layered dynamic textures a novel video representation the layered dynamic texture ldt is proposed the ldt is a generative model which represents a video as a collection of stochastic layers of different appearance and dynamics each layer is modeled as a temporal texture sampled from a different linear dynamical system the ldt model includes these systems a collection of hidden layer assignment variables which control the assignment of pixels to layers and a markov random field prior on these variables which encourages smooth segmentations an em algorithm is derived for maximum likelihood estimation of the model parameters from a training video it is shown that exact inference is intractable a problem which is addressed by the introduction of two approximate inference procedures a gibbs sampler and a computationally efficient variational approximation the trade off between the quality of the two approximations and their complexity is studied experimentally the ability of the ldt to segment videos into layers of coherent appearance and dynamics is also evaluated on both synthetic and natural videos these experiments show that the model possesses an ability to group regions of globally homogeneous but locally heterogeneous stochastic dynamics currently unparalleled in the literature

fitting and testing conditional multinormal partial credit models a multinormal partial credit model for factor analysis of polytomously scored items with ordered response categories is derived using an extension of the dutch identity holland in psychometrika 55 5 18 1990 in the model latent variables are assumed to have a multivariate normal distribution conditional on unweighted sums of item scores which are sufficient statistics attention is paid to maximum likelihood estimation of item parameters multivariate moments of latent variables and person parameters it is shown that the maximum likelihood estimates can be found without the use of numerical integration techniques more general models are discussed which can be used for testing the model and it is shown how models with different numbers of latent variables can be tested against each other in addition multi group extensions are proposed which can be used for testing both measurement invariance and latent population differences models and procedures discussed are demonstrated in an empirical data example

latent variable modeling in heterogeneous populations common applications of latent variable analysis fail to recognize that data may be obtained from several populations with different sets of parameter values this article describes the problem and gives an overview of methodology that can address heterogeneity artificial examples of mixtures are given where if the mixture is not recognized strongly distorted results occur mimic structural modeling is shown to be a useful method for detecting and describing heterogeneity that cannot be handled in regular multiple group analysis other useful methods instead take a random effects approach describing heterogeneity in terms of random parameter variation across groups these random effects models connect with emerging methodology for multilevel structural equation modeling of hierarchical data examples are drawn from educational achievement testing psychopathology and sociology of education estimation is carried out by the liscomp program

comparing latent means without mean structure models a projection based approach the conventional setup for multi group structural equation modeling requires a stringent condition of cross group equality of intercepts before mean comparison with latent variables can be conducted this article proposes a new setup that allows mean comparison without the need to estimate any mean structural model by projecting the observed sample means onto the space of the common scores and the space orthogonal to that of the common scores the new setup allows identifying and estimating the means of the common and specific factors although without replicate measures variances of specific factors cannot be distinguished from those of measurement errors under the new setup testing cross group mean differences of the common scores is done independently from that of the specific factors such independent testing eliminates the requirement for cross group equality of intercepts by the conventional setup in order to test cross group equality of means of latent variables using chi square difference statistics the most appealing piece of the new setup is a validity index for mean differences defined as the percentage of the sum of the squared observed mean differences that is due to that of the mean differences of the common scores by analyzing real data with two groups the new setup is shown to offer more information than what is obtained under the conventional setup

a hierarchical ornstein uhlenbeck model for continuous repeated measurement data in this paper we present a diffusion model for the analysis of continuous time change in multivariate longitudinal data the central idea is to model the data from a single person with an ornstein uhlenbeck diffusion process we extend it hierarchically by allowing the parameters of the diffusion process to vary randomly over different persons with this approach both intra and interindividual differences are analyzed simultaneously furthermore the individual difference parameters can be regressed on covariates thereby providing an explanation of between person differences unstructured and unbalanced data pose no problem for the model to be applied we demonstrate the method on data from an experience sampling study to investigate changes in the core affect it can be concluded that different factors from the five factor model of personality are related to features of the trajectories in the core affect space such as the cross correlation and variability of the changes

invariance in measurement and prediction revisited borsboom psychometrika 71 425 440 2006 noted that recent work on measurement invariance mi and predictive invariance pi has had little impact on the practice of measurement in psychology to understand this contention the definitions of mi and pi are reviewed followed by results on the consistency between the two forms of invariance in the general case the special parametric cases of factor analysis strict factorial invariance and linear regression analyses strong regression invariance are then described along with findings on the inconsistency between the two forms of invariance in this context two numerical examples of inconsistency are reviewed in detail the impact of violations of mi on accuracy of selection is illustrated finally reasons for the slow dissemination of work on invariance are discussed and the prospects for altering this situation are weighed

a model based standardization approach that separates true bias dif from group ability differences and detects test bias dtf as well as item bias dif a model based modification sibtest of the standardization index based upon a multidimensional irt bias modeling approach is presented that detects and estimates dif or item bias simultaneously for several items a distinction between dif and bias is proposed sibtest detects bias dif without the usual type 1 error inflation due to group target ability differences in simulations sibtest performs comparably to mantel haenszel for the one item case sibtest investigates bias dif for several items at the test score level multiple item dif called differential test functioning dtf thereby allowing the study of test bias dif in particular bias dif amplification or cancellation and the cognitive bases for bias dif

a new test for structural stability in the linear regression model abstract we propose a new test for the constancy of regression coefficients in linear models the test does not require that possible change points be known we derive the limiting null distribution of the test statistic prove that the test has non trivial power against many local alternatives and show that it compares favourably to both the cusum and cusum of squares tests

time series segmentation a model and a method abstract the problem of partitioning time series into segments is treated the segments are considered as falling into classes a different probability distribution is associated with each class of segment parametric families of distributions are considered a set of parameter values being associated with each class with each observation is associated an unobservable label indicating from which class the observation arose the label process is modeled as a markov chain segmentation algorithms are obtained by applying a relaxation method to maximize the resulting likelihood function special attention is given to the situation in which the observations are conditionally independent given the labels a numerical example segmentation of the u s gross national product is given choice of the number of classes using statistical model selection criteria is illustrated

might unique factors be common on the possibility of indeterminate common unique covariances the present paper shows that the usual factor analytic structured data dispersion matrix can readily arise from a set of scores y e where the common and unique e factors have nonzero covariance cove 0 implications of this finding are discussed for the indeterminacy of factor scores and for the issue of invariance of factor analytic covariance models the size of the problem is explored with numerical examples

a switching multi scale dynamical network model of eeg meg we introduce a new generative model of the encephalography eeg meg data the inversion of which allows for inferring the locations and temporal evolution of the underlying sources as well as their dynamical interactions the proposed switching mesostate space model smsm builds on the multi scale generative model for eeg meg by daunizeau and friston 2007 smsm inherits the assumptions that 1 bioelectromagnetic activity is generated by a set of distributed sources 2 the dynamics of these sources can be modelled as random fluctuations about a small number of mesostates and 3 the number of mesostates engaged by a cognitive task is small additionally four generalising assumptions are now included 4 the mesostates interact according to a full dynamical causal network dcn that can be estimated 5 the dynamics of the mesostates can switch between multiple approximately linear operating regimes 6 each operating regime remains stable over finite periods of time temporal clusters and 7 the total number of times the mesostates dynamics can switch is small the proposed model adds therefore a level of flexibility by accommodating complex brain processes that cannot be characterised by purely linear and stationary gaussian dynamics importantly the smsm furnishes a new interpretation of the eeg meg data in which the source activity may have multiple discrete modes of behaviour each with approximately linear dynamics this is modelled by assuming that the connection strengths of the underlying mesoscopic dcn are time dependent but piecewise constant i e they can undergo discrete changes over time a variational bayes inversion scheme is derived to estimate all the parameters of the model by maximising a negative free energy lower bound on the model evidence this bound is used to select among different model choices that are defined by the number of mesostates as well as by the number of stationary linear regimes the full model is compared to a simplified version that uses no dynamical assumptions as well as to a standard eeg inversion technique the comparison is carried out using an extensive set of simulations and the application of smsm to a real data set is also demonstrated our results show that for experimental situations in which we have some a priori belief that there are multiple approximately linear dynamical regimes the proposed smsm provides a natural modelling tool

using the criterion predictor factor model to compute the probability of detecting prediction bias with ordinary least squares regression the study of prediction bias is important and the last five decades include research studies that examined whether test scores differentially predict academic or employment performance previous studies used ordinary least squares ols to assess whether groups differ in intercepts and slopes this study shows that ols yields inaccurate inferences for prediction bias hypotheses this paper builds upon the criterion predictor factor model by demonstrating the effect of selection measurement error and measurement bias on prediction bias studies that use ols the range restricted criterion predictor factor model is used to compute type i error and power rates associated with using regression to assess prediction bias hypotheses in short ols is not capable of testing hypotheses about group differences in latent intercepts and slopes additionally a theorem is presented which shows that researchers should not employ hierarchical regression to assess intercept differences with selected samples

essential independence and likelihood based ability estimation for polytomous items a definition ofessential independence is proposed for sequences of polytomous items for items satisfying the reasonable assumption that the expected amount of credit awarded increases with examinee ability we develop a theory ofessential unidimensionality which closely parallels that of stout essentially unidimensional item sequences can be shown to have a unique up to change of scale dominant underlying trait which can be consistently estimated by a monotone transformation of the sum of the item scores in more general polytomous response latent trait models with or without ordered responses anm estimator based upon maximum likelihood may be shown to be consistent for under essentially unidimensional violations of local independence and a variety of monotonicity identifiability conditions a rigorous proof of this fact is given and the standard error of the estimator is explored these results suggest that ability estimation methods that rely on the summation form of the log likelihood under local independence should generally be robust under essential independence but standard errors may vary greatly from what is usually expected depending on the degree of departure from local independence an index of departure from local independence is also proposed

conservation laws of evolution equations generic non existence evolution type partial differential equations in one space variable are formulated in terms of exterior differential systems the space of conservation laws is discussed in this geometric context and a familiar classical condition for conservation laws is derived it is shown that the generic even order evolution equation with one space variable possesses no conservation laws of order greater than the order of the equation

an inequality for correlations in unidimensional monotone latent variable models for binary variables it is shown that a unidimensional monotone latent variable model for binary items implies a restriction on the relative sizes of item correlations the negative logarithm of the correlations satisfies the triangle inequality this inequality is not implied by the condition that the correlations are nonnegative the criterion that coefficient h exceeds 0 30 or manifest monotonicity the inequality implies both a lower bound and an upper bound for each correlation between two items based on the correlations of those two items with every possible third item it is discussed how this can be used in mokken s a theory and procedure of scale analysis mouton the hague 1971 scale analysis

tests of measurement invariance without subgroups a generalization of classical methods the issue of measurement invariance commonly arises in factor analytic contexts with methods for assessment including likelihood ratio tests lagrange multiplier tests and wald tests these tests all require advance definition of the number of groups group membership and offending model parameters in this paper we study tests of measurement invariance based on stochastic processes of casewise derivatives of the likelihood function these tests can be viewed as generalizations of the lagrange multiplier test and they are especially useful for i identifying subgroups of individuals that violate measurement invariance along a continuous auxiliary variable without prespecified thresholds and ii identifying specific parameters impacted by measurement invariance violations the tests are presented and illustrated in detail including an application to a study of stereotype threat and simulations examining the tests abilities in controlled conditions

non gaussian state space modeling of nonstationary time series abstract a non gaussian state space approach to the modeling of nonstationary time series is shown the model is expressed in state space form where the system noise and the observational noise are not necessarily gaussian recursive formulas of prediction filtering and smoothing for the state estimation and identification of the non gaussian state space model are given also given is a numerical method based on piecewise linear approximation to the density functions for realizing these formulas significant merits of non gaussian modeling and the wide range of applicability of the method are illustrated by some numerical examples a typical application of this non gaussian modeling is the smoothing of a time series that has mean value function with both abrupt and gradual changes simple gaussian state space modeling is not adequate for this situation here the model with small system noise variance cannot detect jump whereas the one with large system noise variance yields unfavorable wiggle to work

proof of an exceptional zero conjecture for elliptic curves over function fields based on the analogy between number fields and function fields of one variable over finite fields we formulate and prove an analogue of the exceptional zero conjecture of mazur tate and teitelbaum for elliptic curves defined over function fields the proof uses modular parametrization by drinfeld modular curves and the theory of non archimedean integration as an application we prove a refinement of the birch swinnerton dyer conjecture if the analytic rank of the elliptic curve is zero

identification of confirmatory factor analysis models of different levels of invariance for ordered categorical outcomes this article considers the identification conditions of confirmatory factor analysis cfa models for ordered categorical outcomes with invariance of different types of parameters across groups the current practice of invariance testing is to first identify a model with only configural invariance and then test the invariance of parameters based on this identified baseline model this approach is not optimal because different identification conditions on this baseline model identify the scales of latent continuous responses in different ways once an invariance condition is imposed on a parameter these identification conditions may become restrictions and define statistically non equivalent models leading to different conclusions by analyzing the transformation that leaves the model implied probabilities of response patterns unchanged we give identification conditions for models with invariance of different types of parameters without referring to a specific parametrization of the baseline model tests based on this approach have the advantage that they do not depend on the specific identification condition chosen for the baseline model

bad environments good environments a non gaussian asymmetric volatility model abstract we propose an extension of standard asymmetric volatility models in the generalized autoregressive conditional heteroskedasticity garch class that admits conditional non gaussianities in a tractable fashion our bad environment good environment bege model utilizes two gamma distributed shocks and generates a conditional shock distribution with time varying heteroskedasticity skewness and kurtosis the bege model features nontrivial news impact curves and closed form solutions for higher order moments in an empirical application to stock returns the bege model outperforms asymmetric garch and regime switching models along several dimensions

an application of the lc lstm framework to the self esteem instability case the present research evaluates the stability of self esteem as assessed by a daily version of the rosenberg society and the adolescent self image princeton university press princeton 1965 general self esteem scale rgse the scale was administered to 391 undergraduates for five consecutive days the longitudinal data were analyzed using the integrated lc lstm framework that allowed us to evaluate 1 the measurement invariance of the rgse 2 its stability and change across the 5 day assessment period 3 the amount of variance attributable to stable and transitory latent factors and 4 the criterion related validity of these factors results provided evidence for measurement invariance mean level stability and rank order stability of daily self esteem latent state trait analyses revealed that variances in scores of the rgse can be decomposed into six components stable self esteem 40 ephemeral or temporal state variance 36 stable negative method variance 9 stable positive method variance 4 specific variance 1 and random error variance 10 moreover latent factors associated with daily self esteem were associated with measures of depression implicit self esteem and grade point average

on the misuse of manifest variables in the detection of measurement bias measurement invariance lack of bias of a manifest variabley with respect to a latent variablew is defined as invariance of the conditional distribution ofy givenw over selected subpopulations invariance is commonly assessed by studying subpopulation differences in the conditional distribution ofy given a manifest variablez chosen to substitute forw a unified treatment of conditions that may allow the detection of measurement bias using statistical procedures involving only observed or manifest variables is presented theorems are provided that give conditions for measurement invariance and for invariance of the conditional distribution ofy givenz additional theorems and examples explore the bayes sufficiency ofz stochastic ordering inw local independence ofy andz exponential families and the reliability ofz it is shown that when bayes sufficiency ofz fails the two forms of invariance will often not be equivalent in practice bayes sufficiency holds under rasch model assumptions and in long tests under certain conditions it is concluded that bias detection procedures that rely strictly on observed variables are not in general diagnostic of measurement bias or the lack of bias

bayesian non parametric hidden markov models with applications in genomics we consider the development of bayesian nonparametric methods for product partition models such as hidden markov models and change point models our approach uses a mixture of dirichlet process mdp model for the unknown sampling distribution likelihood for the observations arising in each state and a computationally efficient data augmentation scheme to aid inference the method uses novel mcmc methodology which combines recent retrospective sampling methods with the use of slice sampler variables the methodology is computationally efficient both in terms of mcmc mixing properties and robustness to the length of the time series being investigated moreover the method is easy to implement requiring little or no user interaction we apply our methodology to the analysis of genomic copy number variation

serial correlation in latent discrete variable models abstract we consider the problems of estimation and testing in models with serially correlated discrete latent variables a particular case of this is the time series regression model in which a discrete explanatory variable is measured with error test statistics are derived for detecting serial correlation in such a model we then show that the likelihood function can be evaluated by a recurrence relation and thus maximum likelihood estimation is computationally feasible an illustrative example of these methods is given followed by a brief discussion of their applicability to a markov model of switching regressions

optimization based model fitting for latent class and latent profile analyses statisticians typically estimate the parameters of latent class and latent profile models using the expectation maximization algorithm this paper proposes an alternative two stage approach to model fitting the first stage uses the modified k means and hierarchical clustering algorithms to identify the latent classes that best satisfy the conditional independence assumption underlying the latent variable model the second stage then uses mixture modeling treating the class membership as known the proposed approach is theoretically justifiable directly checks the conditional independence assumption and converges much faster than the full likelihood approach when analyzing high dimensional data this paper also develops a new classification rule based on latent variable models the proposed classification procedure reduces the dimensionality of measured data and explicitly recognizes the heterogeneous nature of the complex disease which makes it perfect for analyzing high throughput genomic data simulation studies and real data analysis demonstrate the advantages of the proposed method

alternative algorithms for the estimation of dynamic factor mimic and varying coefficient regression models this paper provides a general approach to the formulation and estimation of dynamic unobserved component models after introducing the general model two methods for estimating the unknown parameters are presented both are algorithms for maximizing the likelihood function the first is based on the method of scoring the second is the em algorithm a derivative free method each iteration of em requires a kalman filter and smoother followed by straightforward regression calculations the paper suggests using the em methods to quickly locate a neighborhood of the maximum scoring can then be used to pinpoint the maximum and calculate the information matrix

dynamic linear models with switching abstract the problem of modeling change in a vector time series is studied using a dynamic linear model with measurement matrices that switch according to a time varying independent random process we derive filtered estimators for the usual state vectors and also for the state occupancy probabilities of the underlying nonstationary measurement process a maximum likelihood estimation procedure is given that uses a pseudo expectation maximization algorithm in the initial stages and nonlinear optimization we relate the models to those considered previously in the literature and give an application involving the tracking of multiple targets

a new approximate likelihood estimator for arma filtered hidden markov models hidden markov models hmms are successfully applied in various fields of time series analysis colored noise e g due to filtering violates basic assumptions of the model although it is well known how to consider autoregressive ar filtering there is no algorithm to take into account moving average ma filtering in parameter estimation exactly we present an approximate likelihood estimator for ma filtered hmm that is generalized to deal with an autoregressive moving average arma filtered hmm the approximation order of the likelihood calculation can be chosen therefore we obtain a sequence of estimators for the hmm parameters as well as for the filter coefficients the recursion equations for an efficient algorithm are derived from exact expressions for the forward iterations by simulations we show that the derived estimators are unbiased in filter situations where standard hmm s are not able to recover the true dynamics special implementation strategies together with small approximations yield further acceleration of the algorithm

the attack of the psychometricians this paper analyzes the theoretical pragmatic and substantive factors that have hampered the integration between psychology and psychometrics theoretical factors include the operationalist mode of thinking which is common throughout psychology the dominance of classical test theory and the use of construct validity as a catch all category for a range of challenging psychometric problems pragmatic factors include the lack of interest in mathematically precise thinking in psychology inadequate representation of psychometric modeling in major statistics programs and insufficient mathematical training in the psychological curriculum substantive factors relate to the absence of psychological theories that are sufficiently strong to motivate the structure of psychometric models following the identification of these problems a number of promising recent developments are discussed and suggestions are made to further the integration of psychology and psychometrics

measurement invariance factor analysis and factorial invariance several concepts are introduced and defined measurement invariance structural bias weak measurement invariance strong factorial invariance and strict factorial invariance it is shown that factorial invariance has implications for weak measurement invariance definitions of fairness in employment admissions testing and salary equity are provided and it is argued that strict factorial invariance is required for fairness equity to exist implications for item and test bias are developed and it is argued that item or test bias probably depends on the existence of latent variables that are irrelevant to the primary goal of test constructers

conservation laws for multidimensional systems and related linear algebra problems we consider multidimensional systems of pdes of generalized evolution form with t derivatives of arbitrary order on the left hand side and with the right hand side dependent on lower order t derivatives and arbitrary space derivatives for such systems we find an explicit necessary condition for existence of higher conservation laws in terms of the system s symbol for systems that violate this condition we give an effective upper bound on the order of conservation laws using this result we completely describe conservation laws for viscous transonic equations for the brusselator model and the belousov zhabotinskii system to achieve this we determine the conditions for a quadratic matrix a with entries from an arbitrary field to be similar conjugate to its transpose a t or to the matrix a t which is of independent interest

a new item response theory modeling approach with applications to unidimensionality assessment and ability estimation using an infinite item test framework it is argued that the usual assumption of local independence be replaced by a weaker assumption essential independence a fortiori the usual assumption of unidimensionality is replaced by a weaker and arguably more appropriatestatistically testable assumption of essential unidimennsionality essential unidimennsionnality implies the existence of a unique unidimensional latent ability essential unidimensionality is equivalent to the consistent estimation of this latnet ability in an ordinal scaling sense using anybalanced empirical scaling a variation of this estimation approach allows consistent estimation of ability on the given latent ability scale

simulation estimation of dynamic switching regression and dynamic disequilibrium models some monte carlo results abstract this article considers the estimation of dynamic exogenous switching regression models and dynamic endogenous switching models with autocorrelation in disturbances or latent lagged dependent variables likelihood functions of such models involve high dimensional integrals and a huge number of summations over unobserved regime paths simulated likelihood methods and simulated methods of moments are available these approaches simulate both continuous and discrete latent dependent variables by monte carlo experiments it is found that the performances of various approaches depend crucially on how discrete state variables are simulated the valuable approach is to simulate regime paths with regime probabilities based on the current and past sample information

the b spectral sequence lagrangian formalism and conservation laws ii the nonlinear theory notations et faits provenant du calcul differentiel dans des algebres commutatives operateurs adjoints complexes de spencer et formule de green lagrangiens quadratiques et l operateur d euler lois de conservation en theorie lineaire automorphismes et le theoreme de n ether lineaire

bayesian nonparametric inference of switching dynamic linear models many complex dynamical phenomena can be effectively modeled by a system that switches among a set of conditionally linear dynamical modes we consider two such models the switching linear dynamical system slds and the switching vector autoregressive var process our bayesian nonparametric approach utilizes a hierarchical dirichlet process prior to learn an unknown number of persistent smooth dynamical modes we additionally employ automatic relevance determination to infer a sparse set of dynamic dependencies allowing us to learn slds with varying state dimension or switching var processes with varying autoregressive order we develop a sampling algorithm that combines a truncated approximation to the dirichlet process with efficient joint sampling of the mode and state sequences the utility and flexibility of our model are demonstrated on synthetic data sequences of dancing honey bees the ibovespa stock index and a maneuvering target tracking application

doubly robust type estimation for covariate adjustment in latent variable modeling due to the difficulty in achieving a random assignment a quasi experimental or observational study design is frequently used in the behavioral and social sciences if a nonrandom assignment depends on the covariates multiple group structural equation modeling that includes the regression function of the dependent variables on the covariates that determine the assignment can provide reasonable estimates under the condition of correct specification of the regression function however it is usually difficult to specify the correct regression function because the dimensions of the dependent variables and covariates are typically large therefore the propensity score adjustment methods have been proposed since they do not require the specification of the regression function and have been applied to several applied studies however these methods produce biased estimates if the assignment mechanism is incorrectly specified in order to make a more robust inference it would be more useful to develop an estimation method that integrates the regression approach with the propensity score methodology in this study we propose a doubly robust type estimation method for marginal multiple group structural equation modeling this method provides a consistent estimator if either the regression function or the assignment mechanism is correctly specified a simulation study indicates that the proposed estimation method is more robust than the existing methods

regime switching state space models applied to psychological processes handling missing data and making inferences many psychological processes are characterized by recurrent shifts between distinct regimes or states examples that are considered in this paper are the switches between different states associated with premenstrual syndrome hourly fluctuations in affect during a major depressive episode and shifts between a hot hand and a cold hand in a top athlete we model these processes with the regime switching state space model proposed by kim j econom 60 1 22 1994 which results in both maximum likelihood estimates for the model parameters and estimates of the latent variables and the discrete states of the process however the current algorithm cannot handle missing data which limits its applicability to psychological data moreover the performance of standard errors for the purpose of making inferences about the parameter estimates is yet unknown in this paper we modify kim s algorithm so it can handle missing data and we perform a simulation study to investigate its performance in relatively short time series in cases of different kinds of missing data and in case of complete data finally we apply the regime switching state space model to the three empirical data sets described above

une base explicite de symboles modulaires sur les corps de fonctions modular symbols for the congruence subgroup gamma 0 mathfrak n of gl 2 mathbf f q t have been defined by teitelbaum they have a presentation given by a finite number of generators and relations in a formalism similar to manin s for classical modular symbols we completely solve the relations and get an explicit basis of generators when mathfrak n is a prime ideal of odd degree as an application we give a non vanishing statement for l functions of certain automorphic cusp forms for mathbf f q t the main statement also provides a key step for a result towards the uniform boundedness conjecture for drinfeld modules of rank 2

dynamic linear models with markov switching abstract in this paper hamilton s 1988 1989 markov switching model is extended to a general state space model this paper also complements shumway and stoffer s 1991 dynamic linear models with switching by introducing dependence in the switching process and by allowing switching in both measurement and transition equations building upon ideas in hamilton 1989 cosslett and lee 1985 and harrison and stevens 1976 a basic filtering and smoothing algorithm is presented the algorithm and the maximum likelihood estimation procedure is applied in estimating lam s 1990 generalized hamilton model with a general autoregressive component the estimation results show that the approximation employed in this paper performs an excellent job with a considerable advantage in computation time a state space representation is a very flexible form and the approach taken in this paper therefore allows a broad class of models to be estimated that could not be handled before in addition the algorithm for calculating smoothed inferences on the unobserved states is a vastly more efficient one than that in the literature

markov switching model selection using kullback leibler divergence abstract in markov switching regression models we use kullback leibler kl divergence between the true and candidate models to select the number of states and variables simultaneously specifically we derive a new information criterion markov switching criterion msc which is an estimate of kl divergence msc imposes an appropriate penalty to mitigate the over retention of states in the markov chain and it performs well in monte carlo studies with single and multiple states small and large samples and low and high noise we illustrate the usefulness of msc via applications to the u s business cycle and to media advertising

regime switching dynamic correlations for asymmetric and fat tailed conditional returns abstract a non gaussian multivariate regime switching dynamic correlation model for financial asset returns is proposed it incorporates the multivariate generalized hyperbolic law for the conditional distribution of returns all model parameters are estimated consistently using a new two stage expectation maximization algorithm that also allows for incorporation of shrinkage estimation via quasi bayesian priors it is shown that use of markov switching correlation dynamics not only leads to highly accurate risk forecasts but also potentially reduces the regulatory capital requirements during periods of distress in terms of portfolio performance the new regime switching model delivers consistently higher sharpe ratios and smaller losses than the equally weighted portfolio and all competing models finally the regime forecasts are employed in a new dynamic risk control strategy that avoids most losses during the financial crisis and vastly improves risk adjusted returns

generalized symmetries and conservation laws of 1 1 dimensional klein gordon equation using advantages of nonstandard computational techniques based on the light cone variables we explicitly find the algebra of generalized symmetries of the 1 1 dimensional klein gordon equation this allows us to describe this algebra in terms of the universal enveloping algebra of the essential lie invariance algebra of the klein gordon equation then we single out variational symmetries of the corresponding lagrangian and compute the space of local conservation laws of this equation which turns out to be generated up to the action of generalized symmetries by a single first order conservation law moreover for every conservation law we find a conserved current of minimal order contained in this conservation law

the likelihood ratio test for a change point in simple linear regression summary we consider likelihood ratio tests to detect a change point in simple linear regression a when the alternative specifies that only the intercept changes and b when the alternative permits the intercept and the slope to change approximations for the significance level are obtained under reasonably general assumptions about the empirical distribution of the independent variable the approximations are compared with simulations in order to assess their accuracy for the model in which only the intercept is allowed to change a confidence region for the change point and an approximate joint confidence region for the change point the difference in intercepts and the slope are obtained by inversion of the appropriate likelihood ratio tests

a propensity score adjustment for multiple group structural equation modeling in the behavioral and social sciences quasi experimental and observational studies are used due to the difficulty achieving a random assignment however the estimation of differences between groups in observational studies frequently suffers from bias due to differences in the distributions of covariates to estimate average treatment effects when the treatment variable is binary rosenbaum and rubin 1983a proposed adjustment methods for pretreatment variables using the propensity score

learning and inferring motion patterns using parametric segmental switching linear dynamic systems switching linear dynamic system slds models are a popular technique for modeling complex nonlinear dynamic systems an slds can describe complex temporal patterns more concisely and accurately than an hmm by using continuous hidden states however the use of slds models in practical applications is challenging for three reasons first exact inference in slds models is computationally intractable second the geometric duration model induced in standard sldss limits their representational power third standard sldss do not provide a principled way to interpret systematic variations governed by higher order parameters the contributions in this paper address all of these three challenges first we present a data driven mcmc dd mcmc sampling method for approximate inference in sldss we show dd mcmc provides an efficient method for estimation and learning in slds models second we present segmental sldss s slds where the geometric distributions of the switching state durations are replaced with arbitrary duration models third we extend the standard slds model with additional global parameters that can capture systematic temporal and spatial variations the resulting parametric slds model p slds uses em to robustly interpret parametrized motions by incorporating additional global parameters that underly systematic variations of the overall motion the overall development of the extensions for sldss provide a principled framework to interpret complex motions the framework is applied to the honey bee dance interpretation task in the context of the on going biotracking project at the georgia institute of technology the experimental results suggest that the enhanced models provide an effective framework for a wide range of motion analysis applications