Home About us Contact
|
Home About us Contact | ||
|
|
||
General Family (general + family)
Selected AbstractsRapid mixing of Gibbs sampling on graphs that are sparse on averageRANDOM STRUCTURES AND ALGORITHMS, Issue 2 2009Elchanan Mossel Abstract Gibbs sampling also known as Glauber dynamics is a popular technique for sampling high dimensional distributions defined on graphs. Of special interest is the behavior of Gibbs sampling on the Erd,s-Rényi random graph G(n,d/n), where each edge is chosen independently with probability d/n and d is fixed. While the average degree in G(n,d/n) is d(1 - o(1)), it contains many nodes of degree of order log n/log log n. The existence of nodes of almost logarithmic degrees implies that for many natural distributions defined on G(n,p) such as uniform coloring (with a constant number of colors) or the Ising model at any fixed inverse temperature ,, the mixing time of Gibbs sampling is at least n1+,(1/log log n). Recall that the Ising model with inverse temperature , defined on a graph G = (V,E) is the distribution over {±}Vgiven by . High degree nodes pose a technical challenge in proving polynomial time mixing of the dynamics for many models including the Ising model and coloring. Almost all known sufficient conditions in terms of , or number of colors needed for rapid mixing of Gibbs samplers are stated in terms of the maximum degree of the underlying graph. In this work, we show that for every d < , and the Ising model defined on G (n, d/n), there exists a ,d > 0, such that for all , < ,d with probability going to 1 as n ,,, the mixing time of the dynamics on G (n, d/n) is polynomial in n. Our results are the first polynomial time mixing results proven for a natural model on G (n, d/n) for d > 1 where the parameters of the model do not depend on n. They also provide a rare example where one can prove a polynomial time mixing of Gibbs sampler in a situation where the actual mixing time is slower than npolylog(n). Our proof exploits in novel ways the local tree like structure of Erd,s-Rényi random graphs, comparison and block dynamics arguments and a recent result of Weitz. Our results extend to much more general families of graphs which are sparse in some average sense and to much more general interactions. In particular, they apply to any graph for which every vertex v of the graph has a neighborhood N(v) of radius O(log n) in which the induced sub-graph is a tree union at most O(log n) edges and where for each simple path in N(v) the sum of the vertex degrees along the path is O(log n). Moreover, our result apply also in the case of arbitrary external fields and provide the first FPRAS for sampling the Ising distribution in this case. We finally present a non Markov Chain algorithm for sampling the distribution which is effective for a wider range of parameters. In particular, for G(n, d/n) it applies for all external fields and , < ,d, where d tanh(,d) = 1 is the critical point for decay of correlation for the Ising model on G(n, d/n). © 2009 Wiley Periodicals, Inc. Random Struct. Alg., 2009 [source] Skew-symmetric distributions generated by the distribution function of the normal distributionENVIRONMETRICS, Issue 4 2007Héctor W. Gómez Abstract In this paper we study a general family of skew-symmetric distributions which are generated by the cumulative distribution of the normal distribution. For some distributions, moments are computed which allows computing asymmetry and kurtosis coefficients. It is shown that the range for asymmetry and kurtosis parameters is wider than for the family of models introduced by Nadarajah and Kotz (2003). For the skew- t -normal model, we discuss approaches for obtaining maximum likelihood estimators and derive the Fisher information matrix, discussing some of its properties and special cases. We report results of an application to a real data set related to nickel concentration in soil samples. Copyright © 2006 John Wiley & Sons, Ltd. [source] Baroclinic stability for a family of two-level, semi-implicit numerical methods for the 3D shallow water equationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3 2007Francisco J. Rueda Abstract The baroclinic stability of a family of two time-level, semi-implicit schemes for the 3D hydrostatic, Boussinesq Navier,Stokes equations (i.e. the shallow water equations), which originate from the TRIM model of Casulli and Cheng (Int. J. Numer. Methods Fluids 1992; 15:629,648), is examined in a simple 2D horizontal,vertical domain. It is demonstrated that existing mass-conservative low-dissipation semi-implicit methods, which are unconditionally stable in the inviscid limit for barotropic flows, are unstable in the same limit for baroclinic flows. Such methods can be made baroclinically stable when the integrated continuity equation is discretized with a barotropically dissipative backwards Euler scheme. A general family of two-step predictor-corrector schemes is proposed that have better theoretical characteristics than existing single-step schemes. Copyright © 2006 John Wiley & Sons, Ltd. [source] Guaranteed-content prediction intervals for non-linear autoregressionsJOURNAL OF FORECASTING, Issue 4 2001Xavier de LunaArticle first published online: 25 JUL 200 Abstract In this paper we present guaranteed-content prediction intervals for time series data. These intervals are such that their content (or coverage) is guaranteed with a given high probability. They are thus more relevant for the observed time series at hand than classical prediction intervals, whose content is guaranteed merely on average over hypothetical repetitions of the prediction process. This type of prediction inference has, however, been ignored in the time series context because of a lack of results. This gap is filled by deriving asymptotic results for a general family of autoregressive models, thereby extending existing results in non-linear regression. The actual construction of guaranteed-content prediction intervals directly follows from this theory. Simulated and real data are used to illustrate the practical difference between classical and guaranteed-content prediction intervals for ARCH models. Copyright © 2001 John Wiley & Sons, Ltd. [source] Generalized additive models for location, scale and shapeJOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES C (APPLIED STATISTICS), Issue 3 2005R. A. Rigby Summary., A general class of statistical models for a univariate response variable is presented which we call the generalized additive model for location, scale and shape (GAMLSS). The model assumes independent observations of the response variable y given the parameters, the explanatory variables and the values of the random effects. The distribution for the response variable in the GAMLSS can be selected from a very general family of distributions including highly skew or kurtotic continuous and discrete distributions. The systematic part of the model is expanded to allow modelling not only of the mean (or location) but also of the other parameters of the distribution of y, as parametric and/or additive nonparametric (smooth) functions of explanatory variables and/or random-effects terms. Maximum (penalized) likelihood estimation is used to fit the (non)parametric models. A Newton,Raphson or Fisher scoring algorithm is used to maximize the (penalized) likelihood. The additive terms in the model are fitted by using a backfitting algorithm. Censored data are easily incorporated into the framework. Five data sets from different fields of application are analysed to emphasize the generality of the GAMLSS class of models. [source] Impact of Population Substructure on Trend Tests for Genetic Case,Control Association StudiesBIOMETRICS, Issue 1 2010Gang Zheng Summary Hidden population substructure in case,control data has the potential to distort the performance of Cochran,Armitage trend tests (CATTs) for genetic associations. Three possible scenarios that may arise are investigated here: (i) heterogeneity of genotype frequencies across unidentified subpopulations (PSI), (ii) heterogeneity of genotype frequencies and disease risk across unidentified subpopulations (PSII), and (iii) cryptic correlations within unidentified subpopulations. A unified approach is presented for deriving the bias and variance distortion under the three scenarios for any CATT in a general family. Using these analytical formulas, we evaluate the excess type I errors of the CATTs numerically in the presence of population substructure. Our results provide insight into the properties of some proposed corrections for bias and variance distortion and show why they may not fully correct for the effects of population substructure. [source] Comparative Statics Predictions for Changes in Uncertainty in the Portfolio and Savings ProblemsBULLETIN OF ECONOMIC RESEARCH, Issue 1 2001Gyemyung Choi The paper investigates comparative statics effects of changes in uncertainty for a general family of problems that encompasses both the portfolio and saving decisions. Conditions are derived on preferences that are necessary and sufficient for unambiguous comparative statics predictions. The paper consolidates and completes the statement of restrictions on attitudes toward risk,bearing needed for determinate predictions in the portfolio and saving problems. [source] | |||||||||||||