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

exact nonparametric inference when doses are measured with random errors studies that estimate the effects of exposure to a possibly harmful agent often compare exposed subjects who received varied doses with matched controls who received zero dose if the doses are measured with error then one may wish to use the fallible doses to estimate a linear relationship between the unobserved true dose and the observed response if one is willing to assume that the dose errors for exposed subjects are symmetrically distributed about 0 that is the dose errors are pure errors and not say systematic underreporting of exposure then the presence of zero dose controls is all that is needed to obtain exact distribution free confidence intervals and tests and consistent point estimates the method is simpler for matched pairs than for matched sets with two or more matched subjects and it is illustrated using two studies one of each kind with matched pairs as in this first example the method uses wilcoxon s signed rank test as the basis for inference when there are several zero dos

associative and jordan algebras and polynomial time interior point algorithms for symmetric cones we present a general framework whereby analysis of interior point algorithms for semidefinite programming can be extended verbatim to optimization problems over all classes of symmetric cones derivable from associative algebras in particular such analyses are extendible to the cone of positive semidefinite hermitian matrices with complex and quaternion entries and to the lorentz cone we prove the case of the lorentz cone by using the embedding of its associated jordan algebra in the clifford algebra as an example of such extensions we take monterio s polynomial time complexity analysis of the family of similarly scaled directions introduced by monteiro and zhang 1998 and generalize it to cone lp over all representable symmetric cones

estimation of the mean of a multivariate normal distribution estimation of the means of independent normal random variables is considered using sum of squared errors as loss an unbiased estimate of risk is obtained for an arbitrary estimate and certain special classes of estimates are then discussed the results are applied to smoothing by use of moving averages and to trimmed analogs of the james stein estimate a suggestion is made for calculating approximate confidence sets for the mean vector centered at an arbitrary estimate

convergence of newton s method over commutative semirings we give a lower bound on the speed at which newton s method as defined in 11 converges over arbitrary continuous commutative semirings from this result we deduce that newton s method converges within a finite number of iterations over any semiring which is collapsed at some k n i e k k 1 holds in the sense of bloom and esik 2 we apply these results to 1 obtain a generalization of parikh s theorem 2 compute the provenance of datalog queries and 3 analyze weighted pushdown systems we further show how to compute newton s method over any continuous semiring by constructing a grammar unfolding w r t tree dimension we review several concepts equivalent to tree dimension and prove a new relation to pathwidth

superlinear convergence of a symmetric primal dual path following algorithm for semidefinite programming this paper establishes the superlinear convergence of a symmetric primal dual path following algorithm for semidefinite programming sdp under the assumptions that the semidefinite program has a strictly complementary primal dual optimal solution and that the size of the central path neighborhood tends to zero the interior point algorithm considered here closely resembles the mizuno todd ye predictor corrector method for linear programming which is known to be quadratically convergent it is shown that when the iterates are well centered the duality gap is reduced superlinearly after each predictor step indeed if each predictor step is succeeded by r consecutive corrector steps then the predictor reduces the duality gap superlinearly with order 2 1 2 r the proof relies on a careful analysis of the central path for sdp it is shown that under the strict complementarity assumption the primal dual central path converges to the analytic center of the primal dual optimal solution set and the distance from any point on the central path to this analytic center is bounded by the duality gap

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

recursive markov chains stochastic grammars and monotone systems of nonlinear equations we define recursive markov chains rmcs a class of finitely presented denumerable markov chains and we study algorithms for their analysis informally an rmc consists of a collection of finite state markov chains with the ability to invoke each other in a potentially recursive manner rmcs offer a natural abstract model for probabilistic programs with procedures they generalize in a precise sense a number of well studied stochastic models including stochastic context free grammars scfg and multi type branching processes mt bp we focus on algorithms for reachability and termination analysis for rmcs what is the probability that an rmc started from a given state reaches another target state or that it terminatesq these probabilities are in general irrational and they arise as least fixed point solutions to certain monotone systems of nonlinear equations associated with rmcs we address both the qualitative problem of determining whether the probabilities are 0 1 or in between and the quantitative problems of comparing the probabilities with a given bound or approximating them to desired precision we show that all these problems can be solved in pspace using a decision procedure for the existential theory of reals we provide a more practical algorithm based on a decomposed version of multi variate newton s method and prove that it always converges monotonically to the desired probabilities we show this method applies more generally to any monotone polynomial system we obtain polynomial time algorithms for various special subclasses of rmcs among these for scfgs and mt bps equivalently for 1 exit rmcs the qualitative problem can be solved in p time for linearly recursive rmcs the probabilities are rational and can be computed exactly in p time we show that our pspace upper bounds cannot be substantially improved without a breakthrough on long standing open problems the square root sum problem and an arithmetic circuit decision problem that captures p time on the unit cost rational arithmetic ram model we show that these problems reduce to the qualitative problem and to the approximation problem to within any nontrivial error for termination probabilities of general rmcs and to the quantitative decision problem for termination extinction of scfgs mt bps

group axioms for iteration iteration theories provide a sound and complete axiomatization of the equational properties of the iteration or fixed point operation in many models of theoretical computer science including ordered and metric structures trees and synchronization trees all known equational axiomatizations of iteration theories consist of a small set of equational axioms for conway theories and a complicated equation scheme the commutative identity here we associate an identity with each finite semigroup we prove that the set consisting of the conway identities and the group identities associated with the finite simple groups is complete moreover we prove that the conway identities and a subcollection of the semigroup identities associated with a subclass of the finite semigroups is complete iff each finite simple group divides one of the semigroups in the subclass we also formulate a conjecture and study its consequences the results are a generalization of krob s axiomatization of the equational theory of the regular sets

bayesian forecasting of an inhomogeneous poisson process with applications to call center data a call center is a centralized hub where customer and other telephone calls are handled by an organization in today s economy call centers have become the primary points of contact between customers and businesses thus accurate predictions of call arrival rates are indispensable to help call center practitioners staff their call centers efficiently and cost effectively this article proposes a multiplicative model for modeling and forecasting within day arrival rates to a u s commercial bank s call center markov chain monte carlo sampling methods are used to estimate both latent states and model parameters one day ahead density forecasts for the rates and counts are provided the calibration of these predictive distributions is evaluated through probability integral transforms furthermore 1 day ahead forecasts comparisons with classical statistical models are given our predictions show significant improvements of up to 25 over these standards a sequential monte carlo algorithm is also proposed

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

rate based daily arrival process models with application to call centers we propose develop and compare new stochastic models for the daily arrival rate in a call center following standard practice the day is divided into time periods of equal length e g 15 or 30 minutes the arrival rate is assumed random but constant in time in each period and the arrivals are from a poisson process conditional on the rate the random rate for each period is taken as a deterministic base rate or expected rate multiplied by a random busyness factor having mean 1 models in which the busyness factors are independent across periods or in which a common busyness factor applies to all periods have been studied previously but they are not sufficiently realistic we examine alternative models for which the busyness factors have some form of dependence across periods maximum likelihood parameter estimation for these models is not easy mainly because the arrival rates themselves are never observed we develop specialized techniques to perform this estimation we compare the goodness

assessment of the extent of corroboration of an elaborate theory of a causal hypothesis using partial conjunctions of evidence factors an elaborate theory of predictions of a causal hypothesis consists of several falsifiable statements derived from the causal hypothesis statistical tests for the various pieces of the elaborate theory help to clarify how much the causal hypothesis is corroborated in practice the degree of corroboration of the causal hypothesis has been assessed by a verbal description of which of the several tests provides evidence for which of the several predictions this verbal approach can miss quantitative patterns in this paper we develop a quantitative approach we first decompose these various tests of the predictions into independent factors with different sources of potential biases support for the causal hypothesis is enhanced when many of these evidence factors support the predictions a sensitivity analysis is used to assess the potential bias that could make the finding of the tests spurious along with this multiparameter sensitivity analysis we consider the partial conjunctions of the tests these partial conjunctions quantify the evidence supporting various fractions of the collection of predictions a partial conjunction test involves combining tests of the components in the partial conjunction we find the asymptotically optimal combination of tests in the context of a sensitivity analysis our analysis of an elaborate theory of a causal hypothesis controls for the familywise error rate

on the nesterov todd direction in semidefinite programming we study different choices of search direction for primal dual interior point methods for semidefinite programming problems one particular choice we consider comes from a specialization of a class of algorithms developed by nesterov and todd for certain convex programming problems we discuss how the search directions for the nesterov todd nt method can be computed efficiently and demonstrate how they can be viewed as newton directions this last observation also leads to convenient computation of accelerated steps using the mehrotra predictor corrector approach in the nt framework we also provide an analytical and numerical comparison of several methods using different search directions and suggest that the method using the nt direction is more robust than alternative methods

on sensitivity value of pair matched observational studies abstractthis article proposes a new quantity called the sensitivity value which is defined as the minimum strength of unmeasured confounders needed to change the qualitative conclusions of a naive analysis assuming no unmeasured confounder we establish the asymptotic normality of the sensitivity value in pair matched observational studies the theoretical results are then used to approximate the power of a sensitivity analysis and select the design of a study we explore the potential to use sensitivity values to screen multiple hypotheses in the presence of unmeasured confounding using a microarray dataset supplementary materials for this article are available online

markov chain monte carlo for dynamic generalised linear models summary this paper presents a new methodological approach for carrying out bayesian inference about dynamic models for exponential family observations the approach is simulationbased and involves the use of markov chain monte carlo techniques a metropolishastings algorithm is combined with the gibbs sampler in repeated use of an adjusted version of normal dynamic linear models different alternative schemes based on sampling from the system disturbances and state parameters separately and in a block are derived and compared the approach is fully bayesian in obtaining posterior samples with state parameters and unknown hyperparameters illustrations with real datasets with sparse counts and missing values are presented extensions to accommodate more general evolution forms and distributions for observations and disturbances are outlined

bayesian confidence intervals for the cross validated smoothing spline summary we consider the model y t g ti ei i 17 2 n where g t t 0 1 is a smooth function and the ei are independent n 0 a2 errors with g2 unknown the cross validated smoothing spline can be used to estimate g non parametrically from

axiomatizing rational power series over natural numbers iteration semi rings are conway semi rings satisfying conway s group identities we show that the semi rings n r a t of rational power series with coefficients in the semi ring n of natural numbers are the free partial iteration semi rings moreover we characterize the semi rings n r a t as the free semi rings in the variety of iteration semi rings defined by three additional simple identities where n is the completion of n obtained by adding a point of infinity we also show that this latter variety coincides with the variety generated by the complete or continuous semirings as a consequence of these results we obtain that the semi rings n r a t equipped with the sum order are free in the class of symmetric inductive semi rings this characterization corresponds to kozen s axiomatization of regular languages

equational theories of tropical semirings this paper studies the equational theories of various exotic semirings presented in the literature exotic semirings are semirings whose underlying carrier set is some subset of the set of real numbers equipped with binary operations of minimum or maximum as sum and addition as product two prime examples of such structures are the max semiring and the tropical semiring it is shown that none of the exotic semirings commonly considered in the literature has a finite basis for its equations and that similar results hold for the commutative idempotent weak semirings that underlie them for each of these commutative idempotent weak semirings the paper offers characterizations of the equations that hold in them decidability results for their equational theories explicit descriptions of the free algebras in the varieties they generate and relative axiomatization results

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

inductive semirings one of the most well known induction principles in computer science is the fixed point induction rule or least pre fixed point rule inductive semirings are partially ordered semirings equipped with a star operation satisfying the fixed point equation and the fixed point induction rule for linear terms inductive semirings are extensions of continuous semirings and the kleene algebras of conway and kozen we develop in a systematic way the rudiments of the theory of inductive semirings in relation to automata languages and power series in particular we prove that if s is an inductive semiring then so is the semiring of matrices sn n for any integer n 0 and that if s is an inductive semiring then so is any semiring of power series s a as shown by kozen the dual of an inductive semiring may not be inductive in contrast we show that the dual of an iteration semiring is an iteration semiring kuich proved a general kleene theorem for continuous semirings and bloom and esik proved a kleene theorem for all conway semirings since any inductive semiring is a conway semiring and an iteration semiring as we show there results a kleene theorem applicable to all inductive semirings we also describe the structure of the initial inductive semiring and conjecture that any free inductive semiring may be given as a semiring of rational power series with coefficients in the initial inductive semiring we relate this conjecture to recent axiomatization results on the equational theory of the regular sets

a complete system of identities for one letter rational expressions with multiplicities in the tropical semiring abstract we construct a complete system of rational identities for the equational theory of the algebra of one letter rational expressions with multiplicities in the tropical semiring

the root unroot algorithm for density estimation as implemented via wavelet block thresholding we propose and implement a density estimation procedure which begins by turning density estimation into a nonparametric regression problem this regression problem is created by binning the original observations into many small size bins and by then applying a suitable form of root transformation to the binned data counts in principle many common nonparametric regression estimators could then be applied to the transformed data we propose use of a wavelet block thresholding estimator in this paper finally the estimated regression function is un rooted by squaring and normalizing the density estimation procedure achieves simultaneously three objectives computational efficiency adaptivity and spatial adaptivity a numerical example and a practical data example are discussed to illustrate and explain the use of this procedure theoretically it is shown that the estimator simultaneously attains the optimal rate of convergence over a wide range of the besov classes the estimator also automatically adapts to the local smoothness of the underlying function and attains the local adaptive minimax rate for estimating functions at a point there are three key steps in the technical argument poissonization quantile coupling and oracle risk bound for block thresholding in the non gaussian setting some of the technical results may be of independent interest

forecasting time series with complex seasonal patterns using exponential smoothing an innovations state space modeling framework is introduced for forecasting complex seasonal time series such as those with multiple seasonal periods high frequency seasonality non integer seasonality and dual calendar effects the new framework incorporates box cox transformations fourier representations with time varying coefficients and arma error correction likelihood evaluation and analytical expressions for point forecasts and interval predictions under the assumption of gaussian errors are derived leading to a simple comprehensive approach to forecasting complex seasonal time series a key feature of the framework is that it relies on a new method that greatly reduces the computational burden in the maximum likelihood estimation the modeling framework is useful for a broad range of applications its versatility being illustrated in three empirical studies in addition the proposed trigonometric formulation is presented as a means of decomposing complex seasonal time series and it is show

mixture kalman filters in treating dynamic systems sequential monte carlo methods use discrete samples to represent a complicated probability distribution and use rejection sampling importance sampling and weighted resampling to complete the on line filtering task we propose a special sequential monte carlo method the mixture kalman filter which uses a random mixture of the gaussian distributions to approximate a target distribution it is designed for on line estimation and prediction of conditional and partial conditional dynamic linear models which are themselves a class of widely used non linear systems and also serve to approximate many others compared with a few available filtering methods including monte carlo methods the gain in efficiency that is provided by the mixture kalman filter can be very substantial another contribution of the paper is the formulation of many non linear systems into conditional or partial conditional linear form to which the mixture kalman filter can be applied examples in target tracking and digital communications are given to demonstrate the procedures proposed