sign restrictions structural vector autoregressions and useful prior information this paper makes the following original contributions to the literature i we develop a simpler analytical characterization and numerical algorithm for bayesian inference in structural vector autoregressions vars that can be used for models that are overidentified just identified or underidentified ii we analyze the asymptotic properties of bayesian inference and show that in the underidentified case the asymptotic posterior distribution of contemporaneous coefficients in an n variable var is confined to the set of values that orthogonalize the population variance covariance matrix of ordinary least squares residuals with the height of the posterior proportional to the height of the prior at any point within that set for example in a bivariate var for supply and demand identified solely by sign restrictions if the population correlation between the var residuals is positive then even if one has available an infinite sample of data any inference about the demand elasticity is coming exclusively from the prior distribution iii we provide analytical characterizations of the informative prior distributions for impulse response functions that are implicit in the traditional sign restriction approach to vars and we note as a special case of result ii that the influence of these priors does not vanish asymptotically iv we illustrate how bayesian inference with informative priors can be both a strict generalization and an unambiguous improvement over frequentist inference in just identified models v we propose that researchers need to explicitly acknowledge and defend the role of prior beliefs in influencing structural conclusions and we illustrate how this could be done using a simple model of the u s labor market

vortices in holomorphic line bundles over closed kahler manifolds we apply a modified yang mills higgs functional to unitary bundles over closed kahler manifolds and study the equations which govern the global minima the solutions represent vortices in holomorphic bundles and are direct analogs of the vortices overr2 we obtain a complete description of the moduli space of these new vortices where the bundle is of rank one the description is in terms of a class of divisors in the base manifold there is also a dependence on a real valued parameter which can be attributed to the compactness of the base manifold

frequentist validity of posterior quantiles in the presence of a nuisance parameter higher order asymptotics given a random sample from a distribution with density function that depends on an unknown parameter 1 2 we are concerned with frequentist validity up to o n 1 of posterior quantiles of 1 treating 2 as a nuisance parameter we propose to make the best choice of the prior on by matching as far as practicable the posterior and frequentist coverage probabilities up to o n 1

probability matching priors for non regular cases we study probability matching priors in non regular cases both one parameter and multi parameter cases are considered the resulting priors are shown to satisfy certain differential equations several examples are discussed it is observed that the reference prior in the sense of bernardo is in many cases also probability matching as a necessary tool for finding such priors asymptotic expansion of posterior distributions for multi parameter non regular cases is also obtained

on the invariance of noninformative priors various noninformative priors have been proposed in the literature this article explores the invariance or lack thereof of some of these noninformative priors including the reference prior of berger and bernardo the reverse reference prior of j k ghosh and the probabilitymatching prior of peers and stein under reparameterization berger and bernardo s m group ordered reference prior is shown to remain invariant under a special type of reparameterization the reverse reference prior of j k ghosh is shown not to remain invariant under reparameterization however the probability matching prior is shown to remain invariant under any reparameterization also for spherically symmetric distributions certain noninformative priors are derived using the principle of group invariance

generalization of jeffreys divergence based priors for bayesian hypothesis testing summary we introduce objective proper prior distributions for hypothesis testing and model selection based on measures of divergence between the competing models we call them diver gence based db priors db priors have simple forms and desirable properties like information finite sample consistency and are often similar to other existing proposals like intrinsic priors moreover in normal linear model scenarios they reproduce the jeffreys zellner siow priors exactly most importantly in challenging scenarios such as irregular models and mixture mod els db priors are well defined and very reasonable whereas alternative proposals are not we derive approximations to the db priors as well as markov chain monte carlo and asymptotic expressions for the associated bayes factors

the moduli space of twisted holomorphic maps with lagrangian boundary condition compactness abstract let x be a compact symplectic manifold and l be a compact lagrangian submanifold suppose that x l has a hamiltonian s 1 action with moment map take an s 1 invariant compatible almost complex structure and we consider tuples c p a where c is a smooth bordered riemann surface of fixed topological type p c is an s 1 principal bundle a is a connection on p and is a section of p s 1 x satisfying a 0 f a c with boundary condition c p s 1 l here f a is the curvature of a and is a volume form on c and c i r is a constant we compactify the moduli space of isomorphism classes of such objects with energy k where the energy is defined to be the yang mills higgs functional f a l 2 2 d a l 2 2 c l 2 2 this generalizes the compactness theorem of mundet tian 2009 17 in the case of closed riemann surfaces

on priors providing frequentist validity of bayesian inference for multiple parametric functions summary we characterise priors which match up to o n 1 the posterior joint cumulative distribution function of multiple parametric functions with the corresponding frequentist cumulative distribution function this work extends and unifies the work of ghosh mukerjee 1993 and datta ghosh 1995a on the topic of probability matching priors a set of necessary and sufficient conditions is obtained for the above characterisation some of these conditions depend only on the parametric functions and not on the prior examples are given where the joint probability matching is possible and where it is not possible

bayesian prediction with approximate frequentist validity we characterize priors which asymptotically match the posterior coverage probability of a bayesian prediction region with the corresponding frequentist coverage probability this is done considering both posterior quantiles and highest predictive density regions with reference to a future observation the resulting priors are shown to be invariant under reparameterization the role of jeffreys prior in this regard is also investigated it is further shown that for any given prior it may be possible to choose an interval whose bayesian predictive and frequentist coverage probabilities are asymptotically matched

some remarks on noninformative priors abstract this article focuses primarily on a comparison between the reference priors of berger and bernardo and the reverse reference priors suggested by j k ghosh sufficient conditions are given that provide agreement between the two classes of priors several examples are given showing the agreement or disagreement between the two in addition these priors are compared under a criterion that requires the frequentist coverage probability of the posterior region of a real valued parametric function to match a nominal level with a remainder of o n 1 where n denotes the sample size the latter priors first introduced by welch and peers are obtained by solving a differential equation due to peers finally in the presence of several parameters of interest a general class of priors that satisfies the matching criterion separately for each parameter is constructed and examples are given to illustrate how reference or reverse reference priors fit within this class of priors

the effects of measurement error and vowel selection on the locus equation measure of coarticulationa effects on the slope of introducing error in the f2 hz values in locus equations les and of using fewer than ten vowels were investigated for each of the initial consonants b d g 2000 simulated sets were generated using monte carlo techniques the sets were altered with 50 100 or 200 hz error being randomly applied to each f2 value within a set selected vowels were then removed from the sets and the effects on the slopes were measured results suggest that the le slopes are generally resistant to error and reduced number of vowels effects of adding 50 hz of random error to the f2 values in sets using eight or ten vowels were minimal yielding a mean absolute change in slope less than 0 07

compactness in the adiabatic limit of disk vortices this paper is the first input towards an open analogue of the quantum kirwan map we consider the adiabatic limit of the symplectic vortex equation over the unit disk for a hamiltonian g manifold with lagrangian boundary condition by blowing up the metric on the disk we define an appropriate notion of stable solutions in the limit and prove that any sequence of disk vortices with energy uniformly bounded has a subsequence converging to such a stable object we also proved several analytical properties of vortices over the upper half plane which are new type of bubbles appearing in our compactification

noninformative priors for one parameter of many summary we consider the problem of constructing a prior that is noninformative for a single parameter in the presence of nuisance parameters our approach is to require that the resulting marginal posterior intervals have accurate frequentist coverage stein 1985 derived nonrigorously a sufficient condition for such a prior through the use of orthogonal parameters we give a general form for the class of priors satisfying stein s condition the priors are proportional to the square root of the information element for the parameter of interest times an arbitrary function of the nuisance parameters this is in contrast to jeffreys 1946 invariant prior for the overall parameter which is proportional to the square root of the determinant of the information matrix several examples are given and comparisons are made to the reference priors of bernardo 1979

reference prior bayesian analysis for normal mean products abstract two reference priors for the product of means of n normal distributions with common known variance are developed one of them induces an improper posterior distribution and therefore is not of much interest the other is a generalized form of the n 2 case derived by berger and bernardo the latter is compared with the uniform prior the jeffreys prior in posterior inference and the optimal frequentist coverage criterion the reference prior is shown to be better than the uniform prior in the sense of correct frequentist coverage probability of the posterior quantile by numerical computation the computation was performed by gibbs sampling for n 3 and n 10 furthermore it is shown that the reference prior is among the asymptotic optimal frequentist coverage probability priors under a transformation of the parameter space such that the parameter of interest and the nuisance parameters are orthogonal in an example the bayesian credible interval for the product of normal means using the re

the self duality equations on a riemann surface in this paper we shall study a special class of solutions of the self dual yang mills equations the original self duality equations which arose in mathematical physics were defined on euclidean 4 space the physically relevant solutions were the ones with finite action the so called instantons the same equations may be dimensionally reduced to euclidean 3 space by imposing invariance under translation in one direction these equations also have physical relevance the solutions which have finite action in three dimensions are the magnetic monopoles if we take the reduction process one step further and consider solutions which are invariant under two translations we obtain a set of equations in the plane here however there is no clear physical meaning and indeed attempts to find finite action solutions have failed nevertheless these are the equations we shall consider despite the lack of interesting solutions in r2 the equations have the important property conformal invariance which allows them to be defined on manifolds modelled on r2 by conformal maps namely riemann surfaces we shall consider here solutions of the self duality equations defined on a compact riemann surface there are in fact solutions as we shall show and the moduli space of all solutions turns out to be a manifold with an extremely rich geometric structure which will be the focus of our study it brings together in a harmonious way the subjects of riemannian geometry topology algebraic geometry and symplectic geometry illuminating all these facets of the same object accounts for the length of this paper the self duality equations are equations from gauge theory geometrically they are defined in terms of connections on principal bundles while the group of the principal bundle may be chosen arbitrarily for the equations to make sense we restrict attention here to the simplest case of su 2 or so 3 there are two reasons for this the first and most obvious is that it simplifies calculations and avoids the use of inductive processes which are inherent in the consideration of a general lie group of higher rank the second reason is that solutions for su 2 have an intimate relationship with the internal structure of the riemann surface as a consequence of results we shall prove about solutions to the self duality equations we learn something about the moduli space of complex structures on the surface itself namely teichmuller space

enriched conjugate and reference priors for the wishart family on symmetric cones a general wishart family on a symmetric cone is a natural exponential family nef having a homogeneous quadratic variance function using results in the abstract theory of euclidean jordan algebras the structure of conditional reducibility is shown to hold for such a family and we identify the associated parameterization and analyze its properties the enriched standard conjugate family for and the mean parameter are defined and discussed this family is considerably more flexible than the standard conjugate one the reference priors for and are obtained and shown to belong to the enriched standard conjugate family in particular this allows us to verify that reference posteriors are always proper the above results extend those available for nefs having a simple quadratic variance function specifications of the theory to the cone of real symmetric and positive definite matrices are discussed in detail and allow us to perform bayesian inference on the covariance matrix of a multivariate normal model under the enriched standard conjugate family in particular commonly employed bayes estimates such as the posterior expectation of and 1 are provided in closed form

the selection of prior distributions by formal rules abstract subjectivism has become the dominant philosophical foundation for bayesian inference yet in practice most bayesian analyses are performed with so called noninformative priors that is priors constructed by some formal rule we review the plethora of techniques for constructing such priors and discuss some of the practical and philosophical issues that arise when they are used we give special emphasis to jeffreys s rules and discuss the evolution of his viewpoint about the interpretation of priors away from unique representation of ignorance toward the notion that they should be chosen by convention we conclude that the problems raised by the research on priors chosen by formal rules are serious and may not be dismissed lightly when sample sizes are small relative to the number of parameters being estimated it is dangerous to put faith in any default solution but when asymptotics take over jeffreys s rules and their variants remain reasonable choices we also provide an annotated b

a compactification of the moduli space of twisted holomorphic maps abstract given compact symplectic manifold x with a compatible almost complex structure and a hamiltonian action of s 1 with moment map x i r and a real number k 0 we compactify the moduli space of twisted holomorphic maps to x with energy k this moduli space parameterizes equivalence classes of tuples c p a where c is a smooth compact complex curve of fixed genus g p is a principal s 1 bundle over c a is a connection on p and is a section of p s 1 x satisfying a 0 v f a c f a l 2 2 d a l 2 2 c l 2 2 k here f a is the curvature of a v is the restriction to c of a volume form on the universal curve over m g and c is a fixed constant two tuples c p a and c p a are equivalent if there is a morphism of bundles p p lifting a biholomorphism c c such that v v a a and the topology of the moduli space is the quotient topology of the topology of c convergence on the set of tuples c p a we also incorporate marked points in the picture there are two sources of noncompactness first bubbling off phenomena analogous to the one in gromov witten theory second degeneration of c to nodal curves in this case there appears a phenomenon which is not present in gromov witten near the nodes the section may degenerate to a chain of gradient flow lines of i

implications of reference priors for prior information and for sample size abstract here we use posterior densities based on relative entropy reference priors for two purposes the first purpose is to identify data implicit in the use of informative priors we represent an informative prior as the posterior from an experiment with a known likelihood and a reference prior minimizing the relative entropy distance between this posterior and the informative prior over choices of data results in a data set that can be regarded as representative of the information in the informative prior the second implication from reference priors is obtained by replacing the informative prior with a class of densities from which one might wish to make inferences for each density in this class one can obtain a data set that minimizes a relative entropy the maximum of these sample sizes as the inferential density varies over its class can be used as a guess as to how much data is required for the desired inferences we bound this sample size above and below by other techniques that permit it to

evaluation of a strategy for automatic formant tracking variations on an automatic formant tracking strategy developed at alberta will be compared to manual formant measurements from two databases of vowels spoken by men women and children in texas or michigan correct vowel formant candidates for f1 f2 and f3 may be found roughly 85 90 percent of the time for adult male speakers using autocorrelation lpc with the following settings f3 maximum at 3000 hz lpc order of 14 sampling rate of 10 khz j markel and a gray linear prediction of speech springer new york 1975 experience shows good results are also often found with females and children s speech provided the sampling rate and f3 maximum are scaled appropriately for each speaker our new basic strategy involves analyzing each utterance at several distinct sampling rates and coordinated f3 cutoff frequencies with a fixed lpc order each scaling choice provides an independent set of candidates that is post processed by a simple tracking algorithm a correlation measure between a spectrogram of the original signal and one resynthesized from each estimated track set is defined this measure is combined with other heuristic figures of merit based on e g continuity formant ranges and bandwidths to choose the best analysis

second order probability matching priors summary the paper considers priors obtained by ensuring approximate frequentist validity of a posterior quantiles and of b the posterior distribution function it is seen that at the second order of approximation the two approaches do not necessarily lead to identical conclusions examples are given to illustrate this the role of invariance in the context of probability matching is also discussed

invariant connections and vortices we study the vortex equations on a line bundle over a compact kahler manifold these are a generalization of the classical vortex equations over 2 we first prove an invariant version of the theorem of donaldson uhlenbeck and yau relating the existence of a hermitian yang mills metric on a holomorphic bundle to the stability of such a bundle we then show that the vortex equations are a dimensional reduction of the hermitian yang mills equation using this fact and the theorem above we give a new existence proof for the vortex equations and describe the moduli space of solutions

likelihood ratio forensic voice comparison using parametric representations of the formant trajectories of diphthongs non contemporaneous speech samples from 27 male speakers of australian english were compared in a forensic likelihood ratio framework parametric curves polynomials and discrete cosine transforms were fitted to the formant trajectories of the diphthongs a e o a and the estimated coefficient values from the parametric curves were used as input to a generative multivariate kernel density formula for calculating likelihood ratios expressing the probability of obtaining the observed difference between two speech samples under the hypothesis that the samples were produced by the same speaker versus under the hypothesis that they were produced by different speakers cross validated likelihood ratio results from systems based on different parametric curves were calibrated and evaluated using the log likelihood ratio cost function cllr the cross validated likelihood ratios from the best performing system for each vowel phoneme were fused using logistic regression the resulting fused system had a very low error rate thus meeting one of the requirements for admissibility in court

synthesis fidelity and time varying spectral change in vowels recent studies have shown that synthesized versions of american english vowels are less accurately identified when the natural time varying spectral changes are eliminated by holding the formant frequencies constant over the duration of the vowel a limitation of these experiments has been that vowels produced by formant synthesis are generally less accurately identified than the natural vowels after which they are modeled to overcome this limitation a high quality speech analysis synthesis system straight was used to synthesize versions of 12 american english vowels spoken by adults and children vowels synthesized with straight were identified as accurately as the natural versions in contrast with previous results from our laboratory showing identification rates 9 12 lower for the same vowels synthesized using the cascade formant model consistent with earlier studies identification accuracy was not reduced when the fundamental frequency was held constant across the vowel however elimination o

ordered group reference priors with application to the multinomial problem summary noninformative priors are developed using the reference prior approach for multiparameter problems in which there may be parameters of interest and nuisance parameters for a given grouping of parameters and ordering of the groups intuitively according to inferential importance an algorithm for determining the associated reference prior is presented the algorithm is illustrated on the multinomial problem with discussion of the variety and success of various groupings and ordering strategies

compatible prior distributions for directed acyclic graph models summary the application of certain bayesian techniques such as the bayes factor and model averaging requires the specification of prior distributions on the parameters of alternative models we propose a new method for constructing compatible priors on the parameters of models nested in a given directed acyclic graph model using a conditioning approach we define a class of parameterizations that is consistent with the modular structure of the directed acyclic graph and derive a procedure that is invariant within this class which we name reference conditioning

estimating a product of means bayesian analysis with reference priors abstract suppose that we observe x n 1 and independently y n 1 and are concerned with inference mainly estimation and confidence statements about the product of means this problem arises most obviously in situations of determining area based on measurements of length and width it also arises in other practical contexts however for instance in gypsy moth studies the hatching rate of larvae per unit area can be estimated as the product of the mean of egg masses per unit area times the mean number of larvae hatching per egg mass approximately independent samples can be obtained for each mean see southwood 1978 noninformative prior bayesian approaches to the problem are considered in particular the reference prior approach of bernardo 1979 an appropriate reference prior for the problem is developed and relatively easily implementable formulas for posterior moments e g the posterior mean and variance and credible sets are derived comparisons with alternative noninf

on priors providing frequentist validity for bayesian inference summary we derive the differential equation that a prior must satisfy if the posterior probability of a one sided credibility interval for a parametric function and its frequentist probability agree up to o n 1 this equation turns out to be identical with stein s equation for a slightly different problem for which also our method provides a rigorous justification our method is different in details from stein s but similar in spirit to dawid 1991 and bickel ghosh 1990 some examples are provided