a theory of independent fuzzy probability for system reliability fuzzy fault trees provide a powerful and computationally efficient technique for developing fuzzy probabilities based on independent inputs the probability of any event that can be described in terms of a sequence of independent unions intersections and complements may be calculated by a fuzzy fault tree unfortunately fuzzy fault trees do not provide a complete theory many events of substantial practical interest cannot be described only by independent operations thus the standard fuzzy extension based on fuzzy fault trees is not complete since not all events are assigned a fuzzy probability other complete extensions have been proposed but these extensions are not consistent with the calculations from fuzzy fault trees we propose a new extension of crisp probability theory our model is based on n independent inputs each with a fuzzy probability the elements of our sample space describe exactly which of the n input events did and did not occur our extension is complete since a fuzzy probability is assigned to every subset of the sample space our extension is also consistent with all calculations that can be arranged as a fault tree our approach allows the reliability analyst to develop complete and consistent fuzzy reliability models from existing crisp reliability models this allows a comprehensive analysis of the system computational algorithms are provided both to extend existing models and develop new models the technique is demonstrated on a reliability model of a three stage industrial process

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

delay times of sequential procedures for multiple time series regression models we consider a multiple regression model in which the explanatory variables are specified by time series to sequentially test for the stability of the regression parameters in time we introduce a detector which is based on the first excess time of a cusum type statistic over a suitably constructed threshold function the aim of this paper is to study the delay time associated with this detector as our main result we derive the limit distribution of the delay time and provide thereby a theory that extends the benchmark average run length concept utilized in most of the sequential monitoring literature to highlight the applicability of the limit results in finite samples we present a monte carlo simulation study and an application to macroeconomic data

posterior consistency of gaussian process prior for nonparametric binary regression consider binary observations whose response probability is an unknown smooth function of a set of covariates suppose that a prior on the response probability function is induced by a gaussian process mapped to the unit interval through a link function in this paper we study consistency of the resulting posterior distribution if the covariance kernel has derivatives up to a desired order and the bandwidth parameter of the kernel is allowed to take arbitrarily small values we show that the posterior distribution is consistent in the l 1 distance as an auxiliary result to our proofs we show that under certain conditions a gaussian process assigns positive probabilities to the uniform neighborhoods of a continuous function this result may be of independent interest in the literature for small ball probabilities of gaussian processes

stepwise signal extraction via marginal likelihood this article studies the estimation of a stepwise signal to determine the number and locations of change points of the stepwise signal we formulate a maximum marginal likelihood estimator which can be computed with a quadratic cost using dynamic programming we carry out an extensive investigation on the choice of the prior distribution and study the asymptotic properties of the maximum marginal likelihood estimator we propose to treat each possible set of change points equally and adopt an empirical bayes approach to specify the prior distribution of segment parameters a detailed simulation study is performed to compare the effectiveness of this method with other existing methods we demonstrate our method on single molecule enzyme reaction data and on dna array comparative genomic hybridization cgh data our study shows that this method is applicable to a wide range of models and offers appealing results in practice supplementary materials for this article are available online

a fuzzy universal generating function based method for the reliability evaluation of series systems with performance sharing between adjacent units under parametric uncertainty abstract this paper considers fuzzy multi state systems msss with performance sharing between adjacent units in which each fuzzy multi state unit has a random performance and a random demand if the performance of a unit exceeds its individual demand performance demand its surplus performance can be transmitted to its adjacent unit that experiences performance deficiency performance

adaptive nonparametric bayesian inference using location scale mixture priors we study location scale mixture priors for nonparametric statistical problems including multivariate regression density estimation and classification we show that a rate adaptive procedure can be obtained if the prior is properly constructed in particular we show that adaptation is achieved if a kernel mixture prior on a regression function is constructed using a gaussian kernel an inverse gamma bandwidth and gaussian mixing weights

testing single index restrictions with a focus on average derivatives abstract this paper considers a situation where the violation of a single index restriction is a concern only to the extent that it causes bias to the estimates of the average derivatives we propose a method to construct tests that concentrate their asymptotic powers upon only such interesting alternatives the test has a 1 2 limiting distribution under the null hypothesis and even accommodates the case where the parameter estimates have a convergence rate slower than n as in the case of maximum score estimation the testing procedure can be easily modified when the main interest lies in average increment effects of binary covariates multivariate average derivatives or linear restrictions other than those of average derivatives results from monte carlo experiments show that the asymptotic theory is a reasonable approximation of the finite sample distributions and an application of our methods to female labor market participation illustrates the importance of this non omnibus approach

sublinear optimization for machine learning in this article we describe and analyze sublinear time approximation algorithms for some optimization problems arising in machine learning such as training linear classifiers and finding minimum enclosing balls our algorithms can be extended to some kernelized versions of these problems such as svdd hard margin svm and l2 svm for which sublinear time algorithms were not known before these new algorithms use a combination of a novel sampling techniques and a new multiplicative update algorithm we give lower bounds which show the running times of many of our algorithms to be nearly best possible in the unit cost ram model

renyi divergence and kullback leibler divergence renyi divergence is related to renyi entropy much like kullback leibler divergence is related to shannon s entropy and comes up in many settings it was introduced by renyi as a measure of information that satisfies almost the same axioms as kullback leibler divergence and depends on a parameter that is called its order in particular the renyi divergence of order 1 equals the kullback leibler divergence we review and extend the most important properties of renyi divergence and kullback leibler divergence including convexity continuity limits of sigma algebras and the relation of the special order 0 to the gaussian dichotomy and contiguity we also show how to generalize the pythagorean inequality to orders different from 1 and we extend the known equivalence between channel capacity and minimax redundancy to continuous channel inputs for all orders and present several other minimax results

faster and simpler algorithms for multicommodity flow and other fractional packing problems this paper considers the problem of designing fast approximate combinatorial algorithms for multicommodity flows and other fractional packing problems we present new faster and much simpler algorithms for these problems

on line inference for multiple changepoint problems we propose an on line algorithm for exact filtering of multiple changepoint problems this algorithm enables simulation from the true joint posterior distribution of the number and position of the changepoints for a class of changepoint models the computational cost of this exact algorithm is quadratic in the number of observations we further show how resampling ideas from particle filters can be used to reduce the computational cost to linear in the number of observations at the expense of introducing small errors and propose two new optimum resampling algorithms for this problem one a version of rejection control allows the particle filter to automatically choose the number of particles required at each time step the new resampling algorithms substantially out perform standard resampling algorithms on examples we consider and we demonstrate how the resulting particle filter is practicable for segmentation of human gc content

a test of non identifying restrictions and confidence regions for partially identified parameters abstract we propose an easily implementable test of the validity of a set of theoretical restrictions on the relationship between economic variables which do not necessarily identify the data generating process the restrictions can be derived from any model of interactions allowing censoring and multiple equilibria when the restrictions are parameterized the test can be inverted to yield confidence regions for partially identified parameters thereby complementing other proposals primarily chernozhukov et al chernozhukov v hong h tamer e 2007 estimation and confidence regions for parameter sets in econometric models econometrica 75 1243 1285

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

on gibbs sampling for state space models summary we show how to use the gibbs sampler to carry out bayesian inference on a linear state space model with errors that are a mixture of normals and coefficients that can switch over time our approach simultaneously generates the whole of the state vector given the mixture and coefficient indicator variables and simultaneously generates all the indicator variables conditional on the state vectors the states are generated efficiently using the kalman filter we illustrate our approach by several examples and empirically compare its performance to another gibbs sampler where the states are generated one at a time the empirical results suggest that our approach is both practical to implement and dominates the gibbs sampler that generates the states one at a time

a monte carlo implementation of the em algorithm and the poor man s data augmentation algorithms abstract the first part of this article presents the monte carlo implementation of the e step of the em algorithm given the current guess to the maximizer of the posterior distribution latent data patterns are generated from the conditional predictive distribution the expected value of the augmented log posterior is then updated as a mixture of augmented log posteriors mixed over the generated latent data patterns multiple imputations in the m step of the algorithm this mixture is maximized to obtain the update to the maximizer of the observed posterior the gradient and hessian of the observed log posterior are also expressed as mixtures mixed over the multiple imputations the relation between the monte carlo em mcem algorithm and the data augmentation algorithm is noted two modifications to the mcem algorithm the poor man s data augmentation algorithms which allow for the calculation of the entire posterior are then presented these approximations serve as diagnostics for the validity o

computing bayes factors by combining simulation and asymptotic approximations abstract the bayes factor is a ratio of two posterior normalizing constants which may be difficult to compute we compare several methods of estimating bayes factors when it is possible to simulate observations from the posterior distributions via markov chain monte carlo or other techniques the methods that we study are all easily applied without consideration of special features of the problem provided that each posterior distribution is well behaved in the sense of having a single dominant mode we consider a simulated version of laplace s method a simulated version of bartlett correction importance sampling and a reciprocal importance sampling technique we also introduce local volume corrections for each of these in addition we apply the bridge sampling method of meng and wong we find that a simulated version of laplace s method with local volume correction furnishes an accurate approximation that is especially useful when likelihood function evaluations are costly a simple bridge sampli

the intrinsic bayes factor for model selection and prediction abstract in the bayesian approach to model selection or hypothesis testing with models or hypotheses of differing dimensions it is typically not possible to utilize standard noninformative or default prior distributions this has led bayesians to use conventional proper prior distributions or crude approximations to bayes factors in this article we introduce a new criterion called the intrinsic bayes factor which is fully automatic in the sense of requiring only standard noninformative priors for its computation and yet seems to correspond to very reasonable actual bayes factors the criterion can be used for nested or nonnested models and for multiple model comparison and prediction from another perspective the development suggests a general definition of a reference prior for model comparison

noninformative priors and frequentist risks of bayesian estimators of vector autoregressive models in this study we examine posterior properties and frequentist risks of bayesian estimators based on several noninformative priors in vector autoregressive var models we prove existence of the posterior distributions and posterior moments under a general class of priors using a variety of priors in this class we conduct numerical simulations of posteriors we find that in most examples bayesian estimators with a shrinkage prior on the var coefficients and the reference prior of yang and berger ann statist 22 1994 1195 on the var covariance matrix dominate mle bayesian estimators with the diffuse prior and bayesian estimators with the prior used in rats we also examine the informative minnesota prior and find that its performance depends on the nature of the data sample and on the tightness of the minnesota prior a tightly set minnesota prior is better when the data generating processes are similar to random walks but the shrinkage prior or constant prior can be better otherwise

model averaging in semiparametric estimation of treatment effects choosing the covariates and functional form of the propensity score is an important choice for estimating treatment effects this paper proposes a data driven way of averaging the estimators over candidate specifications to resolve the specification uncertainty in the propensity score weighting estimation of the att the proposed procedures minimize the estimated mse of the att estimator in a local asymptotic framework we formulate model averaging as a statistical decision problem in a limit experiment and derive an averaging scheme that is bayes optimal with respect to a given prior the averaging estimator outperforms selection estimators and the estimators in any of the candidate models in terms of bayes asymptotic mse our monte carlo studies illustrate the size of the mse gains we apply the averaging procedure to evaluate the effect of a labor market program

optimal aggregation of classifiers in statistical learning classification can be considered as nonparametric estimation of sets where the risk is defined by means of a specific distance between sets associated with misclassification error it is shown that the rates of convergence of classifiers depend on two parameters the complexity of the class of candidate sets and the margin parameter the dependence is explicitly given indicating that optimal fast rates approaching o n 1 can be attained where n is the sample size and that the proposed classifiers have the property of robustness to the margin the main result of the paper concerns optimal aggregation of classifiers we suggest a classifier that automatically adapts both to the complexity and to the margin and attains the optimal fast rates up to a logarithmic factor

finite sample properties of linear model identification in this paper we consider the finite sample properties of prediction error methods using a quadratic criterion function for system identification the problem we pose is how many data points are required to guarantee with high probability that the expected value of the quadratic identification criterion is close to its empirical mean value the sample sizes are obtained using risk minimization theory which provides uniform probabilistic bounds on the difference between the expected value of the squared prediction error and its empirical mean evaluated on a finite number of data points the bounds are very general no assumption is made about the true system belonging to the model class and the noise sequence is not assumed to be uniformly bounded further analysis shows that in order to maintain a given bound on the deviation the number of data points needed grows no faster than quadratically with the number of parameters for fir and arx models

boundedly pivotal structural change tests in continuous updating gmm with strong weak identification and completely unidentified cases abstract this paper develops structural change tests in the continuous updating gmm framework that are robust to weak identification we propose likelihood ratio like anderson rubin 1949 estimation of the parameters of a single equation in a complete system of stochastic equations annals of mathematical statistics 20 46 63 and kleinbergen 2005 testing parameters in gmm without assuming that they are identified manuscript brown university types of tests since the limits of the test statistics are not nuisance parameter free bounds for the limit of the test statistics are derived the bounds are nuisance parameter free and robust to identification problems simulations show that the anderson rubin 1949 and kleinbergen 2005 testing parameters in gmm without assuming that they are identified manuscript brown university type of tests have very good small sample properties in the case of weak instruments the sup lm test of andrews 1993a tests for parameter instability and structural change with unknown change point econometrica 61 821 856 rejects the true null of parameter stability more than the nominal level and also has low power in the weak instrument setup

sampling based approaches to calculating marginal densities abstract stochastic substitution the gibbs sampler and the sampling importance resampling algorithm can be viewed as three alternative sampling or monte carlo based approaches to the calculation of numerical estimates of marginal probability distributions the three approaches will be reviewed compared and contrasted in relation to various joint probability structures frequently encountered in applications in particular the relevance of the approaches to calculating bayesian posterior densities for a variety of structured models will be discussed and illustrated

how the experts algorithm can help solve lps online we consider the problem of solving packing covering lps online when the columns of the constraint matrix are presented in random order this problem has received much attention and the main focus is to figure out how large the right hand sides of the lps have to be compared to the entries on the left hand side of the constraints to allow 1 approximations online it is known that the right hand sides have to be 2 log m times the left hand sides where m is the number of constraints in this paper we give a primal dual algorithm that achieves this bound for mixed packing covering lps our algorithms construct dual solutions using a regret minimizing online learning algorithm in a black box fashion and use them to construct primal solutions the adversarial guarantee that holds for the constructed duals helps us to take care of most of the correlations that arise in the algorithm the remaining correlations are handled via martingale concentration and maximal inequalities these ideas lead t

two stage plans for estimating the inverse of a monotone function this study investigates two stage plans based on nonparametric procedures for estimating an inverse regression function at a given point specifically isotonic regression is used at stage one to obtain an initial estimate followed by another round of isotonic regression in the vicinity of this estimate at stage two it is shown that such two stage plans accelerate the convergence rate of one stage procedures and are superior to existing two stage procedures that use local parametric approximations at stage two when the available budget is moderate and or the regression function is ill behaved both wald and likelihood ratio type confidence intervals for the threshold value of interest are investigated and the latter are recommended in applications due to their simplicity and robustness the developed plans are illustrated through a comprehensive simulation study and an application to car fuel efficiency data

a simple nonparametric approach to estimating the distribution of random coefficients in structural models abstract we explore least squares and likelihood nonparametric mixtures estimators of the joint distribution of random coefficients in structural models the estimators fix a grid of heterogeneous parameters and estimate only the weights on the grid points an approach that is computationally attractive compared to alternative nonparametric estimators we provide conditions under which the estimated distribution function converges to the true distribution in the weak topology on the space of distributions we verify most of the consistency conditions for three discrete choice models we also derive the convergence rates of the least squares nonparametric mixtures estimator under additional restrictions we perform a monte carlo study on a dynamic programming model

fuzzy reliability assessment of systems with multiple dependent competing degradation processes components are often subject to multiple competing degradation processes for multicomponent systems the degradation dependence within one component or and among components need to be considered physics based models and multistate models are often used for component degradation processes particularly when statistical data are limited in this paper we treat dependence between degradation processes within a piecewise deterministic markov process pdmp modeling framework epistemic subjective uncertainty can arise due to the incomplete or imprecise knowledge about the degradation processes and the governing parameters to take this into account we describe the parameters of the pdmp model as fuzzy numbers then we extend the finite volume method to quantify the fuzzy reliability of the system the proposed method is tested on one subsystem of the residual heat removal system of a nuclear power plant and a comparison is offered with a monte carlo simulation solution the results show that our method can be most efficient

smoothed quantile regression for panel data abstract this paper studies fixed effects estimation of quantile regression models for panel data under an asymptotic framework where both the numbers of individuals and time periods grow at the same rate we show that the fixed effects estimator for the smoothed objective function has a limiting normal distribution with a bias in the mean and provide the analytic form of the asymptotic bias we propose a one step bias correction estimator based on the analytic bias formula obtained from the asymptotic analysis importantly our results cover the case that observations are dependent over time we illustrate the effects of the bias correction through simulations

adwords and generalized online matching how does a search engine company decide what ads to display with each query so as to maximize its revenueq this turns out to be a generalization of the online bipartite matching problem we introduce the notion of a trade off revealing lp and use it to derive an optimal algorithm achieving a competitive ratio of 1 1 e for this problem

fast approximation algorithms for fractional packing and covering problems this paper presents fast algorithms that find approximate solutions for a general class of problems which we call fractional packing and covering problems the only previously known algorithms for solving these problems are based on general linear programming techniques the techniques developed in this paper greatly outperform the general methods in many applications and are extensions of a method previously applied to find approximate solutions to multicommodity flow problems our algorithm is a lagrangian relaxation technique an important aspect of our results is that we obtain a theoretical analysis of the running time of a lagrangian relaxation based algorithm we give several applications of our algorithms the new approach yields several orders of magnitude of improvement over the best previously known running times for algorithms for the scheduling of unrelated parallel machines in both the preemptive and the nonpreemptive models for the job shop problem for the held and karp bound for the tr

on the bootstrap of the maximum score estimator this paper shows that the bootstrap does not consistently estimate the asymptotic distribution of the maximum score estimator the theory developed also applies to other estimators within a cube root convergence class for some single parameter estimators in this class the results suggest a simple method for inference based upon the bootstrap

convex clustering via l1 fusion penalization summary we study the large sample behaviour of a convex clustering framework which minimizes the sample within cluster sum of squares under an l1 fusion constraint on the cluster centroids this recently proposed approach has been gaining in popularity however its asymptotic properties have remained mostly unknown our analysis is based on a novel representation of the sample clustering procedure as a sequence of cluster splits determined by a sequence of maximization problems we use this representation to provide a simple and intuitive formulation for the population clustering procedure we then demonstrate that the sample procedure consistently estimates its population analogue and we derive the corresponding rates of convergence the proof conducts a careful simultaneous analysis of a collection of m estimation problems whose cardinality grows together with the sample size on the basis of the new perspectives gained from the asymptotic investigation we propose a key post processing modification of the original clustering framework we show both theoretically and empirically that the resulting approach can be successfully used to estimate the number of clusters in the population using simulated data we compare the proposed method with existing number of clusters and modality assessment approaches and obtain encouraging results we also demonstrate the applicability of our clustering method to the detection of cellular subpopulations in a single cell virology study

bayesian multiple change points and segmentation application to homogenization of climatic series 1 in this paper we describe a new multiple change point detection technique based on segmenting the time series under study into subsequences these segments correspond to the episodes that are likely to contain a unique jump they are found by applying bayesian decision theory through the minimization of simple cost functions all calculations can be performed explicitly without falling back on markov chain monte carlo methods and resulting in particularly light implementation through prior distributions derived from a stochastic renewal process description of jump occurrences expert knowledge of jump amplitude and return period is also introduced in our decision process comparison to several multiple change point methods on simulated series lead to similar or better performance achieved at lower computational cost

an implicit finite volume scheme for a scalar hyperbolic problem with measure data related to piecewise deterministic markov processes we are interested here in the numerical approximation of a family of probability measures solution of the chapman kolmogorov equation associated to some non diffusion markov process with uncountable state space such an equation contains a transport term and another term which implies redistribution of the probability mass on the whole space an implicit finite volume scheme is proposed which is intermediate between an upstream weighting scheme and a modified lax friedrichs one due to the seemingly unusual probability framework a new weak bounded variation inequality had to be developed in order to prove the convergence of the discretised transport term such an inequality may be used in other contexts such as for the study of finite volume approximations of scalar linear or nonlinear hyperbolic equations with initial data in l 1 also due to the redistribution term the tightness of the family of approximate probability measures had to be proven numerical examples are provided showing the efficiency of the implicit finite volume scheme and its potentiality to be helpful in an industrial reliability context

inference and prediction in a multiple structural break model this paper develops a new bayesian approach to structural break modeling the focuses of the approach are the modeling of in sample structural breaks and forecasting time series allowing out of sample breaks the model has several desirable features first the number of regimes is not fixed but is treated as a random variable second the model adopts a hierarchical prior for regime coefficients which allows for the coefficients of one regime to contain information about coefficients of other regimes third the regime coefficients can be integrated analytically in the posterior density as a consequence the posterior simulator is fast and reliable an application to us real gdp quarterly growth rates links groups of regimes to specific historical periods and provides forecasts of future growth rates

k state switching models with time varying transition distributions does loan growth signal stronger effects of variables on inflation two bayesian sampling schemes are outlined to estimate a time varying markov switching transition distribution using data augmentation transforms the non linear non normal logit transition model into a linear normal one a partial representation of the difference in random utility model in combination with random permutation sampling provides highest sampling efficiency the level of the covariate in the transition distribution which balances the persistence across states is defined to be the threshold level for illustration we estimate a two pillar phillips curve for the euro area in which loan growth affects the transition distribution

u processes and preference learning preference learning has caused great attention in machining learning in this letter we propose a learning framework for pairwise loss based on empirical risk minimization of u processes via rademacher complexity we first establish a uniform version of bernstein inequality of u processes of degree 2 via the entropy methods then we estimate the bound of the excess risk by using the bernstein inequality and peeling skills finally we apply the excess risk bound to the pairwise preference and derive the convergence rates of pairwise preference learning algorithms with squared loss and indicator loss by using the empirical risk minimization with respect to u processes

a bayesian analysis for change point problems a sequence of observations undergoes sudden changes at unknown times we model the process by supposing that there is an underlying sequence of parameters partitioned into contiguous blocks of equal parameter values the beginning of each block is said to be a change point observations are then assumed to be independent in different blocks given the sequence of parameters in a bayesian analysis it is necessary to give probability distributions to both the change points and the parameters we use product partition models barry and hartigan 1992 which assume that the probability of any partition is proportional to a product of prior cohesions one for each block in the partition and that given the blocks the parameters in different blocks have independent prior distributions given the observations a new product partition model holds with posterior cohesions for the blocks and new independent block posterior distributions for parameters the product model thus provides a convenient machinery for allo

a fuzzy set approach to fault tree and reliability analysis abstract conventional fault tree and reliability analysis does not give a picture concerning the tolerances of the probability values of hazards to overcome this shortcoming the relative frequencies of the basic envents are considered as fuzzy numbers using standard approximations for the membership functions n ary possibilistic and or and neg operators are derived allowing a straightforward evaluation of the frequencies of hazard events in complex systems simultaneously with their tolerances the paper shows the use of these operators for constructing possibilistic fault trees the use of the method for numerical calculation is demonstrated on a real like safety problem

bayesian wavelet based methods for the detection of multiple changes of the long memory parameter long memory processes are widely used in many scientific fields such as economics physics and engineering change point detection problems have received considerable attention in the literature because of their wide range of possible applications here we describe a wavelet based bayesian procedure for the estimation and location of multiple change points in the long memory parameter of gaussian autoregressive fractionally integrated moving average models arfima p d q with unknown autoregressive and moving average parameters our methodology allows the number of change points to be unknown the reversible jump markov chain monte carlo algorithm is used for posterior inference the method also produces estimates of all model parameters performances are evaluated on simulated data and on the benchmark nile river dataset

a semiparametric change point regression model for longitudinal observations many longitudinal studies involve relating an outcome process to a set of possibly time varying covariates giving rise to the usual regression models for longitudinal data when the purpose of the study is to investigate the covariate effects when experimental environment undergoes abrupt changes or to locate the periods with different levels of covariate effects a simple and easy to interpret approach is to introduce change points in regression coefficients in this connection we propose a semiparametric change point regression model in which the error process stochastic component is nonparametric and the baseline mean function functional part is completely unspecified the observation times are allowed to be subject specific and the number locations and magnitudes of change points are unknown and need to be estimated we further develop an estimation procedure that combines the recent advance in semiparametric analysis based on counting process argument and multiple change points inference an

stochastic calculus for fractional brownian motion with hurst exponent h a rough path method by analytic extension the d dimensional fractional brownian motion fbm for short b t b 1 t b d t t r with hurst exponent 0 1 is a d dimensional centered self similar gaussian process with covariance e b i s b i t 1 2 i j lsl 2 ltl 2 t s 2 the long standing problem of defining a stochastic integration with respect to fbm and the related problem of solving stochastic differential equations driven by fbm has been addressed successfully by several different methods although in each case with a restriction on the range of either d or the case corresponds to the usual stochastic integration with respect to brownian motion while most computations become singular when gets under various threshhold values due to the growing irregularity of the trajectories as 0 we provide here a new method valid for any d and for 1 4 by constructing an approximation e t e 0 of fbm which allows to define iterated integrals and then applying the geometric rough path theory the approximation relies on the definition of an analytic process z on the cut plane z c r of which fbm appears to be a boundary value and allows to understand very precisely the well known see 5 but as yet a little mysterious divergence of levy s area for 1 4

the efficacy of fuzzy representations of uncertainty advocates of the theory of fuzzy sets as a system for representing uncertainty have based their case on five basic arguments these are 1 the reality hypothesis which holds that imprecision is an inherent property of the world external to an observer 2 the subjectivity hypothesis which holds that probability is an exclusively objective measure of uncertainty and that therefore subjective uncertainty can only be represented with fuzzy sets 3 the behaviorist hypothesis which claims that uncertainty systems should emulate rather than prescribe human behavior in the face of uncertainty 4 the probability as fiction hypothesis which claims that probability does not comprise a field of study in its own right and 5 the superset hypothesis which holds that fuzzy set theory includes probability as a special case and thus provides a richer uncertainty modeling environment we discuss and criticize all five we then criticize the argument that fuzziness represents a type of uncertainty distinct from probability and also the inordinate complexity of fuzzy methods we present a method for assessing the efficacy of fuzzy representations of uncertainty and apply this method in three examples

fuzzy sets as a basis for a theory of possibility the theory of possibility described in this paper is related to the theory of fuzzy sets by defining the concept of a possibility distribution as a fuzzy restriction which acts as an elastic constraint on the values that may be assigned to a variable more specifically if f is a fuzzy subset of a universe of discourse u u which is characterized by its membership function f then a proposition of the form x is f where x is a variable taking values in u induces a possibility distribution tx which equates the possibility of x taking the value u to f u the compatibility of u with f in this way x becomes a fuzzy variable which is associated with the possibility distribution tx in much the same way as a random variable is associated with a probability distribution in general a variable may be associated both with a possibility distribution and a probability distribution with the weak connection between the two expressed as the possibility probability consistency principle a thesis advanced in this paper is that the imprecision that is intrinsic in natural languages is in the main possibilistic rather than probabilistic in nature thus by employing the concept of a possibility distribution a proposition p in a natural language may be translated into a procedure which computes the probability distribution of a set of attributes which are implied by p several types of conditional translation rules are discussed and in particular a translation rule for propositions of the form x is f is possible where is a number in the interval 0 1 is formulated and illustrated by examples

an improved bayesian information criterion for multiple change point models in multiple change point analysis inferring the number of change points is often achieved by minimizing a selection criterion that trades off data fidelity with complexity we address the open problem of defining a selection criterion adapted to the context of multiple change point analysis our approach is inspired by the schwarz seminal formulation of the bayesian information criterion bic similarly we introduce priors here describing the occurrence of change points and we use the laplace approximation to derive a closed form expression of the criterion differently from this previous work we take advantage of the a priori information introduced instead of asymptotically eliminating the dependence on priors results obtained on simulated series show a substantial gain in performance versus recent alternative criteria used in multiple change point analysis results also show that the a priori information introduced in our criterion on the regularity of interevent times is the main driver of this s

tests for change points with epidemic alternatives summary the purpose of this paper is to discuss the tests to detect an epidemic alternative in the mean value of a sequence of independent normal variables various test statistics such as the likelihood ratio the score like statistic levin kline s statistic the semilikelihood ratio and the recursive residual are studied the large deviation approximations to the significance levels and powers are developed by integrating approximations to conditional boundary crossing probabilities some results of monte carlo experiments confirm the accuracy of these approximations a numerical comparison of the different tests is made

estimation and comparison of multiple change point models this paper provides a new bayesian approach for models with multiple change points the centerpiece of the approach is a formulation of the change point model in terms of a latent discrete state variable that indicates the regime from which a particular observation has been drawn this state variable is specified to evolve according to a discrete time discrete state markov process with the transition probabilities constrained so that the state variable can either stay at the current value or jump to the next higher value this parameterization exactly reproduces the change point model the model is estimated by markov chain monte carlo methods using an approach that is based on chib 1996 this methodology is quite valuable since it allows for the fitting of more complex change point models than was possible before methods for the computation of bayes factors are also developed all the techniques are illustrated using simulated and real data sets

the uncertainty of storm season changes quantifying the uncertainty of autocovariance changepoints in oceanography there is interest in determining storm season changes for logistical reasons such as equipment maintenance scheduling in particular there is interest in capturing the uncertainty associated with these changes in terms of the number and location of them such changes are associated with autocovariance changes this article proposes a framework to quantify the uncertainty of autocovariance changepoints in time series motivated by this oceanographic application more specifically the framework considers time series under the locally stationary wavelet lsw framework deriving a joint density for scale processes in the raw wavelet periodogram by embedding this density within a hidden markov model hmm framework we consider changepoint characteristics under this multiscale setting such a methodology allows us to model changepoints and their uncertainty for a wide range of models including piecewise second order stationary processes for example piecewise moving average processes

tailor made tests for goodness of fit to semiparametric hypotheses 1 introduction the practice of statistical testing plays several roles inempirical research these roles range from the careful assessment of theevidence against speci c scienti c hypotheses to the judgment of whetheran estimated model displays decent goodness of t to the empirical data the paradigmatic situation we consider is one where the investigator viewssome departures from the hypothesized model as being of primary impor tance with others of interest if su ciently gross but otherwise secondary for instance low frequency departures from a signal hypothesized to beconstant might be considered of interest even if of low amplitude whilehigh frequency departures are less so unless they are of high amplitude the optimal testing of a simple hypothesis against a simple alternativeis the cornerstone of modern statistical theory however there is no clearnotion of optimality for more complicated situations the h ajek le camasymptotic theory proved that there exist strong concepts of asymptotic ef ciency in parametric estimation these ideas have been extended to semi parametric models see 3 14 22 however there is no compelling sense ofan asymptotically optimum test in either the parametric or the semipara metric asymptotic theories save for some simple one parameter hypotheses

representing parametric probabilistic models tainted with imprecision numerical possibility theory belief functions have been suggested as useful tools to represent imprecise vague or incomplete information they are particularly appropriate in uncertainty analysis where information is typically tainted with imprecision or incompleteness based on their experience or their knowledge about a random phenomenon experts can sometimes provide a class of distributions without being able to precisely specify the parameters of a probability model frequentists use two dimensional monte carlo simulation to account for imprecision associated with the parameters of probability models they hence hope to discover how variability and imprecision interact this paper presents the limitations and disadvantages of this approach and propose a fuzzy random variable approach to treat this kind of knowledge

using a monotone single index model to stabilize the propensity score in missing data problems and causal inference the augmented inverse weighting method is one of the most popular methods for estimating the mean of the response in causal inference and missing data problems an important component of this method is the propensity score popular parametric models for the propensity score include the logistic probit and complementary log log models a common feature of these models is that the propensity score is a monotonic function of a linear combination of the explanatory variables to avoid the need to choose a model we model the propensity score via a semiparametric single index model in which the score is an unknown monotonic nondecreasing function of the given single index under this new model the augmented inverse weighting estimator aiwe of the mean of the response is asymptotically linear semiparametrically efficient and more robust than existing estimators moreover we have made a surprising observation the inverse probability weighting and aiwes based on a correctly specified parametric model may have worse performance than their counterparts based on a nonparametric model a heuristic explanation of this phenomenon is provided a real data example is used to illustrate the proposed methods

parametric rate inference for one sided differentiable parameters suppose one has a collection of parameters indexed by a possibly infinite dimensional set given data generated from some distribution the objective is to estimate the maximal parameter in this

marginal likelihood from the gibbs output abstract in the context of bayes estimation via gibbs sampling with or without data augmentation a simple approach is developed for computing the marginal density of the sample data marginal likelihood given parameter draws from the posterior distribution consequently bayes factors for model comparisons can be routinely computed as a by product of the simulation hitherto this calculation has proved extremely challenging our approach exploits the fact that the marginal density can be expressed as the prior times the likelihood function over the posterior density this simple identity holds for any parameter value an estimate of the posterior density is shown to be available if all complete conditional densities used in the gibbs sampler have closed form expressions to improve accuracy the posterior density is estimated at a high density point and the numerical standard error of resulting estimate is derived the ideas are applied to probit regression and finite mixture models

fuzzy universal generating functions for multi state system reliability assessment the paper considers a multi state system mss where performance rates or and corresponding state probabilities are presented as fuzzy values in many real world msss it is difficult to estimate precise values of performance rates and their probabilities because of two main reasons the first reason is inaccuracy and insufficiency of data the second one is based on the fact that msss are often used as the approximation for continuous state systems in order to simplify computational burden to overcome these deficiencies performance rates levels or and corresponding probabilities are considered as fuzzy values in this paper the fuzzy universal generating function fugf is developed to extend the universal generating function with crisp sets the composition operators are extended for fugfs and introduced in more general forms based on this a special technique for reliability assessment of such msss is developed illustrative examples are presented to demonstrate the technique

new dependence coefficients examples and applications to statistics to measure the dependence between a real valued random variable x and a algebra we consider four distances between the conditional distribution function of x given and the distribution function of x the coefficients obtained are weaker than the corresponding mixing coefficients and may be computed in many situations in particular we show that they are well adapted to functions of mixing sequences iterated random functions and dynamical systems starting from a new covariance inequality we study the mean integrated square error for estimating the unknown marginal density of a stationary sequence we obtain optimal rates for kernel estimators as well as projection estimators on a well localized basis under a minimal condition on the coefficients using recent results we show that our coefficients may be also used to obtain various exponential inequalities a concentration inequality for lipschitz functions and a berry esseen type inequality

elicitation assessment and pooling of expert judgments using possibility theory the problem of modeling expert knowledge about numerical parameters in the field of reliability is reconsidered in the framework of possibility theory usually expert opinions about quantities such as failure rates are modeled assessed and pooled in the setting of probability theory this approach does not seem to always be natural since probabilistic information looks too rich to be currently supplied by individuals indeed information supplied by individuals is often incomplete imprecise rather than tainted with randomness moreover the probabilistic framework looks somewhat restrictive to express the variety of possible pooling modes in this paper the authors formulate a model of expert opinion by means of possibility distributions that are thought to better reflect the imprecision pervading expert judgments they are weak substitutes to unreachable subjective probabilities assessment evaluation is carried out in terms of calibration and level of precision respectively measured by membership grades and fuzzy cardinality indexes finally drawing from previous works on data fusion using possibility theory the authors present various pooling modes with their formal model under various assumptions concerning the experts a comparative experiment between two computerized systems for expert opinion analysis has been carried out and its results are presented in this paper

markov switching models with endogenous explanatory variables ii a two step mle procedure abstract this paper proposes a two step maximum likelihood estimation mle procedure to deal with the problem of endogeneity in markov switching regression models a joint estimation procedure provides us with an asymptotically most efficient estimator but it is not always feasible due to the curse of dimensionality in the matrix of transition probabilities a two step estimation procedure which ignores potential correlation between the latent state variables suffers less from the curse of dimensionality and it provides a reasonable alternative to the joint estimation procedure in addition our monte carlo experiments show that the two step estimation procedure can be more efficient than the joint estimation procedure in finite samples when there is zero or low correlation between the latent state variables

practical filtering with sequential parameter learning summary the paper develops a simulation based approach to sequential parameter learning and filtering in general state space models our approach is based on approximating the target posterior by a mixture of fixed lag smoothing distributions parameter inference exploits a sufficient statistic structure and the methodology can be easily implemented by modifying state space smoothing algorithms we avoid reweighting particles and hence sample degeneracy problems that plague particle filters that use sequential importance sampling the method is illustrated by using two examples a benchmark auto regressive model with observation error and a high dimensional dynamic spatiotemporal model we show that the method provides accurate inference in the presence of outliers model misspecification and high dimensionality

estimation and confidence regions for parameter sets in econometric models this paper develops a framework for performing estimation and inference in econometric models with partial identification focusing particularly on models characterized by moment inequalities and equalities applications of this framework include the analysis of game theoretic models revealed preference restrictions regressions with missing and corrupted data auction models structural quantile regressions and asset pricing models specifically we provide estimators and confidence regions for the set of minimizers i of an econometric criterion function q in applications the criterion function embodies testable restrictions on economic models a parameter value that describes an economic model satisfies these restrictions if q attains its minimum at this value interest therefore focuses on the set of minimizers called the identified set we use the inversion of the sample analog q n of the population criterion q to construct estimators and confidence regions for the identified set and develop consistency rates of convergence and inference results for these estimators and regions to derive these results we develop methods for analyzing the asymptotic properties of sample criterion functions under set identification

reliability and mean time to failure of unrepairable systems with fuzzy random lifetimes in practice the lifetimes of unrepairable systems contain both randomness and fuzziness so it is appropriate to assume the lifetimes of systems to be fuzzy random variables in this paper the definitions of reliability and mean time to failure mttf of unrepairable systems with fuzzy random lifetimes are given respectively then basic mathematical models of unrepairable systems with fuzzy random lifetimes are established furthermore the reliability and mttf of series systems parallel systems series parallel systems parallel series systems and cold standby systems are discussed respectively finally some numerical examples are presented to illustrate how to calculate the reliability and mttf of unrepairable systems with fuzzy random lifetimes

markov switching models with endogenous explanatory variables the maximum likelihood estimation of a markov switching regression model based on the hamilton filter is not valid in the presence of endogenous explanatory variables however we show that there exists an appropriate transformation of the model that allows us to directly employ the hamilton filter the transformed model explicitly allows for a vector of bias correction terms as additional regressors and the new disturbance term is uncorrelated with all the regressors in the transformed model within this framework a quasi maximum likelihood estimation procedure is presented a procedure to test for endogeneity based on the wald statistic or the likelihood ratio statistic is also presented

a note on appointment scheduling with piecewise linear cost functions we consider the problem of determining the optimal schedules for a given sequence of jobs on a single processor the objective is to minimize the expected total cost incurred by job waiting and processor idling where the job processing times are random variables it is known in the prior literature that if the processing times are integers and the costs are linear functions satisfying a mild condition then the problem can be solved in a polynomial number of expected cost evaluations in this work we extend the result to piecewise linear cost functions which include many useful objective functions in practice our analysis explores the hidden dual network flow structure of the appointment scheduling problem and thus greatly simplifies that of prior work we also find the number of samples needed to compute a near optimal solution when only some independent samples of processing times are known

discontinuous hamiltonian monte carlo for discrete parameters and discontinuous likelihoods hamiltonian monte carlo has emerged as a standard tool for posterior computation in this article we present an extension that can efficiently explore target distributions with discontinuous densities our extension in particular enables efficient sampling from ordinal parameters though embedding of probability mass functions into continuous spaces we motivate our approach through a theory of discontinuous hamiltonian dynamics and develop a corresponding numerical solver the proposed solver is the first of its kind with a remarkable ability to exactly preserve the hamiltonian we apply our algorithm to challenging posterior inference problems to demonstrate its wide applicability and competitive performance

efficient shrinkage in parametric models this paper introduces shrinkage for general parametric models we show how to shrink maximum likelihood estimators towards parameter subspaces de ned by general nonlinear restrictions we derive the asymptotic distribution and risk of the generalized shrinkage estimator using a local asymptotic framework we show that if the shrinkage dimension exceeds two the asymptotic risk of the shrinkage estimator is strictly less than that of the mle this reduction holds globally in the parameter space we show that the reduction in asymptotic risk is substantial even for moderately large values of the parameters the formula simplify in a very convenient way in the context of high dimensional models we derive a simple bound for the asymptotic risk we also provide a new large sample minimax e ciency bound we use the concept of local asymptotic minimax bounds a generalization of the conventional asymptotic minimax bounds the

joint propagation and exploitation of probabilistic and possibilistic information in risk assessment random variability and imprecision are two distinct facets of the uncertainty affecting parameters that influence the assessment of risk while random variability can be represented by probability distribution functions imprecision or partial ignorance is better accounted for by possibility distributions or families of probability distributions because practical situations of risk computation often involve both types of uncertainty methods are needed to combine these two modes of uncertainty representation in the propagation step a hybrid method is presented here which jointly propagates probabilistic and possibilistic uncertainty it produces results in the form of a random fuzzy interval this paper focuses on how to properly summarize this kind of information and how to address questions pertaining to the potential violation of some tolerance threshold while exploitation procedures proposed previously entertain a confusion between variability and imprecision thus yielding overly conservative results a new approach is proposed based on the theory of evidence and is illustrated using synthetic examples

covariance structure of the gibbs sampler with applications to the comparisons of estimators and augmentation schemes summary we study the covariance structure of a markov chain generated by the gibbs sampler with emphasis on data augmentation when applied to a bayesian missing data problem the gibbs sampler produces two natural approximations for the posterior distribution of the parameter vector the empirical distribution based on the sampled values of the parameter vector and a mixture of complete data posteriors we prove that rao blackwellization causes a one lag delay for the autocovariances among dependent samples obtained from data augmentation and consequently the mixture approximation produces estimates with smaller variances than the empirical approximation the covariance structure results are used to compare different augmentation schemes it is shown that collapsing and grouping random components in a gibbs sampler with two or three components usually result in more efficient sampling schemes

hierarchical analysis of sur models with extensions to correlated serial errors and time varying parameter models we consider the use of markov chain monte carlo methods to analyze hierarchical versions of zellner s sur model in this context the questions of bayes estimation and model adequacy checking are considered the approach is extended to sur model with vector autoregressive and vector moving average errors of the first order finally an efficient algorithm is developed to estimate a markov time varying parameter sur model the ideas are applied to both simulated and real data

rates of convergence for the gaussian mixture sieve gaussian mixtures provide a convenient method of densityestimation that lies somewhere between parametric models and kernel densityestimators when the number of components of the mixture is allowed to increase as sample size increases the model is called a mixture sieve we establish a bound on the rate of convergence in hellinger distance for densityestimation using the gaussian mixture sieve assuming that the true density is itself a mixture of gaussians the underlying mixing measure of the true densityis not necessarilyassumed to have finite support computing the rate involves some delicate calculations since the size of the sieve as measured bybracketing entropy and the saturation rate cannot be found using standard methods when the mixing measure has compact support using kn n 2 3 log n 1 3 components in the mixture yields a rate of order log n 1 6 n1 6 for every 0 the rates depend heavilyon the tail behavior of the true density the sensitivity to the tail behavior is diminished byusing a robust sieve which includes a long tailed component in the

likelihood ratio tests for monotone functions we study the problem of testing for equality at a fixed point in the setting of nonparametric estimation of a monotone function the likelihood ratio test for this hypothesis is derived in the particular case of interval censoring or current status data and its limiting distribution is obtained the limiting distribution is that of the integral of the difference of the squared slope processes corresponding to a canonical version of the problem involving brownian motion t 2 and greatest convex minorants thereof inversion of the family of tests yields pointwise confidence intervals for the unknown distribution function we also study the behavior of the statistic under local and fixed alternatives 1 introduction we shall consider likelihood ratio tests and the corresponding confidence intervals in a class of problems involving nonparametric estimation of a monotone function the problem in each case involves testing the null hypothesis h 0 that the monotone function has a particular value at afixed point t 0 in the domain of the function of course with each testing problem there is a related problem of finding confidence intervals here are some examples of the problems we have in mind

competitive online algorithms for resource allocation over the positive semidefinite cone we consider a new and general online resource allocation problem where the goal is to maximize a function of a positive semidefinite psd matrix with a scalar budget constraint the problem data arrives online and the algorithm needs to make an irrevocable decision at each step of particular interest are classic experiment design problems in the online setting with the algorithm deciding whether to allocate budget to each experiment as new experiments become available sequentially we analyze two greedy primal dual algorithms and provide bounds on their competitive ratios our analysis relies on a smooth surrogate of the objective function that needs to satisfy a new diminishing returns psd dr property that its gradient is order reversing with respect to the psd cone using the representation for monotone maps on the psd cone given by lowner s theorem we obtain a convex parametrization of the family of functions satisfying psd dr we then formulate a convex optimization problem to directly optimize our competitive ratio bound over this set this design problem can be solved offline before the data start arriving the online algorithm that uses the designed smoothing is tailored to the given cost function and enjoys a competitive ratio at least as good as our optimized bound we provide examples of computing the smooth surrogate for d optimal and a optimal experiment design and demonstrate the performance of the custom designed algorithm

calculating posterior distributions and modal estimates in markov mixture models abstract this paper is concerned with finite mixture models in which the populations from one observation to the next are selected according to an unobserved markov process a new full bayesian approach based on the method of gibbs sampling is developed calculations are simplified by data augmentation achieved by introducing a population index variable into the list of unknown parameters it is shown that the latent variables one for each observation can be simulated from their joint distribution given the data and the remaining parameters this result serves to accelerate the convergence of the gibbs sample modal estimates are also computed by stochastic versions of the em algorithm these provide an alternative to a full bayesian approach and to existing methods of locating the maximum likelihood estimate the ideas are applied in detail to poisson data mixtures of multivariate normal distributions and autoregressive time series