inference from accelerated life tests using filtering in coloured noise summary we present a new approach for inference from accelerated life tests our approach formulates such problems as inference under kalman filter models with correlated observation errors we restrict attention to exponential life distributions and the power rule as a time transformation function extensions to other time transformation functions are straightforward however extensions to other distributions involve non linear filtering and are not considered the advantages of our formulation are that we are able to incorporate uncertainty in the time transformation function and also are able to allow it to change with the stress to validate our approach we consider some simulated data to give it a sense of reality we apply it to actual data

bayesian model monitoring on presente une approche bayesienne basee sur des comparaisons des predictions a partir du modele standard avec celles d un modele alternatif simple

partial non gaussian state space summary in this paper we suggest the use of simulation techniques to extend the applicability of the usual gaussian state space filtering and smoothing techniques to a class of nongaussian time series models this allows a fully bayesian or maximum likelihood analysis of some interesting models including outlier models discrete markov chain components multiplicative models and stochastic variance models finally we discuss at some length the use of a non gaussian model to seasonally adjust the published money supply figures

dynamics of the pendulum with periodically varying length dynamic behavior of a weightless rod with a point mass sliding along the rod axis according to periodic law is studied this is the pendulum with periodically varying length which is also treated as a simple model of a child s swing asymptotic expressions for boundaries of instability domains near resonance frequencies are derived domains for oscillation rotation and oscillation rotation motions in parameter space are found analytically and compared with a numerical study chaotic motions of the pendulum depending on problem parameters are investigated numerically

comparisons between the pendulum with varying length and the pendulum with oscillating support we consider two forced dissipative pendulum systems the pendulum with vertically oscillating support and the pendulum with periodically varying length with a view to draw comparisons between their behaviour we study the two systems for values of the parameters for which the dynamics are non chaotic we focus our investigation on the persisting attractive periodic orbits and their basins of attraction utilising both analytical and numerical techniques although in some respect the two systems have similar behaviour we find that even within the perturbation regime they may exhibit different dynamics in particular for the same value of the amplitude of the forcing the pendulum with varying length turns out to be perturbed to a greater extent furthermore the periodic attractors persist under larger values of the damping coefficient in the pendulum with varying length finally unlike the pendulum with oscillating support the pendulum with varying length cannot be stabilised around the upward position for any values of the parameters

a bivariate autoregressive poisson model and its application to asthma related emergency room visits there are no gold standard methods that perform well in every situation when it comes to the analysis of multiple time series of counts in this paper we consider a positively correlated bivariate time series of counts and propose a parameter driven poisson regression model for its analysis in our proposed model we employ a latent autoregressive process ar p to accommodate the temporal correlations in the two series we compute the familiar maximum likelihood estimators of the model parameters and their standard errors via a bayesian data cloning approach we apply the model to the analysis of a bivariate time series arising from asthma related visits to emergency rooms across the canadian province of ontario

heuristics of instability and stabilization in model selection in model selection usually a best predictor is chosen from a collection hat mu cdot s of predictors where hat mu cdot s is the minimum least squares predictor in a collection mathsf u s of predictors here s is a complexity parameter that is the smaller s the lower dimensional smoother the models in mathsf u s if mathsf l is the data used to derive the sequence hat mu cdot s the procedure is called unstable if a small change in mathsf l can cause large changes in hat mu cdot s with a crystal ball one could pick the predictor in hat mu cdot s having minimum prediction error without prescience one uses test sets cross validation and so forth the difference in prediction error between the crystal ball selection and the statistician s choice we call predictive loss for an unstable procedure the predictive loss is large this is shown by some analytics in a simple case and by simulation results in a more complex comparison of four different linear regression methods unstable procedures can be stabilized by perturbing the data getting a new predictor sequence hat mu cdot s and then averaging over many such predictor sequences

likelihood analysis of non gaussian measurement time series summary in this paper we provide methods for estimating non gaussian time series models these techniques rely on markov chain monte carlo to carry out simulation smoothing and bayesian posterior analysis of parameters and on importance sampling to estimate the likelihood function for classical inference the time series structure of the models is used to ensure that our simulation algorithms are efficient

finding the location of a signal a bayesian analysis abstract we study the problem of determining the location of an emergency transmitter in a downed aircraft the observations are bearings read at fixed stations a bayesian approach yielding a posterior map of probable locations seems reasonable in this situation we therefore develop conjugate prior distributions for the von mises distribution which we use to compute a posterior distribution of the location an approximation to the posterior distribution yields accurate rapidly computable answers a common problem with this kind of data is the possibility that signals will reflect off orographic terrain features resulting in wild bearings such bearings can affect the posterior distribution severely we develop a sensitivity analysis based on the idea of predictive distribution to reject wild bearings the method which is based on an asymptotic argument nonetheless performs well in a small simulation study when the preceding approximation is used the sensitivity analysis is practical in terms

analysis of variance of cross validation estimators of the generalization error this paper brings together methods from two different disciplines statistics and machine learning we address the problem of estimating the variance of cross validation cv estimators of the generalization error in particular we approach the problem of variance estimation of the cv estimators of generalization error as a problem in approximating the moments of a statistic the approximation illustrates the role of training and test sets in the performance of the algorithm it provides a unifying approach to evaluation of various methods used in obtaining training and test sets and it takes into account the variability due to different training and test sets for the simple problem of predicting the sample mean and in the case of smooth loss functions we show that the variance of the cv estimator of the generalization error is a function of the moments of the random variables y card sj sj and y card sjc sj c where sj sj are two training sets and sjc sj c are the corresponding test sets we prove that the distribution of y and y is hypergeometric and we compare our estimator with the one proposed by nadeau and bengio 2003 we extend these results in the regression case and the case of absolute error loss and indicate how the methods can be extended to the classification case we illustrate the results through simulation

combined 5 2 cv f test for comparing supervised classification learning algorithms dietterich 1998 reviews five statistical tests and proposes the 5 2 cv t test for determining whether there is a significant difference between the error rates of two classifiers in our experiments we noticed that the 5 2 cv t test result may vary depending on factors that should not affect the test and we propose a variant the combined 5 2 cv f test that combines multiple statistics to get a more robust test simulation results show that this combined version of the test has lower type i error and higher power than 5 2 cv proper

a sequential smoothing algorithm with linear computational cost in this paper we propose a new particle smoother that has a computational complexity of o n where n is the number of particles this compares favourably with the o n2 computational cost of most smoothers the new method also overcomes some degeneracy problems in existing algorithms through simulation studies we show that substantial gains in efficiency are obtained for practical amounts of computational cost it is shown both through these simulation studies and by the analysis of an athletics dataset that our new method also substantially outperforms the simple filter smoother the only other smoother with computational cost that is o n

markov cross validation for time series model evaluations cross validation cv is a simple and universal tool to estimate generalization ability however existing cvs do not work well for periodicity overlapping or correlation of series the corresponding three criteria aimed at describing these properties are presented based on them we put forward a novel markov cross validation m cv whose data partition can be seen as a markov process the partition ensures that samples in each subset are neither too close nor too far in doing so overfitting model or information loss of series which may result in underestimation or overestimation of the error can be avoided furthermore subsets from m cv partition could well represent the original series and it may be extended to time series or stream data sampling theoretical analysis shows that m cv is the unique one which meets all of above criteria among current cvs in addition the error estimation on subsets is proved to have less variance than that on original series therefore it ensures the stability of m cv experimental results demonstrate that the proposed m cv has lower bias variance and time consumption than other cvs

rotating solutions and stability of parametric pendulum by perturbation method abstract rotating solutions of a parametrically driven pendulum are studied via a perturbation method by assuming the undamped unforced hamiltonian case as basic solution and damping and excitation as small perturbations the existence and stability of the harmonic solution are determined analytically first order terms are mainly considered but the extensions to higher order terms as well as to subharmonic rotations are straightforward setting up the analysis in the phase space instead of in the physical space has facilitated development of simple but comprehensive formulas comparison with numerical simulations shows that the analytical results are very effective in accurate predictions even for fairly large amplitudes and in detecting the saddle node bifurcation where the rotating solution is born a limited accuracy is observed to first order in detecting the period doubling bifurcation where it loses stability and an explanation is proposed

modeling multiple time series with applications abstract an approach to the modeling and analysis of multiple time series is proposed properties of a class of vector autoregressive moving average models are discussed modeling procedures consisting of tentative specification estimation and diagnostic checking are outlined and illustrated by three real examples

time varying combinations of predictive densities using nonlinear filtering abstract we propose a bayesian combination approach for multivariate predictive densities which relies upon a distributional state space representation of the combination weights several specifications of multivariate time varying weights are introduced with a particular focus on weight dynamics driven by the past performance of the predictive densities and the use of learning mechanisms in the proposed approach the model set can be incomplete meaning that all models can be individually misspecified a sequential monte carlo method is proposed to approximate the filtering and predictive densities the combination approach is assessed using statistical and utility based performance measures for evaluating density forecasts of simulated data us macroeconomic time series and surveys of stock market prices simulation results indicate that for a set of linear autoregressive models the combination strategy is successful in selecting with probability close to one the true model when the model set is complete and it is able to detect parameter instability when the model set includes the true model that has generated subsamples of data also substantial uncertainty appears in the weights when predictors are similar residual uncertainty reduces when the model set is complete and learning reduces this uncertainty for the macro series we find that incompleteness of the models is relatively large in the 1970 s the beginning of the 1980 s and during the recent financial crisis and lower during the great moderation the predicted probabilities of recession accurately compare with the nber business cycle dating model weights have substantial uncertainty attached with respect to returns of the s p 500 series we find that an investment strategy using a combination of predictions from professional forecasters and from a white noise model puts more weight on the white noise model in the beginning of the 1990 s and switches to giving more weight to the professional forecasts over time information on the complete predictive distribution and not just on some moments turns out to be very important above all during turbulent times such as the recent financial crisis more generally the proposed distributional state space representation offers great flexibility in combining densities

theory and methods abstract a self organizing filter and smoother for the general nonlinear non gaussian state space model is proposed an expanded state space model is defined by augmenting the state vector with the unknown parameters of the original state space model the state of the augmented state space model and hence the state and the parameters of the original state space model are estimated simultaneously by either a non gaussian filter smoother or a monte carlo filter smoother in contrast to maximum likelihood estimation of model parameters in ordinary state space modeling for which the recursive filter computation has to be done many times model parameter estimation in the proposed self organizing filter smoother is achieved with only two passes of the recursive filter and smoother operations examples such as automatic tuning of dispersion and the shape parameters adaptation to changes of the amplitude of a signal in seismic data state estimation for a nonlinear state space model with unknown parameters

spatiotemporal prediction for log gaussian cox processes space time point pattern data have become more widely available as a result of technological developments in areas such as geographic information systems we describe a flexible class of space time point processes our models are cox processes whose stochastic intensity is a space time ornstein uhlenbeck process we develop moment based methods of parameter estimation show how to predict the underlying intensity by using a markov chain monte carlo approach and illustrate the performance of our methods on a synthetic data set

markov regression models for time series a quasi likelihood approach this paper discusses a quasi likelihood ql approach to regression analysis with time series data we consider a class of markov models referred to by cox 1981 scandinavian journal of statistics 8 93 115 as observation driven models in which the conditional means and variances given the past are explicit functions of past outcomes the class includes autoregressive and markov chain models for continuous and categorical observations as well as models for counts e g poisson and continuous outcomes with constant coefficient of variation e g gamma we focus on poisson and gamma data for illustration analogous to ql for independent observations large sample properties of the regression coefficients depend only on correct specification of the first conditional moment

forecasting records by maximum likelihood abstract a maximum likelihood method of fitting a model to a series of records is proposed using ideas from the analysis of censored data to construct a likelihood function based on observed records this method is tried out by fitting several models to series of athletics records for mile and marathon races a form of residual analysis is proposed for testing the models forecasting consequences are also considered in the case of mile records a steady linear improvement since 1931 is found the marathon data are harder to interpret with a steady improvement until 1965 with only slight improvement in world records since then in both cases the normal distribution appears at least as good as extreme value distributions for the distribution of annual best performances short term forecasts appear satisfactory but serious reservations are expressed about using regression type methods to predict long term performance limits

parametric likelihood inference for record breaking problems summary in this paper we consider the analysis of record breaking data sets where only observations that exceed or only those that fall below the current extreme value are recorded example application areas include industrial stress testing meteorological analysis sporting and athletic events and oil and mining surveys a closely related area is that of threshold modelling where the observations are those that cross a certain threshold value the inherent missing data structure present in these problems leads to likelihood functions that contain possibly high dimensional integrals rendering traditional maximum likelihood methods difficult or not feasible fortunately we may obtain arbitrarily accurate approximations to the likelihood function by iteratively applying monte carlo integration methods geyer thompson 1992 subiteration using the gibbs sampler may help to evaluate any multivariate integrals encountered during this process this approach can handle far more sophisticated parametric models than have been used previously in record breaking and threshold data contexts in particular the methodology allows for observations that are dependent and subject to mean shifts over time we present a numerical example involving records in olympic high jump competition where besides estimation we also address related issues in model selection and prediction

a general framework for the statistical analysis of the sources of variance for classification error estimators estimating the prediction error of classifiers induced by supervised learning algorithms is important not only to predict its future error but also to choose a classifier from a given set model selection if the goal is to estimate the prediction error of a particular classifier the desired estimator should have low bias and low variance however if the goal is the model selection in order to make fair comparisons the chosen estimator should have low variance assuming that the bias term is independent from the considered classifier this paper follows the analysis proposed in 1 about the statistical properties of k fold cross validation estimators and extends it to the most popular error estimators resubstitution holdout repeated holdout simple bootstrap and 0 632 bootstrap estimators without and with stratification we present a general framework to analyze the decomposition of the variance of different error estimators considering the nature of the variance irreducible reducible variance and the different sources of sensitivity internal external sensitivity an extensive empirical study has been performed for the previously mentioned estimators with naive bayes and c4 5 classifiers over training sets obtained from assorted probability distributions the empirical analysis consists of decomposing the variances following the proposed framework and checking the independence assumption between the bias and the considered classifier based on the obtained results we propose the most appropriate error estimations for model selection under different experimental conditions

random effects models for serial observations with binary response this paper presents a general mixed model for the analysis of serial dichotomous responses provided by a panel of study participants each subject s serial responses are assumed to arise from a logistic model but with regression coefficients that vary between subjects the logistic regression parameters are assumed to be normally distributed in the population inference is based upon maximum likelihood estimation of fixed effects and variance components and empirical bayes estimation of random effects exact solutions are analytically and computationally infeasible but an approximation based on the mode of the posterior distribution of the random parameters is proposed and is implemented by means of the em algorithm this approximate method is compared with a simpler two step method proposed by korn and whittemore using data from a panel study of asthmatics originally described in that paper one advantage of the estimation strategy described here is the ability to use all of the data including that from subjects with insufficient data to permit fitting of a separate logistic regression model as required by the korn and whittemore method however the new method is computationally intensive

a general family of distributions for longitudinal dependence with special reference to event histories event histories play an increasingly important role in medical studies examples include times between recurrences of tumours as with bladder cancer and between repeated infections as with chronic granulotomous disease a general method for generating new distributions is proposed by introducing an intensity function into a density this procedure yields as special cases several distributions already proposed in the literature the families of distributions based on the pareto distribution are of particular interest for event history analysis because of their relationship to the laplace transform of a gamma distribution they can yield multivariate distributions with longitudinal serial dependence by a procedure similar to updating in the kalman filter and with uniform dependence in a similar way to copulas for longitudinal dependence several such updating procedures are proposed

estimating bayes factors via posterior simulation with the laplace metropolis estimator abstract the key quantity needed for bayesian hypothesis testing and model selection is the integrated or marginal likelihood of a model we describe a way to use posterior simulation output to estimate integrated likelihoods we describe the basic laplace metropolis estimator for models without random effects for models with random effects we introduce the compound laplace metropolis estimator we apply this estimator to data from the world fertility survey and show it to give accurate results batching of simulation output is used to assess the uncertainty involved in using the compound laplace metropolis estimator the method allows us to test for the effects of independent variables in a random effects model and also to test for the presence of the random effects

prediction rules for exponential family state space models summary we state and prove a simple and general expression for the marginal mean in an exponential family state space model with conjugate state density we then discuss implications of this result on the choice of parameterization of the observation density on the interpretation of the predictive density for steady models and on exponentially weighted moving average and trend free forecasting

the k record processes are i i d let x 1 x 2 be i i d positive random variables and let n be the initial rank of x n that is the rank of x n among x 1 x n those observations whose initial rank is k are collected into a point process n k on called the k record process the fact that itnk k 1 2 are independent and identically distributed point processes is the main result of the paper the proof based on martingales is very rapid we also show that given n 1 n k the lifetimes in rank k of all observations of initial rank at most k are independent geometric random variables these results are generalised to continuous time where the analogue of the i i d sequence is a time space poisson process initially we think of this poisson process as having values in but subsequently we extend to poisson processes with values in more general polish spaces for example brownian excursion space where ranking is performed using real valued attributes

an autoregressive process for beta random variables two stationary first order autoregressive processes with beta marginal distributions are presented they are both linear additive processes but the coefficients are beta random variables their autocorrelation functions are investigated one is positive and the other alternates in sign the usefulness of the models in simulation is discussed the bivariate beta distributions of two consecutive observations are considered in some detail several examples are given including a bivariate uniform process which is also examined in detail the relationship of these bivariate beta distributions to the dirichlet distribution is discussed

a regression model for time series of counts summary this paper discusses a model for regression analysis with a time series of counts correlation is assumed to arise from an unobservable process added to the linear predictor in a log linear model an estimating equation approach used for parameter estimation leads to an iterative weighted and filtered least squares algorithm asymptotic properties for the regression coefficients are presented we illustrate the technique with an analysis of trends in u s polio incidence since 1970

linear growth curve analysis based on exponential dispersion models the paper introduces a class of linear growth curve models based on combinations of exponential dispersion models the models have three components namely a latent markov growth process with stationary and independent increments a noise component and a component describing variation between subjects the models allow a wide range of continuous discrete and mixed distributions estimation for the models is based on an estimating equation derived from an em like algorithm combined with kalman smoothing

block regularized m 2 cross validated estimator of the generalization error a cross validation method based on replications of two fold cross validation is called an cross validation an cross validation is used in estimating the generalization error and comparing of algorithms performance in machine learning however the variance of the estimator of the generalization error in cross validation is easily affected by random partitions poor data partitioning may cause a large fluctuation in the number of overlapping samples between any two training test sets in cross validation this fluctuation results in a large variance in the cross validated estimator the influence of the random partitions on variance becomes serious as increases thus in this study the partitions with a restricted number of overlapping samples between any two training test sets are defined as a block regularized partition set the corresponding cross validation is called block regularized cross validation bcv it can effectively reduce the influence of random partitions we prove that the variance of the bcv estimator of the generalization error is smaller than the variance of cross validated estimator and reaches the minimum in a special situation an analytical expression of the variance can also be derived in this special situation this conclusion is validated through simulation experiments furthermore a practical construction method of bcv by a two level orthogonal array is provided finally a conservative estimator is proposed for the variance of estimator of the generalization error

dynamic generalized linear models and bayesian forecasting abstract dynamic bayesian models are developed for application in nonlinear non normal time series and regression problems providing dynamic extensions of standard generalized linear models a key feature of the analysis is the use of conjugate prior and posterior distributions for the exponential family parameters this leads to the calculation of closed standard form predictive distributions for forecasting and model criticism the structure of the models depends on the time evolution of underlying state variables and the feedback of observational information to these variables is achieved using linear bayesian prediction methods data analytic aspects of the models concerning scale parameters and outliers are discussed and some applications are provided dynamic bayesian models are developed for application in nonlinear non normal time series and regression problems providing dynamic extensions of standard generalized linear models a key feature of the analysis is the use of conjugate prior and

a state space model for multivariate longitudinal count data summary we propose a nonstationary state space model for multivariate longitudinal count data driven by a latent gamma markov process the poisson counts are assumed to be conditionally independent given the latent process both over time and across categories we consider a regression model where time varying covariates may enter via either the poisson model or the latent gamma process estimation is based on the kalman smoother and we consider analysis of residuals from both the poisson model and the latent process a reanalysis of zeger s 1988 polio data shows that the choice between a stationary and nonstationary model is crucial for the correct assessment of the evidence of a long term decrease in the rate of u s polio infection

a negative binomial model for time series of counts we study generalized linear models for time series of counts where serial dependence is introduced through a dependent latent process in the link function conditional on the covariates and the latent process the observation is modelled by a negative binomial distribution to estimate the regression coefficients we maximize the pseudolikelihood that is based on a generalized linear model with the latent process suppressed we show the consistency and asymptotic normality of the generalized linear model estimator when the latent process is a stationary strongly mixing process we extend the asymptotic results to generalized linear models for time series where the observation variable conditional on covariates and a latent process is assumed to have a distribution from a one parameter exponential family thus we unify in a common framework the results for poisson log linear regression models of davis et al 2000 negative binomial logit regression models and other similarly specified generalized linear models language en

exponential family state space models based on a conjugate latent process summary this paper introduces non linear and non gaussian state space models with analytic updating recurnions for filtering and prediction this new class of models involves some well known results in the theory of exponential models and of exponential dispersion models and the latent process is defined in such a way that both the filtering and the prediction distributions turn out to be conjugate to the observation distribution at each step the corresponding analytic and inferential properties are investigated and some simple examples are presented

generalized autoregressive conditional heteroskedasticity a natural generalization of the arch autoregressive conditional heteroskedastic process introduced in engle 1982 to allow for past conditional variances in the current conditional variance equation is proposed stationarity conditions and autocorrelation structure for this new class of parametric models are derived maximum likelihood estimation and testing are also considered finally an empirical example relating to the uncertainty of the inflation rate is presented

fast cross validation for kernel based algorithms cross validation cv is a widely adopted approach for selecting the optimal model however the computation of empirical cross validation error cve has high complexity due to multiple times of learner training in this paper we develop a novel approximation theory of cve and present an approximate approach to cv based on the bouligand influence function bif for kernel based algorithms we first represent the bif and higher order bifs in taylor expansions and approximate cv via the taylor expansions we then derive an upper bound of the discrepancy between the original and approximate cv furthermore we provide a novel computing method to calculate the bif for general distribution and evaluate bif criterion for sample distribution to approximate cv the proposed approximate cv requires training on the full data set only once and is suitable for a wide variety of kernel based algorithms experimental results demonstrate that the proposed approximate cv is sound and effective

no unbiased estimator of the variance of k fold cross validation most machine learning researchers perform quantitative experiments to estimate generalization error and compare the performance of different algorithms in particular their proposed algorithm in order to be able to draw statistically convincing conclusions it is important to estimate the uncertainty of such estimates this paper studies the very commonly used k fold cross validation estimator of generalization performance the main theorem shows that there exists no universal valid under all distributions unbiased estimator of the variance of k fold cross validation the analysis that accompanies this result is based on the eigen decomposition of the covariance matrix of errors which has only three different eigenvalues corresponding to three degrees of freedom of the matrix and three components of the total variance this analysis helps to better understand the nature of the problem and how it can make naive estimators that don t take into account the error correlations due to the overlap between training and test sets grossly underestimate variance this is confirmed by numerical experiments in which the three components of the variance are compared when the difficulty of the learning problem and the number of folds are varied

algorithmic stability and sanity check bounds for leave one out cross validation in this article we prove sanity check bounds for the error of the leave one out cross validation estimate of the generalization error that is bounds showing that the worst case error of this estimate is not much worse than that of the training error estimate the name sanity check refers to the fact that although we often expect the leave one out estimate to perform considerably better than the training error estimate we are here only seeking assurance that its performance will not be considerably worse perhaps surprisingly such assurance has been given only for limited cases in the prior literature on cross validation any nontrivial bound on the error of leave one out must rely on some notion of algorithmic stability previous bounds relied on the rather strong notion of hypothesis stability whose application was primarily limited to nearest neighbor and other local algorithms here we introduce the new and weaker notion of error stability and apply it to obtain sanity check bounds for leave one out for other classes of learning algorithms including training error minimization procedures and bayesian algorithms we also provide lower bounds demonstrating the necessity of some form of error stability for proving bounds on the error of the leave one out estimate and the fact that for training error minimization algorithms in the worst case such bounds must still depend on the vapnik chervonenkis dimension of the hypothesis class

error estimation based on variance analysis of k fold cross validation when the numbers of samples and folds are both large enough we proved that cv variance and its accuracy have the quadratic relationship the relationships between cv variance and its factors have been derived allowing to predict which variance is less before applying k fold cv theoretical explanations have been given for some empirical evidences of rodriguez and kohavi from the respect of variance analysis the proposed normalized variance has significant correlation with the error and is unrelated to k so that it can serve as a stable error measurement cross validation cv is often used to estimate the generalization capability of a learning model the variance of cv error has a considerable impact on the accuracy of cv estimator and the adequacy of the learning model so it is very important to analyze cv variance the aim of this paper is to investigate how to improve the accuracy of the error estimation based on variance analysis we first describe the quantitative relationship between cv variance and its accuracy which can provide guidance for improving the accuracy by reducing the variance we then study the relationships between variance and relevant variables including the sample size the number of folds and the number of repetitions these form the basis of theoretical strategies of regulating cv variance our classification results can theoretically explain the empirical results of rodrguez and kohavi finally we propose a uniform normalized variance which not only measures model accuracy but also is irrelative to fold number therefore it simplifies the selection of fold number in k fold cv and normalized variance can serve as a stable error measurement for model comparison and selection we report the results of experiments using 5 supervised learning models and 20 datasets the results indicate that it is reliable to determine which variance is less before k fold cv by the proposed theorems and thus the accuracy of error estimation can be promoted by reducing variance in so doing we are more likely to select the best parameter or model

the analysis of binary longitudinal data with time independent covariates summary this paper considers extensions of logistic regression to the case where the binary outcome variable is observed repeatedly for each subject we propose two working models that lead to consistent estimates of the regression parameters and of their variances under mild assumptions about the time dependence within each subject s data the efficiency of the proposed estimators is examined an analysis of stress in mothers with infants is presented to illustrate the proposed method

estimating and interpolating a markov chain from aggregate data given aggregated longitudinal data generated by a markov chain which may be nonhomogeneous the problem considered is that of modelling estimating and interpolating the logarithms of partial odds and hence the transition probabilities by partial odds is meant the probability of a transition to another state divided by the probability of no transition a result establishing asymptotic normality leads to vector weighted least squares estimation of parameterised partial odds using standard regression methods it is shown how to obtain estimates of one step transition probabilities from widely or irregularly spaced data the methods are illustrated on an example concerning competing causes of death

a simple risk adjusted exponentially weighted moving average in such contexts as medical monitoring there is a need for a simple procedure to estimate the level of a smoothly changing dynamic process while adjusting for risk factors associated with heterogeneous nonnormal observations standard methods exist for when the data are normal and simple methods have been developed for nonnormal data without covariates the dynamic generalized linear model dglm may be considered a standard for nonnormal data with covariates but perhaps one that is overcomplicated for many contexts we propose adapting the standard exponentially weighted moving average ewma to take into account the effect of risk factors by approximating the correct exponential family likelihood we derive a risk adjusted ewma ra ewma that is essentially a standard ewma applied to pseudo observations which are the original observations adjusted for differential risk the ra ewma can be expressed as a type of filter in which current estimate previous estimate discounted predictive error we

modelling non stationary multivariate time series of counts via common factors we develop a new parameter driven model for multivariate time series of counts the time series is not necessarily stationary we model the mean process as the product of modulating factors and unobserved stationary processes the former characterizes the long run movement in the data whereas the latter is responsible for rapid fluctuations and other unknown or unavailable covariates the unobserved stationary processes evolve independently of the past observed counts and might interact with each other we express the multivariate unobserved stationary processes as a linear combination of possibly low dimensional factors that govern the contemporaneous and serial correlation within and across the observed counts regression coefficients in the modulating factors are estimated via pseudo maximum likelihood estimation and identification of common factor s is carried out through eigenanalysis on a positive definite matrix that pertains to the autocovariance of the observed counts at non zero lags theoretical validity of the two step estimation procedure is documented in particular we establish consistency and asymptotic normality of the pseudo maximum likelihood estimator in the first step and the convergence rate of the second step estimator we also present an exhaustive simulation study to examine the finite sample performance of the estimators and numerical results corroborate our theoretical findings finally we illustrate the use of the proposed model through an application to the numbers of national science foundation fundings awarded to seven research universities from january 2001 to december 2012

monte carlo em estimation for time series models involving counts abstract the observations in parameter driven models for time series of counts are generated from latent unobservable processes that characterize the correlation structure these models result in very complex likelihoods and even the em algorithm which is usually well suited for problems of this type involves high dimensional integration in this article we discuss a monte carlo em mcem algorithm that uses a markov chain sampling technique in the calculation of the expectation in the e step of the em algorithm we propose a stopping criterion for the algorithm and provide rules for selecting the appropriate monte carlo sample size we show that under suitable regularity conditions an mcem algorithm will with high probability get close to a maximizer of the likelihood of the observed data we also discuss the asymptotic efficiency of the procedure we illustrate our monte carlo estimation method on a time series involving small counts the polio incidence time series previously analyzed by zeger

dispersion models and longitudinal data analysis dispersion models provide a flexible class of non normal distributions with many potential applications in biostatistics accommodating a wide range of continuous discrete and mixed data starting with liang and zeger s generalized estimating equation method we review some recent applications of dispersion models in longitudinal data analysis including state space models based on the tweedie class of exponential dispersion models in medical applications the latent process of a state space model may often be interpreted as an unobserved potential morbidity process which is modelled as a function of time varying covariates by allowing a multivariate response vector of symptoms the model integrates several response variables of mixed types into a single model for growth curve models the latent process reflects the true growth

estimating the confidence interval for prediction errors of support vector machine classifiers support vector machine svm is one of the most popular and promising classification algorithms after a classification rule is constructed via the svm it is essential to evaluate its prediction accuracy in this paper we develop procedures for obtaining both point and interval estimators for the prediction error under mild regularity conditions we derive the consistency and asymptotic normality of the prediction error estimators for svm with finite dimensional kernels a perturbation resampling procedure is proposed to obtain interval estimates for the prediction error in practice with numerical studies on simulated data and a benchmark repository we recommend the use of interval estimates centered at the cross validated point estimates for the prediction error further applications of the proposed procedure in model evaluation and feature selection are illustrated with two examples

tweedie family of generalized linear models with distribution free random effects for skewed longitudinal data generalized linear mixed models have played an important role in the analysis of longitudinal data however traditional approaches have limited flexibility in accommodating skewness and complex correlation structures in addition the existing estimation approaches generally rely heavily on the specifications of random effects distributions therefore the corresponding inferences are sometimes sensitive to the choice of random effect distributions under certain circumstance in this paper we incorporate serially dependent distribution free random effects into tweedie generalized linear models to accommodate a wide range of skewness and covariance structures for discrete and continuous longitudinal data an optimal estimation of our model has been developed using the orthodox best linear unbiased predictors of random effects our approach unifies population averaged and subject specific inferences our method is illustrated through the analyses of patient controlled analgesia data and framingham cholesterol data

accurate approximations for posterior moments and marginal densities abstract this article describes approximations to the posterior means and variances of positive functions of a real or vector valued parameter and to the marginal posterior densities of arbitrary i e not necessarily positive parameters these approximations can also be used to compute approximate predictive densities to apply the proposed method one only needs to be able to maximize slightly modified likelihood functions and to evaluate the observed information at the maxima nevertheless the resulting approximations are generally as accurate and in some cases more accurate than approximations based on third order expansions of the likelihood and requiring the evaluation of third derivatives the approximate marginal posterior densities behave very much like saddle point approximations for sampling distributions the principal regularity condition required is that the likelihood times prior be unimodal

robust sequential approximate bayesian estimation summary an approximation to the sequential updating of the distribution of location parameters of a linear time series model is developed for non normal observations the behaviour of the resulting non linear recursive filtering algorithm is examined and shown to have certain desirable properties for a variety of non normal error distributions illustrative examples are given and relationships with previous work on robustness and sequential estimation are mentioned we consider here the problem of sequential estimation of the location vector of a linear time series model termed the dynamic linear model by harrison and stevens 1976 the straightforward exact analysis obtained by assuming normal error and prior structure is generally lost when alternative error distributions are adopted and yet considerations of realism or robustness may strongly suggest such non normal assumptions the multi state model of harrison and stevens provides an approximate analysis based on a discrete variance mixture of normal distributions an approach which has been extensively investigated in the engineering literature under the name of gaussian sum approximations see for example alspach and sorenson 1971 our aim in this paper is to provide an approximate tractible recursive updating procedure for the location parameters which is applicable to a wide range of symmetric unimodal error distributions and is both more realistic and more elegant than the discrete gaussian sum approach in particular for heavy tailed distributions our procedures provide approximate bayesian methods for time series analysis which extend considerably the work of masreliez and martin 1977 and have close connections with classical robustness ideas such as m estimation and influence functions

the multiparameter steady model summary this paper generalizes and extends the idea of a steady evolution of a time series to multiparameter processes with any observational distribution particular examples of such processes are given these include the multivariate steady process univariate normal processes where the observational variance is unknown and series of multinomial observations with a steady model on the cell probabilities

some properties and generalizations of non negative bayesian time series models we study the most basic bayesian forecasting model for exponential family time series the power steady model psm of smith in terms of observable properties of one step forecast distributions and sample paths the psm implies a constraint between location and spread of the forecast distribution including a scale parameter in the models does not always give an exact solution free of this problem but it does suggest how to define related models free of the constraint we define such a class of models which contains the psm we concentrate on the case where observations are non negative probability theory and simulation show that under very mild conditions almost all sample paths of these models converge to some constant making them unsuitable for modelling in many situations the results apply more generally to non negative models defined in terms of exponentially weighted moving averages we use these and related results to motivate define and apply very simple models based on directly specifying the forecast distributions

time series of continuous proportions summary a vector of continuous proportions consists of the proportions of some total accounted for by its constituent components an example is the proportions of world motor vehicle production by japan the usa and all other countries we consider the situation where time series data are available and where interest focuses on the proportions rather than the actual amounts reasons for analysing such times series include estimation of the underlying trend estimation of the effect of covariates and interventions and forecasting we develop a state space model for time series of continuous proportions conditionally on the unobserved state the observations are assumed to follow the dirichlet distribution often considered to be the most natural distribution on the simplex the state follows the dirichlet conjugate distribution which is introduced here thus the model although based on the dirichlet distribution does not have its restrictive independence properties covariates trends seasonality and interventions may be incorporated in a natural way the model has worked well when applied to several examples and we illustrate with components of world motor vehicle production

a non gaussian state space model and application to prediction of records on developpe une classe de modeles qui generalisent le travail de smith 1979 et bathes 1975 pour des donnees censurees

a self organizing state space model a self organizing filter and smoother for the general nonlinear non gaussian state space model is proposed an expanded state space model is defined by augmenting the state vector with the unknown parameters of the original state space model the state of the augmented state space model and hence the state and the parameters of the original state space model are estimated simultaneously by either a non gaussian filter smoother or a monte carlo filter smoother in contrast to maximum likelihood estimation of model parameters in ordinary state space modeling for which the recursive filter computation has to be done many times model parameter estimation in the proposed self organizing filter smoother is achieved with only two passes of the recursive filter and smoother operations examples such as automatic tuning of dispersion and the shape parameters adaptation to changes of the amplitude of a signal in seismic data state estimation for a nonlinear state space model with unknown parameters and seasonal adjustment with a nonlinear model with changing variance parameters are shown to exemplify the usefulness of the proposed method

multivariate regression analyses for categorical data summary it is common to observe a vector of discrete and or continuous responses in scientific problems where the objective is to characterize the dependence of each response on explanatory variables and to account for the association between the outcomes the response vector can comprise repeated observations on one variable as in longitudinal studies or genetic studies of families or can include observations for different variables this paper discusses a class of models for the marginal expectations of each response and for pairwise associations the marginal models are contrasted with log linear models two generalized estimating equation approaches are compared for parameter estimation the first focuses on the regression parameters the second simultaneously estimates the regression and association parameters the robustness and efficiency of each is discussed the methods are illustrated with analyses of two data sets from public health research

local scale models state space alternative to integrated garch processes state space alternative to autoregressive conditional heteroskedasticity models are proposed the initial model which is labelled the gaussian local scale model has a measurement density which is gaussian conditional on the unobservable precision the precision is assumed to be a gamma variable which evolves by being scaled by a beta variable the resulting forecast is a student s t random variable with a scale which is approximately an exponentially weighted moving average ewma of the squares of the past observations the degrees of freedom of the student s t distribution is controlled by the size of the discount parameter of the ewma procedure the gaussianity of the measurement density is potentially inadequate when the model is applied to heavy tailed finance data instead this assumption can be replaced by an exponential power density which allows the observed excess kurtosis to be modelled the choice of the exponential power means that the model still maintains conjugacy so allowing the derivation of an exact filter and likelihood function this model is called the generalised local scale model it has been used to model two exchange rate series

filtering and smoothing via estimating functions abstract we consider the problem of filtering and smoothing in state space models which include nonlinear and non gaussian models we do not make any distributional assumptions about the processes involved our approach to these problems is based on the theory of estimating functions filter and smoother are obtained as solutions of estimating equations that are optimal in appropriate classes we illustrate our procedures by simulation studies of a model where the observational variance depends on the state and a binomial logit model with a covariate in non gaussian cases procedures based on estimating equations often perform considerably better than the existing semiparametric procedures

bayesian estimation of an extended local scale stochastic volatility model a new version of the local scale model of shephard 1994 is presented its features are identically distributed evolution equation disturbances the incorporation of in the mean effects and the incorporation of variance regressors a bayesian posterior simulator and a new simulation smoother are presented the model is applied to publicly available daily exchange rate and asset return series and is compared with t garch and lognormal stochastic volatility formulations using bayes factors

credible intervals for precision and recall based on a k fold cross validated beta distribution in typical machine learning applications such as information retrieval precision and recall are two commonly used measures for assessing an algorithm s performance symmetrical confidence intervals based on k fold cross validated t distributions are widely used for the inference of precision and recall measures as we confirmed through simulated experiments however these confidence intervals often exhibit lower degrees of confidence which may easily lead to liberal inference results thus it is crucial to construct faithful confidence credible intervals for precision and recall with a high degree of confidence and a short interval length in this study we propose two posterior credible intervals for precision and recall based on k fold cross validated beta distributions the first credible interval for precision or recall is constructed based on the beta posterior distribution inferred by all k data sets corresponding to k confusion matrices from a k fold cross validation second considering that each data set corresponding to a confusion matrix from a k fold cross validation can be used to infer a beta posterior distribution of precision or recall the second proposed credible interval for precision or recall is constructed based on the average of k beta posterior distributions experimental results on simulated and real data sets demonstrate that the first credible interval proposed in this study almost always resulted in degrees of confidence greater than 95 with an acceptable degree of confidence both of our two proposed credible intervals have shorter interval lengths than those based on a corrected k fold cross validated t distribution meanwhile the average ranks of these two credible intervals are superior to that of the confidence interval based on a k fold cross validated t distribution for the degree of confidence and are superior to that of the confidence interval based on a corrected k fold cross validated t distribution for the interval length in all 27 cases of simulated and real data experiments however the confidence intervals based on the k fold and corrected k fold cross validated t distributions are in the two extremes thus when focusing on the reliability of the inference for precision and recall the proposed methods are preferable especially for the first credible interval