the form of life i it is possible but not necessary however we deny naive realism it is difficult to describe the form of life in a newtonian paradigm because any formal descriptions of biological systems inevitably include the concept of function they entail the problem of self reference the description of function can be compared to that of meaning of a word and in philosophy we no longer understand that there exists meaning inherent in a word of a language as well as the problem of meaning we cannot describe the aspect resulting from the function because we cannot identify the specific function of a shape or morphology with the relationship between the shape itself and its environment therefore even if we construct a new formal language in which the self contradiction resulting from the self reference is alleviated that language is just one of various possible ones in this sense the form of life in formal description is possible but not necessary the phrase not necessary just refers to the outside of the formal description in this paper reference to the outside of a formal system is discussed in the context of time space complementarity and it is strongly related to the origin of irreversible time we have to introduce both forward and backward time as proposed previously by the author and coworkers even in this context

approximate bayes factors and accounting for model uncertainty in generalised linear models summary ways of obtaining approximate bayes factors for generalised linear models are described based on the laplace method for integrals we propose a new approximation which uses only the output of standard computer programs for estimating generalised linear models this appears to be quite accurate a reference set of proper priors is suggested both to represent the situation where there is not much prior information and to assess the sensitivity of the results to the prior distribution the methods can be used when the dispersion parameter is unknown when there is overdispersion to compare link functions and to compare error distributions and variance functions the methods can be used to implement the bayesian approach to accounting for model uncertainty we describe an application to inference about relative risks in the presence of control factors where model uncertainty is large and important software to implement the methods is available at no cost from statlib

model order selection of damped sinusoids in noise by predictive densities we develop a procedure for the order selection of damped sinusoidal models based on the maximum a posteriori map criterion the proposed method merges the concept of predictive densities with bayesian inference to arrive at a complex multidimensional integral whose solution is achieved by way of the efficient monte carlo importance sampling technique the importance function a multivariate cauchy probability density is employed to produce stratified samples over the hypersurfaces support region centrality location parameters for the cauchy are resolved by exploiting the special structure of the compressed likelihood function clf and applying the fast maximum likelihood fml procedure of umesh and tufts simulation results allow for a comparison between our method and the singular value decomposition svd based information theoretic criteria of reddy and biradar see ieee trans signal processing vol 41 no 9 p 2872 81 1993

bayes factor covariance testing in item response models two marginal one parameter item response theory models are introduced by integrating out the latent variable or random item parameter it is shown that both marginal response models are multivariate probit models with a compound symmetry covariance structure several common hypotheses concerning the underlying covariance structure are evaluated using fractional bayes factor tests the support for a unidimensional factor i e assumption of local independence and differential item functioning are evaluated by testing the covariance components the posterior distribution of common covariance components is obtained in closed form by transforming latent responses with an orthogonal helmert matrix this posterior distribution is defined as a shifted inverse gamma thereby introducing a default prior and a balanced prior distribution based on that an mcmc algorithm is described to estimate all model parameters and to compute fractional bayes factor tests simulation studies are used to show that the fractional bayes factor tests have good properties for testing the underlying covariance structure of binary response data the method is illustrated with two real data studies

exact solution for the stationary kardar parisi zhang equation we obtain the first exact solution for the stationary one dimensional kardar parisi zhang equation a formula for the distribution of the height is given in terms of a fredholm determinant which is valid for any finite time t the expression is explicit and compact enough so that it can be evaluated numerically furthermore by extending the same scheme we find an exact formula for the stationary two point correlation function

hyper markov laws in the statistical analysis of decomposable graphical models this paper introduces and investigates the notion of a hyper markov law which is a probability distribution over the set of probability measures on a multivariate space that i is concentrated on the set of markov probabilities over some decomposable graph and ii satisfies certain conditional independence restrictions related to that graph a stronger version of this hyper markov property is also studied our analysis starts by reconsidering the properties of markov probabilities using an abstract approach which thereafter proves equally applicable to the hyper markov case next it is shown constructively that hyper markov laws exist that they appear as sampling distributions of maximum likelihood estimators in decomposable graphical models and also that they form natural conjugate prior distributions for a bayesian analysis of these models as examples we construct a range of specific hyper markov laws including the hyper multinomial hyper dirichlet and the hyper wishart and inverse wishart laws these laws occur naturally in connection with the analysis of decomposable log linear and covariance selection models

model comparison of coordinate free multivariate skewed distributions with an application to stochastic frontiers we consider classes of multivariate distributions which can model skewness and are closed under orthogonal transformations we review two classes of such distributions proposed in the literature and focus our attention on a particular yet quite flexible subclass of one of these classes members of this subclass are defined by affine transformations of univariate skewed distributions that ensure the existence of a set of coordinate axes along which there is independence and the marginals are known analytically the choice of an appropriate m dimensional skewed distribution is then restricted to the simpler problem of choosing m univariate skewed distributions we introduce a bayesian model comparison setup for selection of these univariate skewed distributions the analysis does not rely on the existence of moments allowing for any tail behaviour and uses equivalent priors on the common characteristics of the different models finally we apply this framework to multi output stochastic frontiers using data from dutch dairy farms

static fluctuations of a thick one dimensional interface in the 1 1 directed polymer formulation numerical study we study numerically the geometrical and free energy fluctuations of a static one dimensional 1d interface with a short range elasticity submitted to a quenched random bond gaussian disorder of finite correlation length ensuremath xi g0 and at finite temperature t using the exact mapping from the static 1d interface to the 1 1 directed polymer dp growing in a continuous space we focus our analysis on the disorder free energy of the dp end point a quantity which is strictly zero in the absence of disorder and whose sample to sample fluctuations at a fixed growing time t inherit the statistical translation invariance of the microscopic disorder explored by the dp constructing a new numerical scheme for the integration of the kardar parisi zhang evolution equation obeyed by the free energy we address numerically the time and temperature dependence of the disorder free energy fluctuations at fixed finite ensuremath xi we examine on one hand the amplitude stackrel ifmmode tilde else fi d t and effective correlation length stackrel ifmmode tilde else fi ensuremath xi t of the free energy fluctuations and on the other hand the imprint of the specific microscopic disorder correlator on the large time shape of the free energy two point correlator we observe numerically the crossover to a low temperature regime below a finite characteristic temperature t c ensuremath xi as previously predicted by gaussian variational method computations and scaling arguments and extensively investigated analytically in phys rev e 87 042406 2013 finally we address numerically the time and temperature dependence of the roughness b t which quantifies the dp end point transverse fluctuations and we show how the amplitude stackrel ifmmode tilde else fi d ensuremath infty t ensuremath xi controls the different regimes experienced by b t in agreement with the analytical predictions of a dp toy model approach

bayesian hypothesis testing in latent variable models hypothesis testing using bayes factors bfs is known not to be well defined under the improper prior in the context of latent variable models an additional problem with bfs is that they are difficult to compute in this paper a new bayesian method based on the decision theory and the em algorithm is introduced to test a point hypothesis in latent variable models the new statistic is a by product of the bayesian mcmc output and hence easy to compute it is shown that the new statistic is appropriately defined under improper priors because the method employs a continuous loss function in addition it is easy to interpret the method is illustrated using a one factor asset pricing model and a stochastic volatility model with jumps

polynuclear growth on a flat substrate and edge scaling of goe eigenvalues we consider the polynuclear growth png model in 1 1 dimension with flat initial condition and no extra constraints through the robinson schensted knuth rsk construction one obtains the multilayer png model which consists of a stack of non intersecting lines the top one being the png height the statistics of the lines is translation invariant and at a fixed position the lines define a point process we prove that for large times the edge of this point process suitably scaled has a limit this limit is a pfaffian point process and identical to the one obtained from the edge scaling of the gaussian orthogonal ensemble goe of random matrices our results give further insight to the universality structure within the kpz class of 1 1 dimensional growth models

scale invariance of the png droplet and the airy process we establish that the static height fluctuations of a particular growth model the png droplet converges upon proper rescaling to a limit process which we call the airy process a y the airy process is stationary it has continuous sample paths its single time fixed y distribution is the tracy widom distribution of the largest eigenvalue of a gue random matrix and the airy process has a slow decay of correlations as y 2 roughly the airy process describes the last line of dyson s brownian motion model for random matrices our construction uses a multi layer version of the png model which can be analyzed through fermionic techniques specializing our result to a fixed value of y one reobtains the celebrated result of baik deift and johansson on the length of the longest increasing subsequence of a random permutation

comparison of objective bayes factors for variable selection in parametric regression models for survival analysis this paper considers the problem of selecting a set of regressors when the response variable is distributed according to a specified parametric model and observations are censored under a bayesian perspective the most widely used tools are bayes factors bfs which are undefined when improper priors are used in order to overcome this issue fractional fbf and intrinsic ibf bfs have become common tools for model selection both depend on the size nt of a minimal training sample mts while the ibf also depends on the specific mts used in the case of regression with censored data the definition of an mts is problematic because only uncensored data allow to turn the improper prior into a proper posterior and also because full exploration of the space of the mtss which includes also censored observations is needed to avoid bias in model selection to address this concern a sequential mts was proposed but it has the drawback of an increase of the number of possible mtss as nt becomes random for this reason we explore the behaviour of the fbf contextualizing its definition to censored data we show that these are consistent providing also the corresponding fractional prior finally a large simulation study and an application to real data are used to compare ibf fbf and the well known bayesian information criterion copyright 2014 john wiley sons ltd

a flexible approach to parametric inference in nonlinear and time varying time series models many structural break and regime switching models have been used with macroeconomic and financial data in this paper we develop an extremely flexible modeling approach which can accommodate virtually any of these specifications we build on earlier work showing the relationship between flexible functional forms and random variation in parameters our contribution is based around the use of priors on the time variation that is developed from considering a hypothetical reordering of the data and distance between neighboring reordered observations the range of priors produced in this way can accommodate a wide variety of nonlinear time series models including those with regime switching and structural breaks by allowing the amount of random variation in parameters to depend on the distance between reordered observations the parameters can evolve in a wide variety of ways allowing for everything from models exhibiting abrupt change e g threshold autoregressive models or standard structural break models to those which allow for a gradual evolution of parameters e g smooth transition autoregressive models or time varying parameter models bayesian econometric methods for inference are developed for estimating the distance function and types of hypothetical reordering conditional on a hypothetical reordering and distance function a simple reordering of the actual data allows us to estimate our models with standard state space methods by a simple adjustment to the measurement equation we use artificial data to show the advantages of our approach before providing two empirical illustrations involving the modeling of real gdp growth

exact scaling functions for one dimensional stationary kpz growth we determine the stationary two point correlation function of the one dimensional kpz equation through the scaling limit of a solvable microscopic model the polynuclear growth model the equivalence to a directed polymer problem with specific boundary conditions allows one to express the corresponding scaling function in terms of the solution to a riemann hilbert problem related to the painleve ii equation we solve these equations numerically with very high precision and compare our up to numerical rounding exact result with the prediction of colaiori and moore 1 obtained from the mode coupling approximation

posterior predictive p values extending work of rubin this paper explores a bayesian counterpart of the classical p value namely a tail area probability of a test statistic under a null hypothesis the bayesian formulation using posterior predictive replications of the data allows a test statistic to depend on both data and unknown nuisance parameters and thus permits a direct measure of the discrepancy between sample and population quantities the tail area probability for a test statistic is then found under the joint posterior distribution of replicate data and the nuisance parameters both conditional on the null hypothesis this posterior predictive p value can also be viewed as the posterior mean of a classical p value averaging over the posterior distribution of nuisance parameters under the null hypothesis and thus it provides one general method for dealing with nuisance parameters two classical examples including the behrens fisher problem are used to illustrate the posterior predictive p value and some of its interesting properties which also reveal a new bayesian interpretation for some classical p values an application to multiple imputation inference is also presented a frequency evaluation shows that in general if the replication is defined by new nuisance parameters and new data then the type i frequentist error of an level posterior predictive test is often close to but less than and will never exceed 2

objective bayesian comparison of constrained analysis of variance models in the social sciences we are often interested in comparing models specified by parametric equality or inequality constraints for instance when examining three group means mu 1 mu 2 mu 3 through an analysis of variance anova a model may specify that mu 1 mu 2 mu 3 while another one may state that mu 1 mu 3 mu 2 and finally a third model may instead suggest that all means are unrestricted this is a challenging problem because it involves a combination of nonnested models as well as nested models having the same dimension we adopt an objective bayesian approach requiring no prior specification from the user and derive the posterior probability of each model under consideration our method is based on the intrinsic prior methodology suitably modified to accommodate equality and inequality constraints focussing on normal anova models a comparative assessment is carried out through simulation studies we also present an application to real data collected in a psychological experiment

on priors and bayes factors abstract by analogy to the authors measure of the influence of observations on bayes factors a new measure is proposed to determine the influence of a prior distribution on a bayes factor this is developed for linear models the method is illustrated for a consumption model using houthakker s international income and consumption data

appearance of hierarchical structure in hyper dilation model model of generalized measurement process we show the appearance of emergent hierarchical structure by a generalized system based on hyper dilation p y gunji s toyoda biosystem 38 1996 127 133 that is a new approach for complex systems hyper dilation comprises a measurement problem hidden in any formal system in hyper dilation the measurement process is expressed as the interface between an infinite lattice which is an infinite loop of a rule and a finite lattice which is a tree structure of a rule hyper dilation shows two intrinsic properties one is degeneracy of a cantor set in return map and the other is generation of 1 f noise we present various versions of hyper dilation and suggest that to generate 1 f noise it is required that the rules of the system are changed through a coherent process and that the system is closed for information from these two properties of hyper dilation we discuss that the degeneracy is regarded as the model of emergence of a new hierarchy and in hyper dilation actually we show the motion of a system that can be regarded as the appearance of a new hierarchy

bayes factors for non homogeneous poisson processes with vague prior information on developpe une approche bayesienne au probleme de la comparaison de modeles pour des processus de poisson non homogenes

limiting distributions for a polynuclear growth model with external sources the purpose of this paper is to investigate the limiting distribution functions for a polynuclear growth model with two external sources which was considered by prahofer and spohn depending on the strength of the sources the limiting distribution functions are either the tracy widom functions of random matrix theory or a new explicit function which has the special property that its mean is zero moreover we obtain transition functions between pairs of the above distribution functions in suitably scaled limits there are also similar results for a discrete totally asymmetric exclusion process

shape fluctuations and random matrices we study a certain random growth model in two dimensions closely related to the one dimensional totally asymmetric exclusion process the results show that the shape fluctuations appropriately scaled converges in distribution to the tracy widom largest eigenvalue distribution for the gaussian unitary ensemble gue

a bayesian model averaging approach with non informative priors for cost effectiveness analyses we consider the problem of assessing new and existing technologies for their cost effectiveness in the case where data on both costs and effects are available from a clinical trial and we address it by means of the cost effectiveness acceptability curve the main difficulty in these analyses is that cost data usually exhibit highly skew and heavy tailed distributions so that it can be extremely difficult to produce realistic probabilistic models for the underlying population distribution here in order to integrate the uncertainty about the model into the analysis of cost data and into cost effectiveness analyses we consider an approach based on bayesian model averaging bma in the particular case of weak prior informations about the unknown parameters of the different models involved in the procedure the main consequence of this assumption is that the marginal densities required by bma are undetermined however in accordance with the theory of partial bayes factors and in particular of fractional bayes factors we suggest replacing each marginal density with a ratio of integrals that can be efficiently computed via path sampling

forms of life unprogrammability constitutes the outside of a system and its autonomy abstract the question what is life has long been discussed and many concepts representing what are regarded as essential properties of life have been proposed namely information generating processes complex systems indefinite boundaries and self reference self referential forms in particular play a central role in autonomous life because both in ontogenetic and phylogenetic processes we find self referential forms and self reference introduces other important features of life however because self reference is strongly connected with self contradiction and or unprogrammability it cannot be described in the paradigm of prediction or dynamics it is inevitable to estimate the problem of instability of the description itself we here discuss self reference and unprogrammability with respect to the mixture between inter and intracellular computations in biological systems and we replace the difference between computation velocities at different levels by the difference between the velocity of observation propagation and that of a particle we also define the formal system of communication and transplant the problem of unprogrammability resulting from the finite velocity of observation propagation in that system here it is illustrated that unprogrammability is isomorphic to the incompleteness of a formal system further we formally estimate the relationship of unprogrammability and one to many type mapping and propose the formalization using a universal arrow based on wittgenstein s idea language games and performativeness because unprogrammability does not exist as a real entity but is constituted we can formalize one to many type mapping and even unstable formal description the concept of autonomy is not beyond formal description however it is beyond the paradigm of prediction

bayes and likelihood calculations from confidence intervals recently there has been considerable progress on setting good approximate confidence intervals for a single parameter in a multi parameter family here we use these frequentist results as a convenient device for making bayes empirical bayes and likelihood inferences about a simple formula is given that produces an approximate likelihood function l x for with all nuisance parameters eliminated based on any system of approximate confidence intervals the statistician can then modify l x with bayes or empirical bayes information for without worrying about nuisance parameters

bayesian regression diagnostics with applications to international consumption and income data abstract three variants of friedman s consumption model are analyzed using houthakker s international consumption and income data and the bayesian regression analysis program brap the analysis is focussed on evaluating friedman s proportionality hypothesis various diagnostic procedures are discussed and applied using diffuse and informative prior distributions of the three models considered the logit transformation model is deemed most appropriate and results based on it suggest a departure from the proportionality hypothesis particularlyat low levels of income this result is at variance with houthakker s earlier conclusion that these data are in accord with the proportionality hypothesis

automatic bayes factors for testing equality and inequality constrained hypotheses on variances in comparing characteristics of independent populations researchers frequently expect a certain structure of the population variances these expectations can be formulated as hypotheses with equality and or inequality constraints on the variances in this article we consider the bayes factor for testing such in equality constrained hypotheses on variances application of bayes factors requires specification of a prior under every hypothesis to be tested however specifying subjective priors for variances based on prior information is a difficult task we therefore consider so called automatic or default bayes factors these methods avoid the need for the user to specify priors by using information from the sample data we present three automatic bayes factors for testing variances the first is a bayes factor with equal priors on all variances where the priors are specified automatically using a small share of the information in the sample data the second is the fractional bayes factor where a fraction of the likelihood is used for automatic prior specification the third is an adjustment of the fractional bayes factor such that the parsimony of inequality constrained hypotheses is properly taken into account the bayes factors are evaluated by investigating different properties such as information consistency and large sample consistency based on this evaluation it is concluded that the adjusted fractional bayes factor is generally recommendable for testing equality and inequality constrained hypotheses on variances

bayesian model comparison with the hyvarinen score computation and consistency the bayes factor is a widely used criterion in model comparison and its logarithm is a difference of out of sample predictive scores under the logarithmic scoring rule however when some of the ca

bayes factors and approximations for variance component models abstract in this article we consider tests of variance components using bayes factors such tests arise in many fields of application including medicine agriculture and engineering when using bayes factors the choice of prior distribution on the parameter of interest is of great importance we propose a unit information reference method for variance component models the calculation of bayes factors in this context is not straightforward there are well documented difficulties with markov chain monte carlo approaches such as gibbs sampling and the usual laplace approximation is not appropriate due to the boundary null hypothesis we describe both an importance sampling approach and an analytical approximation for calculating the numerator and denominator of the bayes factor the importance sampling approach is straightforward to implement and also forms the basis for a rejection algorithm that allows generation of samples from the posterior distributions under the null and alternative hypotheses

bayesian analysis of the error correction model this paper presents a method for estimating the posterior probability density of the cointegrating rank of a multivariate error correction model a second contribution is the careful elicitation of the prior for the cointegrating vectors derived from a prior on the cointegrating space this prior obtains naturally from treating the cointegrating space as the parameter of interest in inference and overcomes problems previously encountered in bayesian cointegration analysis using this new prior and laplace approximation an estimator for the posterior probability of the rank is given the approach performs well compared with information criteria in monte carlo experiments

bayesian inference for the common location parameter of several shifted exponential populations abstract consider k random samples which are independently drawn from k shifted exponential distributions with respective scale parameters 1 2 k and common location parameter on the basis of the given samples and in a bayesian framework we address the problem of point and interval estimation of the location parameter under the conjugate priors which are usually proper priors moreover we also address the problem of testing the equality of the location parameters we propose bayesian hypothesis testing procedures for the equality of the location parameters under the noninformative prior the noninformative prior is usually improper which yields a calibration problem that makes the bayes factor to be defined up to a multiplicative constant so we propose the default bayesian hypothesis testing procedures based on the fractional bayes factor and the intrinsic bayes factors under the reference priors our proposed bayesian procedures are compared and contrasted via a comparison study a simulation study and a real world data analysis to the existing classical exact procedures proposed by tippett tippett s method tippett 1931 fisher fisher s method fisher 1932 stouffer inverse normal method stouffer et al 1949 and george logit method george 1977 and to the generalized variable procedures proposed by tsui and weerahandi generalized p value method tsui and weerahandi 1989

soliton cellular automata abstract we study the evolution of an arbitrary initial configuration of a certain filter cellular automaton introduced by park steiglitz and thurston any given state can be thought of as a collection of particles we find that a the interaction properties of these particles are richer than the usual solitons in particular periodic particles may interact solitonically or they may recombine to form new periodic configurations even if two particles interact solitonically they may interact several times before they get separated with the faster particle moving to the left of the slower one b arbitrary initial data will decompose as t into a number of periodic particles and into a number of certain new periodic coherent structures which we call breathers the particles and the breathers are ordered according to their speed c we formulate the above cellular automaton as a difference equation this formulation implies that the coherent structures found here are a manifestation of the coupling between the linear part and the nonlinear part of the difference equation

autonomic life as the proof of incompleteness and lawvere s theorem of fixed point abstract if finite velocity of observation propagation is taken into consideration one is faced with a paradox or infinite regression in his own logic it is the same as goedel s theorem of incompleteness or wittgenstein s paradox and in general it can be formally replaced by lawvere s theorem of a fixed point to describe time evolution under finite velocity of observation propagation is not to construct a new logic in which the paradox can be removed or improved but to accept the paradox itself given a system in which a paradox is deduced by taking the finite velocity of observation propagation we can regard the whole formal description which consists of the system and a proof sequence toward the paradox as an evolutionary system a formal evolutionary system defined here is one demonstration of autonomic life

short time growth of a kardar parisi zhang interface with flat initial conditions the short time behavior of the 1 1 dimensional kardar parisi zhang kpz growth equation with a flat initial condition is obtained from the exact expressions for the moments of the partition function of a directed polymer with one end point free and the other fixed from these expressions the short time expansions of the lowest cumulants of the kpz height field are exactly derived the results for these two classes of cumulants are checked in high precision lattice numerical simulations the short time limit considered here is relevant for the study of the interface growth in the large diffusivity or weak noise limit and describes the universal crossover between the edwards wilkinson and the kpz universality classes for an initially flat interface

exact solution for the kardar parisi zhang equation with flat initial conditions we provide the first exact calculation of the height distribution at arbitrary time t of the continuum kardar parisi zhang kpz growth equation in one dimension with flat initial conditions we use the mapping onto a directed polymer with one end fixed one free and the bethe ansatz for the replicated attractive boson model we obtain the generating function of the moments of the directed polymer partition sum as a fredholm pfaffian our formula valid for all times exhibits convergence of the free energy i e kpz height distribution to the gaussian orthogonal ensemble tracy widom distribution at large time

bayes factors for outlier models using the device of imaginary observations abstract suppose we think that most observations in a sample have been generated from a distribution with density f x but we fear that a few outliers from a distribution with density g x may have contaminated our sample in many situations we might assume that f x is a density depending on a parameter and that g x is of the same form as f but with parameter or a number of bayesian models for this problem when f is normal have been discussed by freeman he points out that with a vague improper prior for contaminating parameters most posterior weight is put on the model allowing for the largest number of outliers he therefore confines attention to proper priors when trying to answer the question of how many outliers however in many situations we do not have very certain information on the contaminating parameters and would like to make inferences about outliers when using improper priors for the parameters of the model in this article we apply the ideas of spiegelhalter and smith to

variable selection and function estimation in additive nonparametric regression using a data based prior abstract a hierarchical bayesian approach is proposed for variable selection and function estimation in additive nonparametric gaussian regression models and additive nonparametric binary regression models the prior for each component function is an integrated wiener process resulting in a posterior mean estimate that is a cubic smoothing spline each of the explanatory variables is allowed to be in or out of the model and the regression functions are estimated by model averaging to allow variable selection and model averaging data based priors are used for the smoothing parameter and the slope at 0 of each component function a two step markov chain monte carlo method is used to efficiently obtain the data based prior and to carry out variable selection and function estimation it is shown by simulation that significant improvements in the function estimators can be obtained over an approach that estimates all the unknown functions simultaneously the methodology is illustrated for a binary regressio

dynamically changing interface as a model of measurement in complex systems abstract we propose and sketch a novel approach toward the study of complex systems by considering a basic type of measurement problem hidden in any system we call this approach hyper dilation and cover it under the label of measurement oriented physics mop as compared with state oriented physics sop the essential difference between the two concerns the concepts of state to which they refer mop deals with two different concepts of state non measured states with infinite precision and measured states with finite precision the measurement process is expressed as a dynamically changing interface between them sop deals with one single concept of state and does not comprise a corresponding distinction we show fundamental differences between mop and sop with respect to the noise characteristics of complex systems around critical states mop can give rise to exact and universal 1 noise while sop shows 1 noise with 1 in general in mop a self similar return map can be degenerate with a cantor set rendering a solution for a basic measurement paradox the significance of this degeneracy as a model for emergent properties is discussed

a reference bayesian test for nested hypotheses and its relationship to the schwarz criterion abstract to compute a bayes factor for testing h 0 0 in the presence of a nuisance parameter priors under the null and alternative hypotheses must be chosen as in bayesian estimation an important problem has been to define automatic or reference methods for determining priors based only on the structure of the model in this article we apply the heuristic device of taking the amount of information in the prior on equal to the amount of information in a single observation then after transforming to be null orthogonal to we take the marginal priors on to be equal under the null and alternative hypotheses doing so and taking the prior on to be normal we find that the log of the bayes factor may be approximated by the schwarz criterion with an error of order o p n rather than the usual error of order o p 1 this result suggests the schwarz criterion should provide sensible approximate solutions to bayesian testing problems at least when the hypotheses are nested when

bayesian estimation of a multilevel irt model using gibbs sampling in this article a two level regression model is imposed on the ability parameters in an item response theory irt model the advantage of using latent rather than observed scores as dependent variables of a multilevel model is that it offers the possibility of separating the influence of item difficulty and ability level and modeling response variation and measurement error another advantage is that contrary to observed scores latent scores are test independent which offers the possibility of using results from different tests in one analysis where the parameters of the irt model and the multilevel model can be concurrently estimated the two parameter normal ogive model is used for the irt measurement model it will be shown that the parameters of the two parameter normal ogive model and the multilevel model can be estimated in a bayesian framework using gibbs sampling examples using simulated and real data are given

testing a point null hypothesis the irreconcilability of p values and evidence abstract the problem of testing a point null hypothesis or a small interval null hypothesis is considered of interest is the relationship between the p value or observed significance level and conditional and bayesian measures of evidence against the null hypothesis although one might presume that a small p value indicates the presence of strong evidence against the null such is not necessarily the case expanding on earlier work especially edwards lindman and savage 1963 and dickey 1977 it is shown that actual evidence against a null as measured say by posterior probability or comparative likelihood can differ by an order of magnitude from the p value for instance data that yield a p value of 05 when testing a normal mean result in a posterior probability of the null of at least 30 for any objective prior distribution objective here means that equal prior weight is given the two hypotheses and that the prior is symmetric and nonincreasing away from the null other definiti

benchmark priors for bayesian model averaging in contrast to a posterior analysis given a particular sampling model posterior model probabilities in the context of model uncertainty are typically rather sensitive to the speciflcation of the prior in particular difiuse priors on model speciflc parameters can lead to quite unexpected consequences here we focus on the practically relevant situation where we need to entertain a large number of sampling models and we have or wish to use little or no subjective prior information we aim at providing an automatic or benchmark prior structure that can be used in such cases we focus on the normal linear regression model with uncertainty in the choice of re gressors we propose a partly noninformative prior structure related to a natural conjugate g prior speciflcation where the amount of subjective information requested from the user is limited to the choice of a single scalar hyperparameter g0j the consequences of difierent choices for g0j are examined we investigate theoretical properties such as consistency of the implied bayesian procedure links with classical information criteria are provided in addition we examine the flnite sample implications of several choices of g0j in a simulation study the use of the mc 3 algorithm of madigan and york 1995 combined with e cient coding in fortran makes it feasible to conduct large simulations in addition to posterior criteria we shall also compare the predictive performance of difierent priors a classic exam ple concerning the economics of crime will also be provided and contrasted with results in the literature the main flndings of the paper will lead us to propose a benchmark prior speciflcation in a linear regression context with model uncertainty

fractional bayes factors for model comparison bayesian comparison of models is achieved simply by calculation of posterior probabilities of the models themselves however there are difficulties with this approach when prior information about the parameters of the various models is weak partial bayes factors offer a resoiution of the problem by setting aside part of the data as a training sampie the training sampie is used to obtain an initiai informative posterior distribution of the parameters in each model model comparison is then based on a bayes factor calculated from the remaining data properties of partial bayes factors are discussed particularly in the context of weak prior information and they are found to have advantages over other proposed methods of model comparison a new variant of the partial bayes factor the fractional bayes factor is advocated on grounds of consistency simplicity robustness and coherence

on the use of non local prior densities in bayesian hypothesis tests we examine philosophical problems and sampling deficiencies that are associated with current bayesian hypothesis testing methodology paying particular attention to objective bayes methodology because the prior densities that are used to define alternative hypotheses in many bayesian tests assign non negligible probability to regions of the parameter space that are consistent with null hypotheses resulting tests provide exponential accumulation of evidence in favour of true alternative hypotheses but only sublinear accumulation of evidence in favour of true null hypotheses thus it is often impossible for such tests to provide strong evidence in favour of a true null hypothesis even when moderately large sample sizes have been obtained we review asymptotic convergence rates of bayes factors in testing precise null hypotheses and propose two new classes of prior densities that ameliorate the imbalance in convergence rates that is inherited by most bayesian tests using members of these classes we obtain analytic expressions for bayes factors in linear models and derive approximations to bayes factors in large sample settings

bayesian model selection analysis of a survival model with a surviving fraction we describe a methodology for model comparison in a bayesian framework as applied to survival with a surviving fraction this is illustrated using a case study of a randomized and controlled clinical trial investigating time until recurrence of depression posterior distributions are simulated using metropolis within gibbs markov chain methods models reflecting the effects of covariates on the log odds of being in the surviving fraction the log of the hazard rate as well as both and neither are compared bayes factors for comparing the models are obtained by using the bridge sampling method of calculating normalizing constants

robust bayesian inference via coarsening the standard approach to bayesian inference is based on the assumption that the distribution of the data belongs to the chosen model class however even a small violation of this assumption can ha

probability distribution of the free energy of the continuum directed random polymer in 1 1 dimensions we consider the solution of the stochastic heat equation tz d 1 2 x zz p w with delta function initial condition z t d0 x dixd0 whose logarithm with appropriate normalization is the free energy of the con tinuum directed polymer or the hopf cole solution of the kardar parisi zhang equation with narrow wedge initial conditions we obtain explicit formulas for the one dimensional marginal distributions the crossover distributions which interpolate between a standard gaussian dis tribution small time and the gue tracy widom distribution large time the proof is via a rigorous steepest descent analysis of the tracy widom formula for the asymmetric simple exclusion process with antishock initial data which is shown to converge to the continuum equations in an appropriate weakly asymmetric limit the limit also describes the crossover behavior between the symmetric and asymmetric exclusion processes 2010 wiley periodicals inc

a class of adaptive importance sampling weighted em algorithms for efficient and robust posterior and predictive simulation abstract a class of adaptive sampling methods is introduced for efficient posterior and predictive simulation the proposed methods are robust in the sense that they can handle target distributions that exhibit non elliptical shapes such as multimodality and skewness the basic method makes use of sequences of importance weighted expectation maximization steps in order to efficiently construct a mixture of student t densities that approximates accurately the target distribution typically a posterior distribution of which we only require a kernel in the sense that the kullback leibler divergence between target and mixture is minimized we label this approach mixture of t by importance sampling weighted expectation maximization mitisem the constructed mixture is used as a candidate density for quick and reliable application of either importance sampling is or the metropolis hastings mh method we also introduce three extensions of the basic mitisem approach first we propose a method for applying mitisem in a sequential manner so that the candidate distribution for posterior simulation is cleverly updated when new data become available our results show that the computational effort reduces enormously while the quality of the approximation remains almost unchanged this sequential approach can be combined with a tempering approach which facilitates the simulation from densities with multiple modes that are far apart second we introduce a permutation augmented mitisem approach this is useful for importance or metropolis hastings sampling from posterior distributions in mixture models without the requirement of imposing identification restrictions on the model s mixture regimes parameters third we propose a partial mitisem approach which aims at approximating the joint distribution by estimating a product of marginal and conditional distributions this division can substantially reduce the dimension of the approximation problem which facilitates the application of adaptive importance sampling for posterior simulation in more complex models with larger numbers of parameters our results indicate that the proposed methods can substantially reduce the computational burden in econometric models like dcc or mixture garch models and a mixture instrumental variables model

training samples in objective bayesian model selection central to several objective approaches to bayesian model selection is the use of training samples subsets of the data so as to allow utilization of improper objective priors the most common prescription for choosing training samples is to choose them to be as small as possible subject to yielding proper posteriors these are called minimal training samples when data can vary widely in terms of either information content or impact on the improper priors use of minimal training samples can be inadequate important examples include certain cases of discrete data the presence of censored observations and certain situations involving linear models and explanatory variables such situations require more sophisticated methods of choosing training samples a variety of such methods are developed in this paper and successfully applied in challenging situations

bayesian analysis of a poisson process with a change point summary a bayesian approach to estimation and hypothesis testing for a poisson process with a change point is developed and an example given

a new approach to bayesian hypothesis testing abstract in this paper a new bayesian approach is proposed to test a point null hypothesis based on the deviance in a decision theoretical framework the proposed test statistic may be regarded as the bayesian version of the likelihood ratio test and appeals in practical applications with three desirable properties first it is immune to jeffreys concern about the use of improper priors second it avoids jeffreys lindley s paradox third it is easy to compute and its threshold value is easily derived facilitating the implementation in practice the method is illustrated using some real examples in economics and finance it is found that the leverage effect is insignificant in an exchange time series and that the fama french three factor model is rejected

practical bayesian density estimation using mixtures of normals abstract mixtures of normals provide a flexible model for estimating densities in a bayesian framework there are some difficulties with this model however first standard reference priors yield improper posteriors second the posterior for the number of components in the mixture is not well defined if the reference prior is used third posterior simulation does not provide a direct estimate of the posterior for the number of components we present some practical methods for coping with these problems finally we give some results on the consistency of the method when the maximum number of components is allowed to grow with the sample size

an intrinsic limiting procedure for model selection and hypotheses testing abstract improper priors typically arise in default bayesian estimation problems in the bayesian approach to model selection or hypothesis testing the main tool is the bayes factor when improper priors for the parameters appearing in the models are used the bayes factor is not well defined the intrinsic bayes factor introduced by berger and pericchi is an interesting method for overcoming that difficulty that method is of particular interest as a means for generating proper prior distributions intrinsic priors for model comparison from the improper priors typically used in estimation the goal of this article is to develop a limiting procedure that provides a solid justification for the use of bayes factor with intrinsic priors the procedure is formalized and discussed for nested and nonnested models illustrations and comparisons with other approximations to bayes factors such as the bayesian information criterion of schwarz and the fractional bayes factor of o hagan are provided

nonparametric seemingly unrelated regression abstract a method is presented for simultaneously estimating a system of nonparametric regressions which may seem unrelated but where the errors are potentially correlated between equations we show that the advantage of estimating such a seemingly unrelated system of nonparametric regressions is that less observations can be required to obtain reliable function estimates than if each of the regression equations is estimated separately and the correlation ignored this increase in efficiency is investigated empirically using both simulated and real data the method uses a bayesian hierarchical framework where each regression function is represented as a linear combination of a large number of basis terms all the regression coefficients and the variance matrix of the errors are estimated simultaneously by their posterior means the computation is carried out using a markov chain monte carlo sampling scheme that employs a focused sampling step to combat the high dimensional representation of the unknown regression functions the methodology extends easily to other nonparametric multivariate regression models

bayesianly justifiable and relevant frequency calculations for the applied statistician a common reaction among applied statisticians is that the bayesian statistician s energies in an applied problem must be directed at the a priori elicitation of one model specification from which an optimal design and all inferences follow automatically by applying bayes s theorem to calculate conditional distributions of unknowns given knowns i feel however that the applied bayesian statistician s tool kit should be more extensive and include tools that may be usefully labeled frequency calculations three types of bayesianly justifiable and relevant frequency calculations are presented using examples to convey their use for the applied statistician

measuring the effect of observations on bayes factors summary in this paper we consider a measure of the effect of single observations on a logarithmic bayes factor defined via the difference in the logarithms of the bayes factors conditional first on all the data and then omitting an observation the measure is related to the conditional predictive ordinate the form of the measure and examples of its use are presented for a variety of situations normal samples linear models log linear models and the checking of distributional assumptions

optimal predictive model selection often the goal of model selection is to choose a model for future prediction and it is natural to measure the accuracy of a future prediction by squared error loss under the bayesian approach it is commonly perceived that the optimal predictive model is the model with highest posterior probability but this is not necessarily the case in this paper we show that for selection among normal linear models the optimal predictive model is often the median probability model which is defined as the model consisting of those variables which have overall posterior probability greater than or equal to 1 2 of being in a model the median probability model often differs from the highest probability model

non local priors for high dimensional estimation abstractjointly achieving parsimony and good predictive power in high dimensions is a main challenge in statistics nonlocal priors nlps possess appealing properties for model choice but their use for estimation has not been studied in detail we show that for regular models nlp based bayesian model averaging bma shrink spurious parameters either at fast polynomial or quasi exponential rates as the sample size n increases while nonspurious parameter estimates are not shrunk we extend some results to linear models with dimension p growing with n coupled with our theoretical investigations we outline the constructive representation of nlps as mixtures of truncated distributions that enables simple posterior sampling and extending nlps beyond previous proposals our results show notable high dimensional estimation for linear models with p n at low computational cost nlps provided lower estimation error than benchmark and hyper g priors scad and lasso in simulations and in gene expression data

bayesian model choice asymptotics and exact calculations abstract model determination is a fundamental data analytic task here we consider the problem of choosing amongst a finite with loss of generality we assume two set of models after briefly reviewing classical and bayesian model choice strategies we present a general predictive density which includes all proposed bayesian approaches we are aware of using laplace approximations we can conveniently assess and compare asymptotic behavior of these approaches concern regarding the accuracy of these approximation for small to moderate sample sizes encourages the use of monte carlo techniques to carry out exact calculations a data set fit with nested non linear models enables comparison between proposals and between exact and asymptotic values

variable selection and functional form uncertainty in cross country growth regressions regression analyses of cross country economic growth data are complicated by two main forms of model uncertainty the uncertainty in selecting explanatory variables and the uncertainty in specifying the functional form of the regression function most discussions in the literature address these problems independently yet a joint treatment is essential we present a new framework that makes such a joint treatment possible using flexible nonlinear models specified by gaussian process priors and addressing the variable selection problem by means of bayesian model averaging using this framework we extend the linear model to allow for parameter heterogeneity of the type suggested by new growth theory while taking into account the uncertainty in selecting explanatory variables controlling for variable selection uncertainty we confirm the evidence in favor of parameter heterogeneity presented in several earlier studies however controlling for functional form uncertainty we find that the effects of many of the explanatory variables identified in the literature are not robust across countries and variable selections

objective bayesian model selection in gaussian graphical models summary this paper presents a default model selection procedure for gaussian graphical models that involves two new developments first we develop a default version of the hyper inverse wishart prior for restricted covariance matrices called the hyper inverse wishart g prior and show how it corresponds to the implied fractional prior for selecting a graph using fractional bayes factors second we apply a class of priors that automatically handles the problem of multiple hypothesis testing we demonstrate our methods on a variety of simulated examples concluding with a real example analyzing covariation in mutual fund returns these studies reveal that the combined use of a multiplicity correction prior on graphs and fractional bayes factors for computing marginal likelihoods yields better performance than existing bayesian methods

empirical bayes methods for combining likelihoods abstract suppose that several independent experiments are observed each one yielding a likelihood l k k for a real valued parameter of interest k for example k might be the log odds ratio for a 2 2 table relating to the kth population in a series of medical experiments this article concerns the following empirical bayes question how can we combine all of the likelihoods l k to get an interval estimate for any one of the k s say 1 the results are presented in the form of a realistic computational scheme that allows model building and model checking in the spirit of a regression analysis no special mathematical forms are required for the priors or the likelihoods this scheme is designed to take advantage of recent methods that produce approximate numerical likelihoods l k k even in very complicated situations with all nuisance parameters eliminated the empirical bayes likelihood theory is extended to situations where the k s have a regression structure as well as an empiri

universal distributions for growth processes in 1 1 dimensions and random matrices we develop a scaling theory for kardar parisi zhang growth in one dimension by a detailed study of the polynuclear growth model in particular we identify three universal distributions for shape fluctuations and their dependence on the macroscopic shape these distribution functions are computed using the partition function of gaussian random matrices in a cosine potential

height distribution of the kardar parisi zhang equation with sharp wedge initial condition numerical evaluations the time dependent probability distribution function of the height for the kardar parisi zhang equation with sharp wedge initial conditions has been obtained recently as a convolution between the gumbel distribution and a difference of two fredholm determinants we evaluate numerically this distribution over the whole time span the crossover from the short time behavior which is gaussian to the long time behavior which is governed by the gaussian unitary ensemble gue tracy widom distribution is clearly visible