conjunction with other synchrony measures improve the detection of Alzheimer\u27s disease onset

Fisher Information in Weighted Distributions

Standard inference procedures assume a random sample from a population with density fμ(x) for estimating the parameter μ. However, there are many applications in which the available data are a biased sample instead. Fisher modeled biased sampling using a weight function w(x) ¸ 0, and constructed a weighted distribution with a density fμw(x) that is proportional to w(x)fμ(x). In this paper, we assume that fμ(x) belongs to an exponential family, and study the Fisher information about μ in observations obtained from some commonly arising weighted distributions: (i) the kth order statistic of a random sample of size m, (ii) observations from the stationary distribution of the residual lifetime of a renewal process, and (iii) truncated distributions. We give general conditions under which the weighted distribution has greater Fisher information than the original distribution, and specialize to the normal, gamma, and Weibull distributions. These conditions involve the distributions\u27 hazard rate and the reversed hazard rate functions

Fusing Dependent Decisions for Hypothesis Testing with Heterogeneous Sensors

In this paper, we consider a binary decentralized detection problem where the local sensor observations are quantized before their transmission to the fusion center. Sensor observations, and hence their quantized versions, may be heterogeneous as well as statistically dependent. A composite binary hypothesis testing problem is formulated, and a copula-based generalized likelihood ratio test (GLRT) based fusion rule is derived given that the local sensors are uniform multi-level quantizers. An alternative computationally efficient fusion rule is also designed which involves injecting a deliberate random disturbance to the local sensor decisions before fusion. Although the introduction of external noise causes a reduction in the received signal to noise ratio, it is shown that the proposed approach can result in a detection performance comparable to the GLRT detector without external noise, especially when the number of quantization levels is larg

Lower Tail Independence of Hitting Times of Two-Dimensional Diffusions

This article has been published in a revised form in Probability in the Engineering and Informational Sciences https://doi.org/10.1017/S0269964817000353. This version is free to view and download for private research and study only. Not for re-distribution, re-sale or use in derivative works. © Cambridge University Press 2017.The coefficient of tail dependence is a quantity that measures how extreme events in one component of a bivariate distribution depend on extreme events in the other component. It is well known that the Gaussian copula has zero tail dependence, a shortcoming for its application in credit risk modeling and quantitative risk management in general. We show that this property is shared by the joint distributions of hitting times of bivariate (uniformly elliptic) diffusion processes

Pediatric functional magnetic resonance neuroimaging: tactics for encouraging task compliance

<p>Abstract</p> <p>Background</p> <p>Neuroimaging technology has afforded advances in our understanding of normal and pathological brain function and development in children and adolescents. However, noncompliance involving the inability to remain in the magnetic resonance imaging (MRI) scanner to complete tasks is one common and significant problem. Task noncompliance is an especially significant problem in pediatric functional magnetic resonance imaging (fMRI) research because increases in noncompliance produces a greater risk that a study sample will not be representative of the study population.</p> <p>Method</p> <p>In this preliminary investigation, we describe the development and application of an approach for increasing the number of fMRI tasks children complete during neuroimaging. Twenty-eight healthy children ages 9-13 years participated. Generalization of the approach was examined in additional fMRI and event-related potential investigations with children at risk for depression, children with anxiety and children with depression (N = 120). Essential features of the approach include a preference assessment for identifying multiple individualized rewards, increasing reinforcement rates during imaging by pairing tasks with chosen rewards and presenting a visual 'road map' listing tasks, rewards and current progress.</p> <p>Results</p> <p>Our results showing a higher percentage of fMRI task completion by healthy children provides proof of concept data for the recommended tactics. Additional support was provided by results showing our approach generalized to several additional fMRI and event-related potential investigations and clinical populations.</p> <p>Discussion</p> <p>We proposed that some forms of task noncompliance may emerge from less than optimal reward protocols. While our findings may not directly support the effectiveness of the multiple reward compliance protocol, increased attention to how rewards are selected and delivered may aid cooperation with completing fMRI tasks</p> <p>Conclusion</p> <p>The proposed approach contributes to the pediatric neuroimaging literature by providing a useful way to conceptualize and measure task noncompliance and by providing simple cost effective tactics for improving the effectiveness of common reward-based protocols.</p

Care team and practice-level implementation strategies to optimize pediatric collaborative care: Study protocol for a cluster-randomized hybrid type III trial

BACKGROUND: Implementation facilitation is an effective strategy to support the implementation of evidence-based practices (EBPs), but our understanding of multilevel strategies and the mechanisms of change within the black box of implementation facilitation is limited. This implementation trial seeks to disentangle and evaluate the effects of facilitation strategies that separately target the care team and leadership levels on implementation of a collaborative care model in pediatric primary care. Strategies targeting the provider care team (TEAM) should engage team-level mechanisms, and strategies targeting leaders (LEAD) should engage organizational mechanisms. METHODS: We will conduct a hybrid type 3 effectiveness-implementation trial in a 2 × 2 factorial design to evaluate the main and interactive effects of TEAM and LEAD and test for mediation and moderation of effects. Twenty-four pediatric primary care practices will receive standard REP training to implement Doctor-Office Collaborative Care (DOCC) and then be randomized to (1) Standard REP only, (2) TEAM, (3) LEAD, or (4) TEAM + LEAD. Implementation outcomes are DOCC service delivery and change in practice-level care management competencies. Clinical outcomes are child symptom severity and quality of life. DISCUSSION: This statewide trial is one of the first to test the unique and synergistic effects of implementation strategies targeting care teams and practice leadership. It will advance our knowledge of effective care team and practice-level implementation strategies and mechanisms of change. Findings will support efforts to improve common child behavioral health conditions by optimizing scale-up and sustainment of CCMs in a pediatric patient-centered medical home. TRIAL REGISTRATION: ClinicalTrials.gov, NCT04946253 . Registered June 30, 2021

Stability of Satellite Planes in M31 II: Effects of the Dark Subhalo Population

The planar arrangement of nearly half the satellite galaxies of M31 has been a source of mystery and speculation since it was discovered. With a growing number of other host galaxies showing these satellite galaxy planes, their stability and longevity have become central to the debate on whether the presence of satellite planes are a natural consequence of prevailing cosmological models, or represent a challenge. Given the dependence of their stability on host halo shape, we look into how a galaxy plane's dark matter environment influences its longevity. An increased number of dark matter subhalos results in increased interactions that hasten the deterioration of an already-formed plane of satellite galaxies in spherical dark halos. The role of total dark matter mass fraction held in subhalos in dispersing a plane of galaxies present non trivial effects on plane longevity as well. But any misalignments of plane inclines to major axes of flattened dark matter halos lead to their lifetimes being reduced to < 3 Gyrs. Distributing > 40% of total dark mass in subhalos in the overall dark matter distribution results in a plane of satellite galaxies that is prone to change through the 5 Gyr integration time period.Comment: 11 pages, 9 figures, accepted to MNRAS September 22 201

Effects of comorbid anxiety disorders on the longitudinal course of pediatric bipolar disorders

OBJECTIVE: To examine the longitudinal effects of comorbid anxiety disorders in youth with bipolar spectrum disorder (BP). METHOD: As part of the Course and Outcome of Bipolar Youth study, 413 youth, who were 7 through 17 years or age and who met criteria for DSM-IV BP-I (n = 244), BP-II (n = 28), and operationally defined bipolar disorder not otherwise specified (BP-NOS) (n = 141) were included. Subjects were followed on average 5 years using the Longitudinal Interval Follow-up Evaluation. Effects of anxiety on the time to mood recovery and recurrence and percentage of time with syndromal and subsyndromal mood symptomatology during the follow-up period were analyzed. RESULTS: At intake and during the follow-up, 62% of youth with BP met criteria for at least 1 anxiety disorder. About 50% of the BP youth with anxiety had ≥2 anxiety disorders. Compared to BP youth without anxiety, those with anxiety had significantly more depressive recurrences and significantly longer median time to recovery. The effects of anxiety on recovery disappeared when the severity of depression at intake was taken into account. After adjusting for confounding factors, BP youth with anxiety, particularly those with ≥2 anxiety disorders, spent significantly less follow-up time asymptomatic and more time with syndromal mixed/cycling and subsyndromal depressive symptomatology compared to those without anxiety. CONCLUSIONS: Anxiety disorders are common and adversely affect the course of BP in youth, as characterized by more mood recurrences, longer time to recovery, less time euthymic, and more time in mixed/cycling and depressive episodes. Prompt recognition and the development of treatments for BP youth with anxiety are warranted

Child/Adolescent Anxiety Multimodal Study (CAMS): rationale, design, and methods

<p>Abstract</p> <p>Objective</p> <p>To present the design, methods, and rationale of the Child/Adolescent Anxiety Multimodal Study (CAMS), a recently completed federally-funded, multi-site, randomized placebo-controlled trial that examined the relative efficacy of cognitive-behavior therapy (CBT), sertraline (SRT), and their combination (COMB) against pill placebo (PBO) for the treatment of separation anxiety disorder (SAD), generalized anxiety disorder (GAD) and social phobia (SoP) in children and adolescents.</p> <p>Methods</p> <p>Following a brief review of the acute outcomes of the CAMS trial, as well as the psychosocial and pharmacologic treatment literature for pediatric anxiety disorders, the design and methods of the CAMS trial are described.</p> <p>Results</p> <p>CAMS was a six-year, six-site, randomized controlled trial. Four hundred eighty-eight (N = 488) children and adolescents (ages 7-17 years) with DSM-IV-TR diagnoses of SAD, GAD, or SoP were randomly assigned to one of four treatment conditions: CBT, SRT, COMB, or PBO. Assessments of anxiety symptoms, safety, and functional outcomes, as well as putative mediators and moderators of treatment response were completed in a multi-measure, multi-informant fashion. Manual-based therapies, trained clinicians and independent evaluators were used to ensure treatment and assessment fidelity. A multi-layered administrative structure with representation from all sites facilitated cross-site coordination of the entire trial, study protocols and quality assurance.</p> <p>Conclusions</p> <p>CAMS offers a model for clinical trials methods applicable to psychosocial and psychopharmacological comparative treatment trials by using state-of-the-art methods and rigorous cross-site quality controls. CAMS also provided a large-scale examination of the relative and combined efficacy and safety of the best evidenced-based psychosocial (CBT) and pharmacologic (SSRI) treatments to date for the most commonly occurring pediatric anxiety disorders. Primary and secondary results of CAMS will hold important implications for informing practice-relevant decisions regarding the initial treatment of youth with anxiety disorders.</p> <p>Trial registration</p> <p>ClinicalTrials.gov NCT00052078.</p