order based dependent dirichlet processes in this article we propose a new framework for bayesian nonparametric modeling with continuous covariates in particular we allow the nonparametric distribution to depend on covariates through ordering the random variables building the weights in the stick breaking representation we focus mostly on the class of random distributions that induces a dirichlet process at each covariate value we derive the correlation between distributions at different covariate values and use a point process to implement a practically useful type of ordering two main constructions with analytically known correlation structures are proposed practical and efficient computational methods are introduced we apply our framework through mixtures of these processes to regression modeling the modeling of stochastic volatility in time series data and spatial geostatistical modeling

a time series ddp for functional proteomics profiles using a new type of array technology the reverse phase protein array rppa we measure time course protein expression for a set of selected markers that are known to co regulate biological functions in a pathway structure to accommodate the complex dependent nature of the data including temporal correlation and pathway dependence for the protein markers we propose a mixed effects model with temporal and protein specific components we develop a sequence of random probability measures rpm to account for the dependence in time of the protein expression measurements marginally for each rpm we assume a dirichlet process dp model the dependence is introduced by defining multivariate beta distributions for the unnormalized weights of the stick breaking representation we also acknowledge the pathway dependence among proteins via a conditionally autoregressive car model applying our model to the rppa data we reveal a pathway dependent functional profile for the set of proteins as well as marginal expression profiles over time for individual markers

modeling for dynamic ordinal regression relationships an application to estimating maturity of rockfish in california abstractwe develop a bayesian nonparametric framework for modeling ordinal regression relationships which evolve in discrete time the motivating application involves a key problem in fisheries research on estimating dynamically evolving relationships between age length and maturity the latter recorded on an ordinal scale the methodology builds from nonparametric mixture modeling for the joint stochastic mechanism of covariates and latent continuous responses this approach yields highly flexible inference for ordinal regression functions while at the same time avoiding the computational challenges of parametric models that arise from estimation of cut off points relating the latent continuous and ordinal responses a novel dependent dirichlet process prior for time dependent mixing distributions extends the model to the dynamic setting the methodology is used for a detailed study of relationships between maturity age and length for chilipepper rockfish using data collected over 15 years along th

estimating normal means with a dirichlet process prior abstract in this article the dirichlet process prior is used to provide a nonparametric bayesian estimate of a vector of normal means in the past there have been computational difficulties with this model this article solves the computational difficulties by developing a gibbs sampler algorithm the estimator developed in this article is then compared to parametric empirical bayes estimators peb and nonparametric empirical bayes estimators npeb in a monte carlo study the monte carlo study demonstrates that in some conditions the peb is better than the npeb and in other conditions the npeb is better than the peb the monte carlo study also shows that the estimator developed in this article produces estimates that are about as good as the peb when the peb is better and produces estimates that are as good as the npeb estimator when that method is better

gibbs sampling methods for stick breaking priors a rich and flexible class of random probability measures which we call stick breaking priors can be constructed using a sequence of independent beta random variables examples of random measures that have this characterization include the dirichlet process its two parameter extension the two parameter poisson dirichlet process finite dimensional dirichlet priors and beta two parameter processes the rich nature of stick breaking priors offers bayesians a useful class of priors for nonparametric problems while the similar construction used in each prior can be exploited to develop a general computational procedure for fitting them in this article we present two general types of gibbs samplers that can be used to fit posteriors of bayesian hierarchical models based on stick breaking priors the first type of gibbs sampler referred to as a polya urn gibbs sampler is a generalized version of a widely used gibbs sampling method currently employed for dirichlet process computing this method applies t

a bayesian population model with hierarchical mixture priors applied to blood count data abstract population pharmacokinetic and pharmacodynamic studies require analyzing nonlinear growth curves fit to multiple measurements from study subjects we propose a class of nonlinear population models with nonparametric second stage priors for analyzing such data the proposed models apply a flexible class of mixtures to implement the nonparametric second stage the discussion is based on a pharmacodynamic study involving longitudinal data consisting of hematologic profiles i e blood counts measured over time of cancer patients undergoing chemotherapy we describe a full posterior analysis in a bayesian framework this includes prediction of future observations profiles and end points for new patients estimation of the mean response function for observed individuals and inference on population characteristics the mixture model is specified and given a hyperprior distribution by means of a dirichlet processes prior on the mixing measure estimation is implemented by a combination of various m

smoothly mixing regressions this paper extends the conventional bayesian mixture of normals model by permitting state probabilities to depend on observed covariates the dependence is captured by a simple multinomial probit model a conventional and rapidly mixing mcmc algorithm provides access to the posterior distribution at modest computational cost this model is competitive with existing econometric models as documented in the paper s illustrations the first illustration studies quantiles of the distribution of earnings of men conditional on age and education and shows that smoothly mixing regressions are an attractive alternative to nonbayesian quantile regression the second illustration models serial dependence in the s p 500 return and shows that the model compares favorably with arch models using out of sample likelihood criteria

theory and numerical analysis for exact distributions of functionals of a dirichlet process the distribution of a mean or more generally of a vector of means of a dirichlet process is considered some characterizing aspects of this paper are i a review of a few basic results providing new formulations free from many of the extra assumptions considered to date in the literature and giving essentially new simpler and more direct proofs ii new numerical evaluations with any prescribed error of approximation of the distribution at issue iii a new form for the law of a vector of means moreover as applications of these results we give iv the sharpest condition sufficient for the distribution of a mean to be symmetric v forms for the probability distribution of the variance of the dirichlet random measure vi some hints for determining the finite dimensional distributions of a random function connected with bayesian methods for queuing models

permutation tests for least absolute deviation regression a permutation test based on proportionate reduction in sums of absolute deviations when passing from reduced to full parameter models is developed for testing hypotheses about least absolute deviation lad estimates of conditional medians in linear regression models sampling simulations demonstrated that the permutation test on full model lad estimates had greater relative power 1 06 1 43 than normal theory tests on least squares estimates for asymmetric chi square error distributions and symmetric double exponential error distributions for models with one n 35 and n 63 and three n 63 independent variables relative power was 77 84 for normal error distributions power simulations demonstrated the low sensitivity of lad estimates and permutation tests to outlier contamination and heteroscedasticity that was a linear function of x and increased sensitivity to heteroscedasticity that was a function of x2 for simple regression models three permutation procedures for testing partial models in multiple regression were compared permuting residuals from the reduced model permuting residuals from the full model and permuting the dependent variable permuting residuals from the reduced model maintained nominal error rates best under the null hypothesis for all error distributions and for correlated and uncorrelated independent variables power under the alternative hypotheses for this partial testing procedure was similar to full lad regression model tests four example applications of lad regression are provided

a geometric growth model interpolating between regular and small world networks we propose a geometric growth model which interpolates between one dimensional linear graphs and small world networks the model undergoes a transition from large to small worlds we study the topological characteristics by both theoretical predictions and numerical simulations which are in good accordance with each other our geometrically growing model is a complementarity for the static ws model

erratum apollonian networks simultaneously scale free small world euclidean space filling and with matching graphs phys rev lett 94 018702 2005

semiparametric bayes analysis of longitudinal data treatment models this paper is concerned with the problem of determining the effect of a binary treatment variable on a continuous outcome given longitudinal observational data and non randomly assigned treatments a general semiparametric bayesian model based on dirichlet process mixing is developed which contains potential outcomes and subject level outcome specific random effects the model is subjected to a fully bayesian analysis based on markov chain monte carlo simulation methods the methods are used to compute the posterior distribution of the parameters and potential outcomes the sampled posterior output from the simulation is also used to construct treatment effect distributions at the unit level and at other levels of aggregation marginalized over all unknowns of the model including the unknown distribution of responses and treatments and treatment effects matched by treatment probability a real data example dealing with the wage premium associated with union membership is considered in detail where quantities such as the average treatment effect the treatment effect on the treated and matched treatment effects are derived and illustrated

distinct clusterings and characteristic path lengths in dynamic small world networks with identical limit degree distribution many real world networks belong to a particular class of structures known as small world networks that display short distance between pair of nodes in this paper we introduce a simple family of growing small world networks where both addition and deletion of edges are possible by tuning the deletion probability q t the model undergoes a transition from large worlds to small worlds by making use of analytical or numerical means we determine the degree distribution clustering coefficient and average path length of our networks surprisingly we find that two similar evolving mechanisms which provide identical degree distribution under a reciprocal scaling as t goes to infinity can lead to quite different clustering behaviors and characteristic path lengths it is also worth noting that farey graphs constitute the extreme case q t 0 of our random construction

construction of permutation tests abstract a general method for constructing permutation tests for various experimental designs follows from invariance and sufficiency in this framework randomization or rerandomization tests are just special cases of permutation tests the methodology extends the applicability of permutation tests an example demonstrates a test for an interaction effect in a factorial experiment a problem thought to be unapproachable by permutation or randomization methods tests are constructed as follows the modeling of block and treatment effects closely parallels classical analysis of variance anova the anova assumptions of iid normal random errors are replaced however by the much weaker assumption of exchangeability of subsets of random errors distributional dependences on the unknown nuisance parameters for blocks covariates and untested treatments and on the unknown error distribution are eliminated by invariance and sufficiency respectively initial reduction of the data by invariance appears to ex

additive cubic spline regression with dirichlet process mixture errors abstract the goal of this article is to develop a flexible bayesian analysis of regression models for continuous and categorical outcomes in the models we study covariate or regression effects are modeled additively by cubic splines and the error distribution that of the latent outcomes in the case of categorical data is modeled as a dirichlet process mixture we employ a relatively unexplored but attractive basis in which the spline coefficients are the unknown function ordinates at the knots we exploit this feature to develop a proper prior distribution on the coefficients that involves the first and second differences of the ordinates quantities about which one may have prior knowledge we also discuss the problem of comparing models with different numbers of knots or different error distributions through marginal likelihoods and bayes factors which are computed within the framework of chib 1995 as extended to dpm models by basu and chib 2003 the techniques are illustrated with simulated and real data

generalized poya urn for time varying pitman yor processes this article introduces a class of first order stationary time varying pitman yor processes subsuming our construction of time varying dirichlet processes presented in caron et al 2007 these models can be used for time dynamic density estimation and clustering our intuitive and simple construction relies on a generalized polya urn scheme significantly this construction yields marginal distributions at each time point that can be explicitly characterized and easily controlled inference is performed using markov chain monte carlo and sequential monte carlo methods we demonstrate our models and algorithms on epidemiological and video tracking data

semiparametric bayesian inference for stochastic frontier models in this paper we propose a semiparametric bayesian framework for the analysis of stochastic frontiers and efficiency measurement the distribution of inefficiencies is modelled nonparametrically through a dirichlet process prior we suggest prior distributions and implement a bayesian analysis through an efficient markov chain monte carlo sampler which allows us to deal with practically relevant sample sizes we also consider the case where the efficiency distribution varies with firm characteristics the methodology is applied to a cost frontier estimated from a panel data set on 382 u s hospitals

a method for combining inference across related nonparametric bayesian models summary we consider the problem of combining inference in related nonparametric bayes models analogous to parametric hierarchical models the hierarchical extension formalizes borrowing strength across the related submodels in the nonparametric context modelling is complicated by the fact that the random quantities over which we define the hierarchy are infinite dimensional we discuss a formal definition of such a hierarchical model the approach includes a regression at the level of the nonparametric model for the special case of dirichlet process mixtures we develop a markov chain monte carlo scheme to allow efficient implementation of full posterior inference in the given model

an anova model for dependent random measures we consider dependent nonparametric models for related random probability distributions for example the random distributions might be indexed by a categorical covariate indicating the treatment levels in a clinical trial and might represent random effects distributions under the respective treatment combinations we propose a model that describes dependence across random distributions in an analysis of variance anova type fashion we define a probability model in such a way that marginally each random measure follows a dirichlet process dp and use the dependent dirichlet process to define the desired dependence across the related random measures the resulting probability model can alternatively be described as a mixture of anova models with a dp prior on the unknown mixing measure the main features of the proposed approach are ease of interpretation and computational simplicity because the model follows the standard anovastructure interpretation and inference parallels conventions for anova mode

on the stick breaking representation of normalized inverse gaussian priors random probability measures are the main tool for bayesian nonparametric inference with their laws acting as prior distributions many well known priors used in practice admit different though equivalent representations in terms of computational convenience stick breaking representations stand out in this paper we focus on the normalized inverse gaussian process and provide a completely explicit stick breaking representation for it this result is of interest both from a theoretical viewpoint and for statistical practice copyright 2012 oxford university press

bayesian nonparametric estimation for incomplete data via successive substitution sampling in the problem of estimating an unknown distribution function f in the presence of censoring one can use a nonparametric estimator such as the kaplan meier estimator or one can consider parametric modeling there are many situations where physical reasons indicate that a certain parametric model holds approximately in these cases a nonparametric estimator may be very inefficient relative to a parametric estimator on the other hand if the parametric model is only a crude approximation to the actual model then the parametric estimator may perform poorly relative to the nonparametric estimator and may even be inconsistent the bayesian paradigm provides a reasonable framework for this problem in a bayesian approach one would try to put a prior distribution on f that gives most of its mass to small neighborhoods of the entire parametric family we show that certain priors based on the dirichlet process prior can be used to accomplish this for these priors the posterior distribution of f given the censored data appears to be analytically intractable we provide a method for approximating this posterior distribution through the use of a successive substitution sampling algorithm we also show convergence of the algorithm

reinforced urn processes for credit risk models abstract we propose a bayesian nonparametric model to estimate rating migration matrices and default probabilities using the reinforced urn processes rup introduced in muliere et al 2000 the estimated default probability becomes our prior information in a parametric model for the prediction of the number of bankruptcies with the only assumption of exchangeability within rating classes the polya urn construction of the transition matrix justifies a beta distributed de finetti measure dependence among the processes is introduced through the dependence among the default probabilities with the bivariate beta distribution proposed in olkin and liu 2003 and its multivariate generalization

bayesian nonparametric calibration and combination of predictive distributions abstractwe introduce a bayesian approach to predictive density calibration and combination that accounts for parameter uncertainty and model set incompleteness through the use of random calibration functionals and random combination weights building on the work of ranjan and gneiting we use infinite beta mixtures for the calibration the proposed bayesian nonparametric approach takes advantage of the flexibility of dirichlet process mixtures to achieve any continuous deformation of linearly combined predictive distributions the inference procedure is based on combination gibbs and slice sampling we provide some conditions under which the proposed probabilistic calibration converges in terms of weak posterior consistency to the true underlying density for both cases of iid and markovian observations this calibration property improves upon the earlier calibration approaches we study the methodology in simulation examples with fat tails and multimodal densities and apply it to density forecasts of dail

threshold free cluster enhancement addressing problems of smoothing threshold dependence and localisation in cluster inference many image enhancement and thresholding techniques make use of spatial neighbourhood information to boost belief in extended areas of signal the most common such approach in neuroimaging is cluster based thresholding which is often more sensitive than voxel wise thresholding however a limitation is the need to define the initial cluster forming threshold this threshold is arbitrary and yet its exact choice can have a large impact on the results particularly at the lower e g t z 4 cluster forming thresholds frequently used furthermore the amount of spatial pre smoothing is also arbitrary given that the expected signal extent is very rarely known in advance of the analysis in the light of such problems we propose a new method which attempts to keep the sensitivity benefits of cluster based thresholding and indeed the general concept of clusters of signal while avoiding or at least minimising these problems the method takes a raw statistic image and produces an output image in which the voxel wise values represent the amount of cluster like local spatial support the method is thus referred to as threshold free cluster enhancement tfce we present the tfce approach and discuss in detail roc based optimisation and comparisons with cluster based and voxel based thresholding we find that tfce gives generally better sensitivity than other methods over a wide range of test signal shapes and snr values we also show an example on a real imaging dataset suggesting that tfce does indeed provide not just improved sensitivity but richer and more interpretable output than cluster based thresholding

validating cluster size inference random field and permutation methods cluster size tests used in analyses of brain images can have more sensitivity compared to intensity based tests the random field rf theory has been widely used in implementation of such tests however the behavior of such tests is not well understood especially when the rf assumptions are in doubt in this paper we carried out a simulation study of cluster size tests under varying smoothness thresholds and degrees of freedom comparing rf performance to that of the permutation test which is known to be exact for gaussian images we find that the rf methods are generally conservative especially for low smoothness and low threshold for t images the rf tests are found to be conservative at lower thresholds and do not perform well unless the threshold is high and images are sufficiently smooth the permutation test performs well for any settings though the discreteness in cluster size must be accounted for we make specific recommendations on when permutation tests are to be preferred to rf tests

markov chain monte carlo in approximate dirichlet and beta two parameter process hierarchical models summary we present some easy to construct random probability measures which approximate the dirichlet process and an extension which we will call the beta two parameter process the nature of these constructions makes it simple to implement markov chain monte carlo algorithms for fitting nonparametric hierarchical models and mixtures of nonparametric hierarchical models for the dirichlet process we consider a truncation approximation as well as a weak limit approximation based on a mixture of dirichlet processes the same type of truncation approximation can also be applied to the beta two parameter process both methods lead to posteriors which can be fitted using markov chain monte carlo algorithms that take advantage of blocked coordinate updates these algorithms promote rapid mixing of the markov chain and can be readily applied to normal mean mixture models and to density estimation problems we prefer the truncation approximations since a simple device for monitoring the adequacy of the approximation can be easily computed from the output of the gibbs sampler furthermore for the dirichlet process the truncation approximation offers an exponentially higher degree of accuracy over the weak limit approximation for the same computational effort we also find that a certain beta two parameter process may be suitable for finite mixture modelling because the distinct number of sampled values from this process tends to match closely the number of components of the underlying mixture distribution

bayesian density regression summary the paper considers bayesian methods for density regression allowing a random probability distribution to change flexibly with multiple predictors the conditional response distribution is expressed as a non parametric mixture of regression models with the mixture distribution changing with predictors a class of weighted mixture of dirichlet process priors is proposed for the uncountable collection of mixture distributions it is shown that this specification results in a generalized polya urn scheme which incorporates weights that are dependent on the distance between subjects predictor values to allow local dependence in the mixture distributions we propose a kernel based weighting scheme a gibbs sampling algorithm is developed for posterior computation the methods are illustrated by using simulated data examples and an epidemiologic application

bayesian analysis of binary and polychotomous response data abstract a vast literature in statistics biometrics and econometrics is concerned with the analysis of binary and polychotomous response data the classical approach fits a categorical response regression model using maximum likelihood and inferences about the model are based on the associated asymptotic theory the accuracy of classical confidence statements is questionable for small sample sizes in this article exact bayesian methods for modeling categorical response data are developed using the idea of data augmentation the general approach can be summarized as follows the probit regression model for binary outcomes is seen to have an underlying normal regression structure on latent continuous data values of the latent data can be simulated from suitable truncated normal distributions if the latent data are known then the posterior distribution of the parameters can be computed using standard results for normal linear models draws from this posterior are used to sample new latent data and t

estimating a semiparametric asymmetric stochastic volatility model with a dirichlet process mixture in this paper we extend the parametric asymmetric stochastic volatility model asv where returns are correlated with volatility by flexibly modeling the bivariate distribution of the return and volatility innovations nonparametrically its novelty is in modeling the joint conditional return volatility distribution with an infinite mixture of bivariate normal distributions with mean zero vectors but having unknown mixture weights and covariance matrices this semiparametric asv model nests stochastic volatility models whose innovations are distributed as either normal or student t distributions plus the response in volatility to unexpected return shocks is more general than the fixed asymmetric response with the asv model the unknown mixture parameters are modeled with a dirichlet process prior this prior ensures a parsimonious finite posterior mixture that best represents the distribution of the innovations and a straightforward sampler of the conditional posteriors we develop a bayesian markov chain monte carlo sampler to fully characterize the parametric and distributional uncertainty nested model comparisons and out of sample predictions with the cumulative marginal likelihoods and one day ahead predictive log bayes factors between the semiparametric and parametric versions of the asv model shows the semiparametric model projecting more accurate empirical market returns a major reason is how volatility responds to an unexpected market movement when the market is tranquil expected volatility reacts to a negative positive price shock by rising initially declining but then rising when the positive shock is large however when the market is volatile the degree of asymmetry and the size of the response in expected volatility is muted in other words when times are good no news is good news but when times are bad neither good nor bad news matters with regards to volatility

the collapsed gibbs sampler in bayesian computations with applications to a gene regulation problem abstract this article describes a method of grouping and collapsing in using the gibbs sampler and proves from an operator theory viewpoint that the method is in general beneficial the norms of the forward operators associated with the corresponding nonreversible markov chains are used to discriminate among different simulation schemes when applied to bayesian missing data problems the idea of collapsing suggests skipping the steps of sampling parameter s values in standard data augmentation by doing this we obtain a predictive update version of the gibbs sampler a procedure of calculating the posterior odds ratio via the collapsed gibbs sampler when incomplete observations are involved is presented as an illustration of possible applications three examples along with a bayesian treatment for identifying common protein binding sites in unaligned dna sequences are provided

bayesian nonparametric inference for random distributions and related functions in recent years bayesian nonparametric inference both theoretical and computational has witnessed considerable advances however these advances have not received a full critical and comparative analysis of their scope impact and limitations in statistical modelling many aspects of the theory and methods remain a mystery to practitioners and many open guestions remain in this paper we discuss and illustrate the rich modelling and analytic possibilities that are available to the statistician within the bayesian nonparametric and or semiparametric framework

the two parameter poisson dirichlet distribution derived from a stable subordinator the two parameter poisson dirichlet distribution denoted mathsf pd alpha theta is a probability distribution on the set of decreasing positive sequences with sum 1 the usual poisson dirichlet distribution with a single parameter theta introduced by kingman is mathsf pd 0 theta known properties of mathsf pd 0 theta including the markov chain description due to vershik shmidt and ignatov are generalized to the two parameter case the size biased random permutation of mathsf pd alpha theta is a simple residual allocation model proposed by engen in the context of species diversity and rediscovered by perman and the authors in the study of excursions of brownian motion and bessel processes for 0 alpha 1 mathsf pd alpha 0 is the asymptotic distribution of ranked lengths of excursions of a markov chain away from a state whose recurrence time distribution is in the domain of attraction of a stable law of index alpha formulae in this case trace back to work of darling lamperti and wendel in the 1950s and 1960s the distribution of ranked lengths of excursions of a one dimensional brownian motion is mathsf pd 1 2 0 and the corresponding distribution for a brownian bredge is mathsf pd 1 2 1 2 the mathsf pd alpha 0 and mathsf pd alpha alpha distributions admit a similar interpretation in terms of the ranked lengths of excursions of a semistable markov process whose zero set is the range of a stable subordinator of index alpha

farey graphs as models for complex networks farey sequences of irreducible fractions between 0 and 1 can be related to graph constructions known as farey graphs these graphs were first introduced by matula and kornerup in 1979 and further studied by colbourn in 1982 and they have many interesting properties they are minimally 3 colorable uniquely hamiltonian maximally outerplanar and perfect in this paper we introduce a simple generation method for a farey graph family and we study analytically relevant topological properties order size degree distribution and correlation clustering transitivity diameter and average distance we show that the graphs are a good model for networks associated with some complex systems

clustering coefficients of large networks abstract let g be a network with n nodes and eigenvalues 1 2 n then g is called an n d network if it is d regular and max 2 3 n it is shown that if g is an n d network and o d the average clustering coefficient c g of g satisfies c g d n for large d we show that this description also holds for strongly regular graphs and erd s renyi graphs although most real world networks are not constructed theoretically we find that many of them have c g close to d n and many close to 1 2 n d 1 d d 1 where d is the average degree of g and 2 is the average of the numbers of common neighbors over all non adjacent pairs of nodes

semiparametric bayesian inference in autoregressive panel data models this paper develops bayesian methods for inference in dynamic panel data models with individual effects and applies them to study longitudinal data on earnings from the panel study of income dynamics psid we study semiparametric versions of commonly used random effects autoregressive models in which the distribution of the disturbances is not restricted to fall in a parametric class to model the unknown distributions without resorting to strong parametric assumptions we draw upon recent advances in the theory and computation of nonparametric bayesian models using dirichlet process priors the overall approach can be viewed as an application of the general semiparametric bayesian approach of west muller and escobar 1994 which in turn makes use of results on bayesian density estimation by escobar 1994 and escobar and west 1995 most conventional panel data methods e g anderson and hsiao 1981 macurdy

regression analysis using dependent polya trees many commonly used models for linear regression analysis force overly simplistic shape and scale constraints on the residual structure of data we propose a semiparametric bayesian model for regression analysis that produces data driven inference by using a new type of dependent polya tree prior to model arbitrary residual distributions that are allowed to evolve across increasing levels of an ordinal covariate e g time in repeated measurement studies by modeling residual distributions at consecutive covariate levels or time points using separate but dependent polya tree priors distributional information is pooled while allowing for broad pliability to accommodate many types of changing residual distributions we can use the proposed dependent residual structure in a wide range of regression settings including fixed effects and mixed effects linear and nonlinear models for cross sectional prospective and repeated measurement data a simulation study illustrates the flexibility of our novel semiparametric regression model to accurately capture evolving residual distributions in an application to immune development data on immunoglobulin g antibodies in children our new model outperforms several contemporary semiparametric regression models based on a predictive model selection criterion copyright 2013 john wiley sons ltd

fractality in complex networks critical and supercritical skeletons fractal scaling char22 a power law behavior of the number of boxes needed to tile a given network with respect to the lateral size of the box char22 is studied we introduce a box covering algorithm that is a modified version of the original algorithm introduced by song et al nature london 433 392 2005 this algorithm enables easy implementation fractal networks are viewed as comprising a skeleton and shortcuts the skeleton embedded underneath the original network is a special type of spanning tree based on the edge betweenness centrality it provides a scaffold for the fractality of the network when the skeleton is regarded as a branching tree it exhibits a plateau in the mean branching number as a function of the distance from a root for nonfractal networks on the other hand the mean branching number decays to zero without forming a plateau based on these observations we construct a fractal network model by combining a random branching tree and local shortcuts the scaffold branching tree can be either critical or supercritical depending on the small worldness of a given network for the network constructed from the critical supercritical branching tree the average number of vertices within a given box grows with the lateral size of the box according to a power law an exponential form in the cluster growing method the critical and supercritical skeletons are observed in protein interaction networks and the world wide web respectively the distribution of box masses i e the number of vertices within each box follows a power law p m m ensuremath sim m ensuremath ensuremath eta the exponent ensuremath eta depends on the box lateral size ensuremath ell b for small values of ensuremath ell b ensuremath eta is equal to the degree exponent ensuremath gamma of a given scale free network whereas ensuremath eta approaches the exponent ensuremath tau ensuremath gamma ensuremath gamma ensuremath 1 as ensuremath ell b increases which is the exponent of the cluster size distribution of the random branching tree finally we study the perimeter h ensuremath alpha of a given box ensuremath alpha i e the number of edges connected to different boxes from a given box ensuremath alpha as a function of the box mass m b ensuremath alpha it is obtained that the average perimeter over the boxes with box mass m b is likely to scale as h m b ensuremath sim m b irrespective of the box size ensuremath ell b

pseudofractal scale free web we find that scale free random networks are excellently modeled by simple deterministic graphs our graph has a discrete degree distribution degree is the number of connections of a vertex which is characterized by a power law with exponent gamma 1 ln 3 ln 2 properties of this compact structure are surprisingly close to those of growing random scale free networks with gamma in the most interesting region between 2 and 3 we succeed to find exactly and numerically with high precision all main characteristics of the graph in particular we obtain the exact shortest path length distribution for a large network ln n 1 the distribution tends to a gaussian of width approximately sqrt ln n centered at l approximately ln n we show that the eigenvalue spectrum of the adjacency matrix of the graph has a power law tail with exponent 2 gamma

bayesian semiparametric modeling of realized covariance matrices this paper introduces several new bayesian nonparametric models suitable for capturing the unknown conditional distribution of realized covariance rcov matrices existing dynamic wishart models are extended to countably infinite mixture models of wishart and inverse wishart distributions in addition to mixture models with constant weights we propose models with time varying weights to capture time dependence in the unknown distribution each of our models can be combined with returns to provide a coherent joint model of returns and rcov the extensive forecast results show the new models provide very significant improvements in density forecasts for rcov and returns and competitive point forecasts of rcov

rao blackwellisation of sampling schemes summary this paper proposes a post simulation improvement for two common monte carlo methods the accept reject and metropolis algorithms the improvement is based on a rao blackwellisation method that integrates over the uniform random variables involved in the algorithms and thus post processes the standard estimators we show how the rao blackwellised versions of these algorithms can be implemented and through examples illustrate the improvement in variance brought by these new procedures we also compare the improved version of the metropolis algorithm with ordinary and rao blackwellised importance sampling procedures for independent and general metropolis set ups

small world to fractal transition in complex networks a renormalization group approach we show that renormalization group rg theory applied to complex networks is useful to classify network topologies into universality classes in the space of configurations the rg flow readily identifies a small world fractal transition by finding i a trivial stable fixed point of a complete graph ii a nontrivial point of a pure fractal topology that is stable or unstable according to the amount of long range links in the network and iii another stable point of a fractal with shortcuts that exist exactly at the small world fractal transition as a collateral the rg technique explains the coexistence of the seemingly contradicting fractal and small world phases and allows us to extract information on the distribution of shortcuts in real world networks a problem of importance for information flow in the system

nonparametric bayesian bioassay including ordered polytomous response abstract previous attempts at implementing fully bayesian nonparametric bioassay have enjoyed limited success due to computational difficulties we show here how this problem may be generally handled using a sampling based approach to develop desired marginal posterior distributions and their features a useful extension is presented which treats the case of ordered polytomous response illustrative examples are provided

retrospective markov chain monte carlo methods for dirichlet process hierarchical models inference for dirichlet process hierarchical models is typically performed using markov chain monte carlo methods which can be roughly categorized into marginal and conditional methods the former integrate out analytically the infinite dimensional component of the hierarchical model and sample from the marginal distribution of the remaining variables using the gibbs sampler conditional methods impute the dirichlet process and update it as a component of the gibbs sampler since this requires imputation of an infinite dimensional process implementation of the conditional method has relied on finite approximations in this paper we show how to avoid such approximations by designing two novel markov chain monte carlo algorithms which sample from the exact posterior distribution of quantities of interest the approximations are avoided by the new technique of retrospective sampling we also show how the algorithms can obtain samples from functionals of the dirichlet process the marginal and the conditional methods are compared and a careful simulation study is included which involves a non conjugate model different datasets and prior specifications

stick breaking autoregressive processes this paper considers the problem of defining a time dependent nonparametric prior for use in bayesian nonparametric modelling of time series a recursive construction allows the definition of priors whose marginals have a general stick breaking form the processes with poisson dirichlet and dirichlet process marginals are investigated in some detail we develop a general conditional markov chain monte carlo mcmc method for inference in the wide subclass of these models where the parameters of the marginal stick breaking process are nondecreasing sequences we derive a generalised polya urn scheme type representation of the dirichlet process construction which allows us to develop a marginal mcmc method for this case we apply the proposed methods to financial data to develop a semi parametric stochastic volatility model with a time varying nonparametric returns distribution finally we present two examples concerning the analysis of regional gdp and its growth

symmetry models and hypotheses for structured data layouts on peut utiliser des proprietes de symetrie pour deriver des tests valides d hypotheses nulles et pour construire des modeles statistiques appropries pour les donnees on developpe des idees generales et on les illustre dans le contexte d une classification a deux criteres

inverted berezinskii kosterlitz thouless singularity and high temperature algebraic order in an ising model on a scale free hierarchical lattice small world network we have obtained exact results for the ising model on a hierarchical lattice incorporating three key features characterizing many real world networks a scale free degree distribution a high clustering coefficient and the small world effect by varying the probability p of long range bonds the entire spectrum from an unclustered non small world network to a highly clustered small world system is studied using the self similar structure of the network we obtain analytic expressions for the degree distribution p k and clustering coefficient c for all p as well as the average path length ensuremath ell for p 0 and 1 the ferromagnetic ising model on this network is studied through an exact renormalization group transformation of the quenched bond probability distribution using up to 562 phantom rule 0 2em 0ex 500 renormalized probability bins to represent the distribution for pl0 494 we find power law critical behavior of the magnetization and susceptibility with critical exponents continuously varying with p and exponential decay of correlations away from t c for p ensuremath ge 0 494 in fact where the network exhibits small world character the critical behavior radically changes we find a highly unusual phase transition namely an inverted berezinskii kosterlitz thouless singularity between a low temperature phase with nonzero magnetization and finite correlation length and a high temperature phase with zero magnetization and infinite correlation length with power law decay of correlations throughout the phase approaching t c from below the magnetization and the susceptibility respectively exhibit the singularities of mathrm exp ensuremath c sqrt t c ensuremath t and mathrm exp d sqrt t c ensuremath t with c and d positive constants with long range bond strengths decaying with distance we see a phase transition with power law critical singularities for all p and evaluate an unusually narrow critical region and important corrections to power law behavior that depend on the exponent characterizing the decay of long range interactions

bayesian analysis of stochastic volatility models with fat tails and correlated errors abstract the basic univariate stochastic volatility model specifies that conditional volatility follows a log normal auto regressive model with innovations assumed to be independent of the innovations in the conditional mean equation since the introduction of practical methods for inference in the basic volatility model j business econom statist 12 4 371 it has been observed that the basic model is too restrictive for many financial series we extend the basic svol to allow for a so called leverage effect via correlation between the volatility and mean innovations and for fat tails in the mean equation innovation a bayesian markov chain monte carlo algorithm is developed for the extended volatility model thus far likelihood based inference for the correlated svol model has not appeared in the literature we develop bayes factors to assess the importance of the leverage and fat tail extensions sampling experiments reveal little loss in precision from adding the model extensions but a large loss from using the basic model in the presence of mis specification there is overwhelming evidence of a leverage effect for weekly and daily equity indices the evidence in favor of fat tails is very strong for daily exchange rate and equity indices but less so for weekly data we also find that volatility estimates from the extended model are markedly different from those produced by the basic svol