nonparametric bayes conditional distribution modeling with variable selection this article considers a methodology for flexibly characterizing the relationship between a response and multiple predictors goals are 1 to estimate the conditional response distribution addressing the distributional changes across the predictor space and 2 to identify important predictors for the response distribution change both within local regions and globally we first introduce the probit stick breaking process psbp as a prior for an uncountable collection of predictor dependent random distributions and propose a psbp mixture psbpm of normal regressions for modeling the conditional distributions a global variable selection structure is incorporated to discard unimportant predictors while allowing estimation of posterior inclusion probabilities local variable selection is conducted relying on the conditional distribution estimates at different predictor points an efficient stochastic search sampling algorithm is proposed for posterior computation the methods are illustrated through simulation and applied to an epidemiologic study

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 note on k theory and triangulated categories we provide an example of two closed model categories having equivalent homotopy categories but different waldhausen k theories we also show that there cannot exist a functor from small triangulated categories to spaces which recovers quillen s k theory for exact categories and which satisfies localization

stein compacts in levi flat hypersurfaces we explore connections between geometric properties of the levi foliation of a levi flat hypersurface m and holomorphic convexity of compact sets in m or bounded in part by m applications include extendability of cauchy riemann functions solvability of the b equation approximation of cauchy riemann and holomorphic functions and global regularity of the neumann operator

on the analyticity of cr diffeomorphisms in any positive cr dimension and cr codimension we provide a construction of real analytic embedded cr structures which are c infty cr equivalent but are inequivalent holomorphically

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

on the cr structure of compact group orbits associated with bounded symmetric domains let e be a complex vector space of finite dimension and let k gl e be a compact connected subgroup then for fixed a e the orbit k k a is a real analytic submanifold of e that inherits various structures from e for instance choosing a k invariant positive definite inner product x y on e makes k a riemannian manifold on which k acts transitively by isometries on the other hand k inherits from e a cauchy riemann structure cr structure that is given by the distribution of the maximal complex subspaces hx k tx k itx k of the real tangent spaces tx k e x k together with the complex structure on every hx k multiplication by i the subspace hx k is called the holomorphic tangent space to k at x see 9 and 4 as general references for cr manifolds of interest for the geometry of the orbit k k a with respect to its cr structure is the study of the cr functions or more generally cr mappings on k i e of smooth functions f k c that satisfy the tangential cauchy riemann differential equations in the sense that the restriction of the differential df to every holomorphic tangent space is complex linear for instance all holomorphic functions defined in an open neighbourhood of k e give by restriction real analytic cr functions on k actually we deal with the more general continuous cr functions on k which satisfy by definition the tangential cr equations in the distribution sense or equivalently which are locally uniform limits of sequences of smooth cr functions due to the approximation theorem of baouenditreves 6 in this context it is of interest to determine the space of all

necessary and sufficient conditions for the local solvability in hyperfunctions of a class of systems of complex vector fields a necessary and sufficient condition is proved for the validity of the poincare lemma in degreeq 1 in the differential complex attached to a locally integrable structure of codimension one in spaces of hyperfunctions the base manifold is only assumed to be smooth the hyperfunctions are defined in the hypo analytic structure associated to a smooth first integral z the condition is that the singular homology of the fibres of the map z be trivial in dimensionq 1 by the approximation formula of bt the germ of this fibration at a point is independent of the choice of the first integral z

the localization sequence for the algebraic k theory of topological k theory we verify a conjecture of rognes by establishing a localization cofiber sequence of spectra k mathbb z to k ku to k ku to sigma k mathbb z for the algebraic k theory of topological k theory we deduce the existence of this sequence as a consequence of a devissage theorem identifying the k theory of the waldhausen category of finitely generated finite stage postnikov towers of modules over a connective a infty ring spectrum r with the quillen k theory of the abelian category of finitely generated pi 0 r modules

complex manifolds in q convex boundaries we consider a c infty boundary b omega subset mathbb c n which is q convex in the sense that its levi form has positive trace on every complex q plane we prove that b omega is tangent of infinite order to the complexification of each of its submanifolds which is complex tangential and of finite bracket type this generalizes diederich and fornaess ann math 107 371 384 1978 from pseudoconvex to q convex domains we also readily prove that the rows of the levi form are frac 1 2 subelliptic multipliers for the bar partial neumann problem on q forms cf ho in math ann 290 3 18 1991 this allows to run the kohn algorithm of acta math 142 79 122 1979 in the chain of ideals of subelliptic multipliers for q forms if b omega is real analytic and the algorithm gets stuck on q forms then it produces a variety of holomorphic dimension q and in fact by our result above a complex q manifold which is not only tangent but indeed contained in b omega altogether the absence of complex q manifolds in b omega produces a subelliptic estimate on q forms

ω hypoelliptic differential operators of constant strength abstract we study hypoelliptic differential operators of constant strength we show that any operator with constant strength and coefficients in e which is homogeneous hypoelliptic is also hypoelliptic for any weight function o we also present a sufficient condition in order to ensure that a differential operator admits a parametrix and as a consequence we obtain some conditions on the weights to conclude that for any operator p x d with constant strength the hypoellipticity of the frozen operator p x0 d implies the hypoellipticity of p x d this requires the use of pseudodifferential operators

the mizohata structure on the sphere we prove that a compact surface that admits a mizohata structure is homeomorphic to a sphere and that there exists exactly one such structure l up to conjugation by diffeomorphisms we also characterize the range and the kernel of the operator 0 induced by l i e obtained from the exterior derivative on functions by passing to the quotient modulo l

negative k theory of derived categories we define negative k groups for exact categories and for derived categories in the framework of frobenius pairs generalizing definitions of bass karoubi carter pedersen weibel and thomason we prove localization and vanishing theorems for these groups devissage for noetherian abelian categories additivity and resolution hold we show that the first negative k group of an abelian category vanishes and that in general negative k groups of a noetherian abelian category vanish our methods yield an explicit non connective delooping of the k theory of exact categories and chain complexes generalizing constructions of wagoner and pedersen weibel extending a theorem of auslander and sherman we discuss the k theory homotopy fiber of e e and its implications for negative k groups in the appendix we replace waldhausen s cylinder functor by a slightly weaker form of non functorial factorization which is still sufficient to prove his approximation and fibration theorems

efficient calculation of the normalizing constant of the autologistic and related models on the cylinder and lattice motivated by the autologistic model for the analysis of spatial binary data on the two dimensional lattice we develop efficient computational methods for calculating the normalizing constant for models for discrete data defined on the cylinder and lattice because the normalizing constant is generally unknown analytically statisticians have developed various ad hoc methods to overcome this difficulty our aim is to provide computationally and statistically efficient methods for calculating the normalizing constant so that efficient likelihood based statistical methods are then available for inference we extend the so called transition method to find a feasible computational method of obtaining the normalizing constant for the cylinder boundary condition to extend the result to the free boundary condition on the lattice we use an efficient path sampling markov chain monte carlo scheme the methods are generally applicable to association patterns other than spatial such as clustered binary data and to variables taking three or more values described by for example potts models

extension of cr functions into weighted wedges through families of nonsmooth analytic discs the goal of this paper is to develop a theory of nonsmooth analytic discs attached to domains with lipschitz boundary in real submanifolds of c n we then apply this technique to establish a propagation principle for wedge extendibility of cr functions on these domains along cr curves and along boundaries of attached analytic discs the technique from this paper has been also extensively used by the authors recently to obtain sharp results on wedge extension of cr functions on wedges in prescribed directions extending results of boggess polking and eastwood graham

compactness of the neumann problem on convex domains the neumann operator on 0 q forms 1 q n on a bounded convex domain in cnis compact if and only if the boundary of contains no complex analytic equivalently affine variety of dimension greater than or equal toq

a rudin carleson theorem for planar vector fields this paper generalizes the rudin carleson theorem for homogeneous solutions of locally solvable real analytic vector fields

on the analyticity of solutions of first order nonlinear pde let x t e r m r and u e c 2 r m r we discuss local and microlocal analyticity for solutions u to the nonlinear equation u t f x t u u x here f x t 0 is complex valued and analytic in all arguments we also assume f to be holomorphic in 0 e c c m in particular we show that wf a u char l u where wf a denotes the analytic wave front set and char l u is the characteristic set of the linearized operator l u f j x t u u x x j

on noncompactness of the neumann problem on pseudoconvex domains in c3 abstract we prove that a smooth bounded pseudoconvex domain c 3 with a one dimensional complex manifold m in its boundary has a noncompact neumann operator on 0 1 forms under the additional assumption that b has finite regular d angelo 2 type at a point of m

kernel stick breaking processes we propose a class of kernel stick breaking processes for uncountable collections of dependent random probability measures the process is constructed by first introducing an infinite sequence of random locations independent random probability measures and beta distributed random weights are assigned to each location predictor dependent random probability measures are then constructed by mixing over the locations with stick breaking probabilities expressed as a kernel multiplied by the beta weights some theoretical properties of the process are described including a covariate dependent prediction rule a retrospective markov chain monte carlo algorithm is developed for posterior computation and the methods are illustrated using a simulated example and an epidemiological application

bayesian curve fitting with free knot splines we describe a bayesian method for fitting curves to data drawn from an exponential family that uses splines for which the number and locations of knots are free parameters the method uses reversible jump markov chain monte carlo to change the knot configurations and a locality heuristic to speed up mixing for nonnormal models we approximate the integrated likelihood ratios needed to compute acceptance probabilities by using the bayesian information criterion bic under priors that make this approximation accurate our technique is based on a marginalised chain on the knot number and locations but we provide methods for inference about the regression coefficients and functions of them in both normal and nonnormal models simulation results suggest that the method performs well and we illustrate the method in two neuroscience applications

removable singularities of cr functions on singular boundaries the problem of analytic representation of integrable cr functions on hypersurfaces with singularities is treated the nature of singularities does not matter while the set of singularities has surface measure zero for simple singularities like cuspidal points edges corners etc also the behaviour of representing analytic functions near singular points is studied

holomorphic extension of cr functions from quadratic cones it is proved that cr functions on a quadratic cone m in mathbb c n n 1 admit one sided holomorphic extension if and only if m does not have two sided support a geometric condition on m which generalizes minimality in the sense of tumanov a biholomorphic classification of quadratic cones in mathbb c 2 is also given

an efficient markov chain monte carlo method for distributions with intractable normalising constants maximum likelihood parameter estimation and sampling from bayesian posterior distributions are problematic when the probability density for the parameter of interest involves an intractable normalising constant which is also a function of that parameter in this paper an auxiliary variable method is presented which requires only that independent samples can be drawn from the unnormalised density at any particular parameter value the proposal distribution is constructed so that the normalising constant cancels from the metropolis hastings ratio the method is illustrated by producing posterior samples for parameters of the ising model given a particular lattice realisation

versal embeddings of compact 3 pseudoconcave cr submanifolds we prove that for an induced cr structure on a compact generic regular 3 pseudoconcave cr submanifold open image in new window of a complex manifold g satisfying condition dim h1 m t g m 0 all the close cr structures are induced by close embeddings

local solvability for top degree forms in a class of systems of vector fields we study the local exactness at the top degree level in the differential complex defined by a smooth locally integrable structure of rank n in inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i if z denotes a local first integral of the structure it is proved that the vanishing of the local cohomology in degree n is implied by the absence of compact connected components of the fibers z const this adds one more result towards the verification of a conjecture due to f treves regarding the vanishing of the local cohomology of such complexes of differential operators

algebraic k theory and abstract homotopy theory abstract we decompose the k theory space of a waldhausen category in terms of its dwyer kan simplicial localization this leads to a criterion for functors to induce equivalences of k theory spectra that generalizes and explains many of the criteria appearing in the literature we show that under mild hypotheses a weakly exact functor that induces an equivalence of homotopy categories induces an equivalence of k theory spectra

analytic discs attached to conormal bundles of cr manifolds abstract letmbe a cr submanifold ofx c n t m xthe conormal bundle tominx zo resp po a point ofm resp t m x def t m x 0 with po zo aa small analytic disc c1up to the boundary attached tomthroughzo a aliftofatot xthroughpoattachedt m x if the levi form ofmhas a constant number of negative eigenvalues in a neighborhood ofp0then we show that in factais contained inmanda int m x whenmis a hypersurface and it is pseudoconvex i e the number of its negative levi eigenvalues is identically 0 then the inclusiona mis classical and follows from the hopf lemma applied to a plurisubharmonic exhaustion function as in d f note that in this case the existence of a lifta t m xis automatic according to b f 1980 math subject classification 1985 revision 32 f

the hartogs phenomenon on weakly pseudoconcave hypersurfaces in 2002 henkin and michel proved a local hartogs phenomenon for real analytic cr functions on real analytic weakly pseudoconcave cr manifolds the aim of the present article is to remove the assumptions on real analyticity in the case of weakly pseudoconcave hypersurfaces m subset mathbb c n if m is a graph of class mathcal c 2 and n 3 a global theorem is proved for the extension of holomorphic germs along m if the appearing domains have nicely shaped boundary a hartogs theorem even holds for continuous cr functions where the difference to the case of holomorphic germs relies on the possible presence of lower dimensional cr orbits levi flat hypersurfaces in mathbb c 2 require a separate treatment here an affirmative answer is given to the question of tomassini whether 2 spheres bound 3 balls in m

extension of cr functions on wedges we generalize the extension theorem of ajrapetyan henkin ah81 and boggess polking bp82 to wedge like domains v in a generic manifold m for each complex tangent vector to m we introduce its complex angle with respect to v and show that cr functions on v have natural extension in the direction of the levi form of any tangent vector whose angle is greater than 2 this gives an explanation of the extension phenomenon recently discovered by eastwood graham eg99 eg01 we further demonstrate by an example that the angle 2 is optimal and cannot be replaced by any smaller angle we conclude by giving applications to holomorphic extension to a full neighborhood of the reference point

on boundary properties of solutions of complex vector fields abstract this work presents results on the boundary properties of solutions of a complex planar smooth vector field l classical results in the h p theory of holomorphic functions of one variable are extended to the solutions of a class of nonelliptic complex vector fields

a property of the functions and distributions annihilated by a locally integrable system of complex vector fields page introduction 387 1 basic notation and ingredients 389 2 approximation and constancy on the fibers of the classical solutions of the homogeneous equations 393 3 first consequences and interpretation of the fundamental theorem 398 4 distribution solutions of the homogeneous equations 402 5 regularity of the solutions of the homogeneous equations 409 6 example of a system that is analytic hypo elliptic but not co hypo elliptic 413 references 420

global homotopy with ck estimates for a family of compact regular q pseudoconcave cr manifolds let m 0 be a compact regular q pseudoconcave cr submanifold of a complex manifold g and open image in new window a holomorphic vector bundle on g such that dim open image in new window for some fixed r q we prove a global homotopy formula with c k estimates for r cohomology of open image in new window on arbitrary cr submanifold m close enough to m 0

analytic discs plurisubharmonic hulls and non compactness of the neumann operator we show that a complex manifold m in the boundary of a smooth bounded pseudoconvex domain in open image in new window is an obstruction to compactness of the open image in new window neumann operator on provided that at some point of m the levi form of b has the maximal possible rank n 1 dim m i e the boundary is strictly pseudoconvex in the directions transverse to m in particular an analytic disc is an obstruction provided that at some point of the disc the levi form has only one zero eigenvalue i e the eigenvalue zero has multiplicity one we also show that a boundary point where the levi form has only one zero eigenvalue can be picked up by the plurisubharmonic hull of a set only via an analytic disc in the boundary

a bayesian nonparametric regression model with normalized weights a study of hippocampal atrophy in alzheimer s disease hippocampal volume is one of the best established biomarkers for alzheimer s disease however for appropriate use in clinical trials research the evolution of hippocampal volume needs to be well understood recent theoretical models propose a sigmoidal pattern for its evolution to support this theory the use of bayesian nonparametric regression mixture models seems particularly suitable due to the flexibility that models of this type can achieve and the unsatisfactory predictive properties of semiparametric methods in this article our aim is to develop an interpretable bayesian nonparametric regression model which allows inference with combinations of both continuous and discrete covariates as required for a full analysis of the dataset simple arguments regarding the interpretation of bayesian nonparametric regression mixtures lead naturally to regression weights based on normalized sums difficulty in working with the intractable normalizing constant is overcome thanks to recent advances in mcmc

k theory and derived equivalences we show that if two rings have equivalent derived categories then they have the same algebraic k theory similar results are given for g theory and for a large class of abelian categories

analytic regularity for an operator with treves curves we study a partial differential operator h with analytic coefficients which is of the form sum of squares h is hypoelliptic on any open subset of r3 yet possesses the following properties 1 h is not analytic hypoelliptic on any open subset of r3 that contains 0 2 if u is any distribution defined near 0 r3 with the property that hu is analytic near 0 then u must be analytic near 0 3 the point 0 lies on the projection of an infinite number of treves curves bicharacteristics these results are consistent with the treves conjectures however it follows that the analog of treves conjecture in the sense of germs is false as far as we know h is the first example of a sum of squares operator which is not analytic hypoelliptic in the usual sense yet is analytic hypoelliptic in the sense of germs

reversible jump markov chain monte carlo computation and bayesian model determination markov chain monte carlo methods for bayesian computation have until recently been restricted to problems where the joint distribution of all variables has a density with respect to some fixed standard underlying measure they have therefore not been available for application to bayesian model determination where the dimensionality of the parameter vector is typically not fixed this paper proposes a new framework for the construction of reversible markov chain samplers that jump between parameter subspaces of differing dimensionality which is flexible and entirely constructive it should therefore have wide applicability in model determination problems the methodology is illustrated with applications to multiple change point analysis in one and two dimensions and to a bayesian comparison of binomial experiments

admissible boundary values of bounded holomorphic functions in wedges if m c n is a generic cauchy riemann manifold and w c n is a wedge domain with edge m then every bounded holomorphic function on w has an admissible limit at almost every point of m moreover if a holomorphic function f on w has a distribution boundary value bv f on m that is a bounded measurable function then f is bounded on every finer wedge near m and its admissible limit equals bv f p at almost every point p m

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

on the f and m riesz theorem on wedges with edges of class c 1 α this work extends the classical f and m riesz theorem to measures that are boundary values of holomorphic functions defined on wedges in mathbb c n with edges that are in the class c1

on the integrals of a singular real analytic differential form in ⁿ in this paper we study the constancy on the fibers for the continuous integrals of a complex valued real analytic differential form in rn then we prove an isomorphism result between the space of smooth integrals and a space built from spaces of whitney functions

thin discs and a morera theorem for cr functions f z dz 0 for every closed curve in d there are generalizations of this theorem to domains and real hypersurfaces in cn see a and gs and references there in this paper we obtain a version of the morera theorem for cr functions on manifolds of higher codimension let m be a smooth real manifold in cn recall that m is generic if the tangent space tz m spans the whole space cn for z m a cr function on m is a continuous function that satisfies the weak tangential cauchy riemann equations an analytic disc is a continuous mapping a cn holomorphic in the standard disc c 1 we say that the disc a is attached to m if it maps the circle b to m that is a b m let f be a continuous function on a real manifold m cn we say that f has the morera property with respect to an analytic disc a attached to m if

derived l adic zeta functions abstract let k 0 v k be the grothendieck group of k varieties campbell and zakharevich have constructed a higher algebraic k theory spectrum k v k such that 0 k v k k 0 v k in this paper we construct non trivial classes in the higher homotopy groups of k v k when k is finite or a subfield of c to do this we give a recipe for lifting motivic measures k 0 v k k 0 e to maps of spectra k v k k e we consider two special cases the classical local zeta function thought of as a homomorphism k 0 v f q k 0 end q l and the compactly supported euler characteristic thought of as a homomorphism k 0 v c k 0 q we use lifts of these motivic measures to prove that the grothendieck spectrum of varieties contains nontrivial geometric information in its higher homotopy groups by showing that the map s k v k is nontrivial in higher dimensions when k is finite or a subfield of c and moreover that when k is finite this map is not surjective on higher homotopy groups