High-dimensional Dependence Research Articles

A new serially correlated gamma-frailty process for longitudinal count data

We describe a new multivariate gamma distribution and discuss its implication in a Poisson-correlated gamma-frailty model. This model is introduced to account for between-subjects correlation occurring in longitudinal count data. For likelihood-based inference involving distributions in which high-dimensional dependencies are present, it may be useful to approximate likelihoods based on the univariate or bivariate marginal distributions. The merit of composite likelihood is to reduce the computational complexity of the full likelihood. A 2-stage composite-likelihood procedure is developed for estimating the model parameters. The suggested method is applied to a meta-analysis study for survival curves.

Eliciting conditional and unconditional rank correlations from conditional probabilities

Causes of uncertainties may be interrelated and may introduce dependencies. Ignoring these dependencies may lead to large errors. A number of graphical models in probability theory such as dependence trees, vines and (continuous) Bayesian belief nets [Cooke RM. Markov and entropy properties of tree and vine-dependent variables. In: Proceedings of the ASA section on Bayesian statistical science, 1997; Kurowicka D, Cooke RM. Distribution-free continuous Bayesian belief nets. In: Proceedings of mathematical methods in reliability conference, 2004; Bedford TJ, Cooke RM. Vines—a new graphical model for dependent random variables. Ann Stat 2002; 30(4):1031–68; Kurowicka D, Cooke RM. Uncertainty analysis with high dimensional dependence modelling. New York: Wiley; 2006; Hanea AM, et al. Hybrid methods for quantifying and analyzing Bayesian belief nets. In: Proceedings of the 2005 ENBIS5 conference, 2005; Shachter RD, Kenley CR. Gaussian influence diagrams. Manage Sci 1998; 35(5) [15].] have been developed to capture dependencies between random variables. The input for these models are various marginal distributions and dependence information, usually in the form of conditional rank correlations. Often expert elicitation is required. This paper focuses on dependence representation, and dependence elicitation. The techniques presented are illustrated with an application from aviation safety.

A note on pseudolikelihood constructed from marginal densities

For likelihood-based inference involving distributions in which high-dimensional dependencies are present it may be useful to use approximate likelihoods based, for example, on the univariate or bivariate marginal distributions. The asymptotic properties of formal maximum likelihood estimators in such cases are outlined. In particular, applications in which only a single q x I vector of observations is observed are examined. Conditions under which consistent estimators of parameters result from the approximate likelihood using only pairwise joint distributions are studied. Some examples are analysed in detail.

A Systolic Design Methodology with Application to Full-Search Block-Matching Architectures

We present a systematic methodology to support the design tradeoffs of array processors in several emerging issues, such as (1) high performance and high flexibility, (2) low cost, low power, (3) efficient memory usage, and (4) system-on-a-chip or the ease of system integration. This methodology is algebraic based, so it can cope with high-dimensional data dependence. The methodology consists of some transformation rules of data dependency graphs for facilitating flexible array designs. For example, two common partitioning approaches, LPGS and LSGP, could be unified under the methodology. It supports the design of high-speed and massively parallel processor arrays with efficient memory usage. More specifically, it leads to a novel systolic cache architecture comprising of shift registers only (cache without tags). To demonstrate how the methodology works, we have presented several systolic design examples based on the block-matching motion estimation algorithm (BMA). By multiprojecting a 4D DG of the BMA to 2D mesh, we can reconstruct several existing array processors. By multiprojecting a 6D DG of the BMA, a novel 2D systolic array can be derived that features significantly improved rates in data reusability (96%) and processor utilization (99%).