nonparametric bayes modelling of count processes data on count processes arise in a variety of applications including longitudinal spatial and imaging studies measuring count responses the literature on statistical models for dependent count data is dominated by models built from hierarchical poisson components the poisson assumption is not warranted in many applied contexts and hierarchical poisson models make restrictive assumptions about overdispersion in marginal distributions in this article we propose a class of nonparametric bayes count process models constructed through rounding real valued underlying processes the proposed class of models accommodates situations in which separate count valued functional data are observed for each subject under study theoretical results on large support and posterior consistency are established and computational algorithms are developed based on markov chain monte carlo simulation the methods are evaluated via simulation and illustrated by application to longitudinal tumour counts and to asthma inhaler usage copyright 2013 oxford university press

monotone discriminant functions and their applications in rheumatology abstract some applications of discriminant analysis e g in rheumatology naturally require that the discriminator satisfies certain monotonicity constraints in terms of the measurements on which the classification is based this article presents a dynamic programming approach to the problem of finding the monotone function that minimizes the total misclassification cost incurred when classifying two types of cases on the basis of two variables measured on each case questions of uniqueness and convexity are explored and the way in which the solution varies with choice of misclassification costs is investigated the use of the bootstrap to estimate the accuracy of summary statistics of interest is discussed the methodology is illustrated using data on rheumatology patients some comparisons with linear discriminant functions and classification tree methods are made

bayesian isotonic regression and trend analysis in many applications the mean of a response variable can be assumed to be a nondecreasing function of a continuous predictor controlling for covariates in such cases interest often focuses on estimating the regression function while also assessing evidence of an association this article proposes a new framework for bayesian isotonic regression and order restricted inference approximating the regression function with a high dimensional piecewise linear model the nondecreasing constraint is incorporated through a prior distribution for the slopes consisting of a product mixture of point masses accounting for flat regions and truncated normal densities to borrow information across the intervals and smooth the curve the prior is formulated as a latent autoregressive normal process this structure facilitates efficient posterior computation since the full conditional distributions of the parameters have simple conjugate forms point and interval estimates of the regression function and posterior probabilities of an association for different regions of the predictor can be estimated from a single mcmc run generalizations to categorical outcomes and multiple predictors are described and the approach is applied to an epidemiology application

testing for monotonicity of a regression mean by calibrating for linear functions a new approach to testing for monotonicity of a regression mean not requiring computation of a curve estimator or a bandwidth is suggested it is based on the notion of running gradients over short intervals although from some viewpoints it may be regarded as an analogue for monotonicity testing of the dip excess mass approach for testing modality hypotheses about densities like the latter methods the new technique does not suffer difficulties caused by almost flat parts of the target function in fact it is calibrated so as to work well for flat response curves and as a result it has relatively good power properties in boundary cases where the curve exhibits shoulders in this respect as well as in its construction the running gradients approach differs from alternative techniques based on the notion of a critical bandwidth

combining registration and fitting for functional models a registration method can be defined as a process of aligning features of a sample of curves by monotone transformations of their domain the aligned curves exhibit only amplitude variation and the domain transformations called warping functions capture the phase variation in the original curves in this article we precisely define a new type of registration process in which the warping functions optimize the fit of a principal components decomposition to the aligned curves the principal components are effectively the features that this process aligns we discuss the relationship of registration to closure of a function space under convex operations and define consistency for registration methods we define an explicit decomposition of functional variation into amplitude and phase partitions and develop an algorithm for combining registration with principal components analysis and apply it to simulated and real data

estimating the accuracy of polymerase chain reaction based tests using endpoint dilution polymerase chain reaction pcr based tests for various microorganisms or target dna sequences are generally acknowledged to be highly sensitive yet the concept of sensitivity is ill defined in the literature on these tests we propose that sensitivity should be expressed as a function of the number of target dna molecules in the sample or specificity when the target number is 0 however estimating this sensitivity curve is problematic since it is difficult to construct samples with a fixed number of targets nonetheless using serially diluted replicate aliquots of a known concentration of the target dna sequence we show that it is possible to disentangle random variations in the number of target dna molecules from the underlying test sensitivity we develop parametric nonparametric and semiparametric spline based models for the sensitivity curve the methods are compared on a new test for m genitalium

smoothing spline nonlinear nonparametric regression models almost all of the current nonparametric regression methods such as smoothing splines generalized additive models and varyingcoefficients models assume a linear relationship when nonparametric functions are regarded as parameters in this article we propose a general class of smoothing spline nonlinear nonparametric models that allow nonparametric functions to act nonlinearly they arise in many fields as either theoretical or empirical models our new estimation methods are based on an extension of the gauss newton method to infinite dimensional spaces and the backfitting procedure we extend the generalized cross validation and generalized maximum likelihood methods to estimate smoothing parameters we establish connections between some nonlinear nonparametric models and nonlinear mixed effects models we derive approximate bayesian confidence intervals for inference we illustrate the methods with an application to term structure of interest rates and conduct simulations to evaluate the finite sampl

on the estimation of an instantaneous transformation for time series summary we modify ramsay s algorithm for estimating monotonic transformations in regression and extend it to autoregression where strict monotonicity is an essential requirement compared with other methods our method can capture some characteristics that are pertinent to the time series and is much easier to implement an order selection method is introduced and developed some real data sets are analysed

estimating smooth monotone functions many situations call for a smooth strictly monotone function f of arbitrary flexibility the family of functions defined by the differential equation d 2 f w df where w is an unconstrained coefficient function comprises the strictly monotone twice differentiable functions the solution to this equation is f c 0 c 1 d 1 exp d 1 w where c 0 and c 1 are arbitrary constants and d 1 is the partial integration operator a basis for expanding w is suggested that permits explicit integration in the expression of f in fitting data it is also useful to regularize f by penalizing the integral of w 2 since this is a measure of the relative curvature in f applications are discussed to monotone nonparametric regression to the transformation of the dependent variable in non linear regression and to density estimation

hammerstein system identification by non parametric instrumental variables a mixed parametric non parametric routine for hammerstein system identification is presented parameters of a non linear characteristic and of arma linear dynamical part of hammerstein system are estimated by least squares and instrumental variables assuming poor a priori knowledge about the random input and random noise both subsystems are identified separately thanks to the fact that the unmeasurable interaction inputs and suitable instrumental variables are estimated in a preliminary step by the use of a non parametric regression function estimation method a wide class of non linear characteristics including functions which are not linear in the parameters is admitted it is shown that the resulting estimates of system parameters are consistent for both white and coloured noise the problem of generating optimal instruments is discussed and proper non parametric method of computing the best instrumental variables is proposed the analytical findings are validated using numerical simulation results

an extension of multiple correspondence analysis for identifying heterogeneous subgroups of respondents an extension of multiple correspondence analysis is proposed that takes into account cluster level heterogeneity in respondents preferences choices the method involves combining multiple correspondence analysis and k means in a unified framework the former is used for uncovering a low dimensional space of multivariate categorical variables while the latter is used for identifying relatively homogeneous clusters of respondents the proposed method offers an integrated graphical display that provides information on cluster based structures inherent in multivariate categorical data as well as the interdependencies among the data an empirical application is presented which demonstrates the usefulness of the proposed method and how it compares to several extant approaches

parameter estimation for differential equations a generalized smoothing approach summary we propose a new method for estimating parameters in models that are defined by a system of non linear differential equations such equations represent changes in system outputs by linking the behaviour of derivatives of a process to the behaviour of the process itself current methods for estimating parameters in differential equations from noisy data are computationally intensive and often poorly suited to the realization of statistical objectives such as inference and interval estimation the paper describes a new method that uses noisy measurements on a subset of variables to estimate the parameters defining a system of non linear differential equations the approach is based on a modification of data smoothing methods along with a generalization of profiled estimation we derive estimates and confidence intervals and show that these have low bias and good coverage properties respectively for data that are simulated from models in chemical engineering and neurobiology the performance of the method is demonstrated by using real world data from chemistry and from the progress of the autoimmune disease lupus

modeling price dynamics in ebay auctions using differential equations empirical research of online auctions has grown dramatically in recent years studies using publicly available bid data from such websites as ebay com have found many divergences of bidding behavior and auction outcomes compared with ordinary offline auctions and auction theory among the main differences between online and offline auctions are the former s longer duration anonymity of bidders and sellers and low barriers of entry all of these factors lead to dynamics in the bid arrival and price process that change throughout the auction in this work we examine the price process in a large and diverse set of ebay auctions for both low and high valued items in terms of item auction bidder and seller characteristics we propose a family of differential equation models that captures online auction dynamics in particular we show that a second order linear differential equation well approximates the dynamics that occur in our diverse set of auctions we also introduce a multiple comparisons test fo

high dimensional maximum marginal likelihood item factor analysis by adaptive quadrature although the bock aitkin likelihood based estimation method for factor analysis of dichotomous item response data has important advantages over classical analysis of item tetrachoric correlations a serious limitation of the method is its reliance on fixed point gauss hermite g h quadrature in the solution of the likelihood equations and likelihood ratio tests when the number of latent dimensions is large computational considerations require that the number of quadrature points per dimension be few but with large numbers of items the dispersion of the likelihood given the response pattern becomes so small that the likelihood cannot be accurately evaluated with the sparse fixed points in the latent space in this paper we demonstrate that substantial improvement in accuracy can be obtained by adapting the quadrature points to the location and dispersion of the likelihood surfaces corresponding to each distinct pattern in the data in particular we show that adaptive g h quadrature combined with mean and covariance adjustments at each iteration of an em algorithm produces an accurate fast converging solution with as few as two points per dimension evaluations of this method with simulated data are shown to yield accurate recovery of the generating factor loadings for models of upto eight dimensions unlike an earlier application of adaptive gibbs sampling to this problem by meng and schilling the simulations also confirm the validity of the present method in calculating likelihood ratio chi square statistics for determining the number of factors required in the model finally we apply the method to a sample of real data from a test of teacher qualifications

a class of grouped brunk estimators and penalized spline estimators for monotone regression we study a class of monotone univariate regression estimators we use b splines to approximate an underlying regression function and estimate spline coefficients based on grouped data we investigate asymptotic properties of two monotone estimators a grouped brunk estimator and a penalized monotone estimator these estimators are consistent at the boundary and their mean square errors achieve optimal convergence rates under suitable assumptions of the true regression function asymptotic distributions are developed and are shown to be independent of spline degrees and the number of knots simulation results and car data illustrate performance of the proposed estimators

bayesian isotonic density regression density regression models allow the conditional distribution of the response given predictors to change flexibly over the predictor space such models are much more flexible than nonparametric mean regression models with nonparametric residual distributions and are well supported in many applications a rich variety of bayesian methods have been proposed for density regression but it is not clear whether such priors have full support so that any true data generating model can be accurately approximated this article develops a new class of density regression models that incorporate stochastic ordering constraints which are natural when a response tends to increase or decrease monotonely with a predictor theory is developed showing large support methods are developed for hypothesis testing with posterior computation relying on a simple gibbs sampler frequentist properties are illustrated in a simulation study and an epidemiology application is considered

improving point and interval estimators of monotone functions by rearrangement suppose that a target function is monotonic and an available original estimate of this target function is not monotonic rearrangements univariate and multivariate transform the original estimate to a monotonic estimate that always lies closer in common metrics to the target function furthermore suppose an original confidence interval which covers the target function with probability at least 1 is defined by an upper and lower endpoint functions that are not monotonic then the rearranged confidence interval defined by the rearranged upper and lower endpoint functions is monotonic shorter in length in common norms than the original interval and covers the target function with probability at least 1 we illustrate the results with a growth chart example

direct regression models for longitudinal rates of change comparing rates of growth or rates of change across covariate defined subgroups is a primary objective for many longitudinal studies in the special case of a linear trend over time the interaction between a covariate and time will characterize differences in longitudinal rates of change however in the presence of a non linear longitudinal trajectory the standard mean regression approach does not permit parsimonious description or inference regarding differences in rates of change therefore we propose regression methodology for longitudinal data that allows a direct structured comparison of rates across subgroups even in the presence of a non linear trend over time our basic longitudinal rate regression method assumes a proportional difference across covariate groups in the rate of change across time but this assumption can be relaxed rates are compared relative to a generally specified time trend for which we discuss both parametric and non parametric estimating approaches we develop mixed model longitudinal methodology that explicitly characterizes subject to subject variation in rates as well as a marginal estimating equation based method in addition we detail a score test to detect violations of the proportionality assumption and we allow time varying rate effects as a natural generalization simulation results demonstrate potential gains in power for the longitudinal rate regression model relative to a linear mixed effects model in the presence of a non linear trend in time we apply our method to a study of growth among infants born to hiv infected mothers and conclude with a discussion of possible extensions for our methods

explicit volume preserving and symplectic integrators for trigonometric polynomial flows we introduce explicit volume preserving and symplectic integrators for the case of generalized trigonometric polynomial flows the method is demonstrated using the arter flow and computational trials are conducted using a 4 dimensional vector field

semiparametric estimation of the frequency of unknown periodic functions and its application to laser vibrometry signals we propose a semiparametric approach to fundamental frequency estimation of an unknown periodic signal in additive white noise based on model selection our estimator maximizes a penalized version of the cumulated periodogram and is proved to be consistent and asymptotically efficient under very general conditions when the number of observations is fixed an implementation of this estimation method is proposed and illustrated on specific synthetic signals which arise in laser vibrometry we extend this method for estimating the fundamental frequencies of two periodic functions having different fundamental frequencies when the data consist of their sum and additive white noise we also compare the performances of our procedure with the so called microdoppler technique which is commonly used for laser vibrometry signals analysis we show on simulated data that the penalized cumulated periodogram yields an accurate estimation of the frequencies at very low signal to noise ratios

bayesian nonparametric estimation of continuous monotone functions with applications to dose response analysis in this article we consider monotone nonparametric regression in a bayesian framework the monotone function is modeled as a mixture of shifted and scaled parametric probability distribution functions and a general random probability measure is assumed as the prior for the mixing distribution we investigate the choice of the underlying parametric distribution function and find that the two sided power distribution function is well suited both from a computational and mathematical point of view the model is motivated by traditional nonlinear models for dose response analysis and provides possibilities to elicitate informative prior distributions on different aspects of the curve the method is compared with other recent approaches to monotone nonparametric regression in a simulation study and is illustrated on a data set from dose response analysis

a bayesian approach to non parametric monotone function estimation the paper proposes two bayesian approaches to non parametric monotone function estimation the first approach uses a hierarchical bayes framework and a characterization of smooth monotone functions given by ramsay that allows unconstrained estimation the second approach uses a bayesian regression spline model of smith and kohn with a mixture distribution of constrained normal distributions as the prior for the regression coefficients to ensure the monotonicity of the resulting function estimate the small sample properties of the two function estimators across a range of functions are provided via simulation and compared with existing methods asymptotic results are also given that show that bayesian methods provide consistent function estimators for a large class of smooth functions an example is provided involving economic demand functions that illustrates the application of the constrained regression spline estimator in the context of a multiple regression model where two functions are constrained to be monotone

nonparametric kernel regression subject to monotonicity constraints we suggest a method for monotonizing general kernel type estimators for example local linear estimators and nadaraya watson estimators attributes of our approach include the fact that it produces smooth estimates indeed with the same smoothness as the unconstrained estimate the method is applicable to a particularly wide range of estimator types it can be trivially modified to render an estimator strictly monotone and it can be employed after the smoothing step has been implemented therefore an experimenter may use his or her favorite kernel estimator and their favorite bandwidth selector to construct the basic nonparametric smoother and then use our technique to render it monotone in a smooth way implementation involves only an off the shelf programming routine the method is based on maximizing fidelity to the conventional empirical approach subject to monotonicity we adjust the unconstrained estimator by tilting the empirical distribution so as to make the least possible change in the sense of a distance measure subject to imposing the constraint of monotonicity

hamiltonian conserving discrete canonical equations based on variational difference quotients abstract new discrete mechanics based on the assumption of the discrete time is proposed the discrete mechanics does not contain any continuous differentiation but contains only difference quotients resulting discrete hamiltonian s canonical equations are single time step difference equations and exactly conserve the hamiltonian the canonical equations give the numerical results more accurately than the heun scheme and the 4th order runge kutta scheme

numerical integrators that preserve symmetries and reversing symmetries we consider properties of flows the relationships between them and whether numerical integrators can be made to preserve these properties this is done in the context of automorphisms and antiautomorphisms of a certain group generated by maps associated to vector fields this new framework unifies several known constructions we also use the concept of covariance of a numerical method with respect to a group of coordinate transformations the main application is to explore the relationship between spatial symmetries reversing symmetries and time symmetry of flows and numerical integrators

nonparametric maximum likelihood estimation for shifted curves the analysis of a sample of curves can be done by self modelling regression methods within this framework we follow the ideas of nonparametric maximum likelihood estimation known from event history analysis and the counting process set up we derive an infinite dimensional score equation and from there we suggest an algorithm to estimate the shape function for a simple shape invariant model the nonparametric maximum likelihood estimator that we find turns out to be a nadaraya watson like estimator but unlike in the usual kernel smoothing situation we do not need to select a bandwidth or even a kernel function since the score equation automatically selects the shape and the smoothing parameter for the estimation we apply the method to a sample of electrophoretic spectra to illustrate how it works

methods for assessing the accuracy of pcr based tests comparisons and extensions polymerase chain reaction pcr based tests are commonly used to diagnose various infections such tests are assumed to be highly sensitive however no consensus definition of or method for estimating sensitivity exists hughes and totten proposed that sensitivity be defined as a function of the number of target dna molecules in the sample with specificity corresponding to the case where there is no target dna molecule present they then developed parametric non parametric and semi parametric models for estimating the sensitivity curve in this paper a general model is proposed that yields their three models as special cases when specificity is assumed to be 1 0 we also extend the general model to incorporate covariates simulation studies are used to compare the different estimators the methods are applied to data from a pcr based test for mycoplasma genitalium

on nonparametric identification of wiener systems in this paper a new method for the identification of the wiener nonlinear system is proposed the system being a cascade connection of a linear dynamic subsystem and a nonlinear memoryless element is identified by a two step semiparametric approach the impulse response function of the linear part is identified via the nonlinear least squares approach with the system nonlinearity estimated by a pilot nonparametric kernel regression estimate the obtained estimate of the linear part is then used to form a nonparametric kernel estimate of the nonlinear element of the wiener system the proposed method permits recovery of a wide class of nonlinearities which need not be invertible as a result the proposed algorithm is computationally very efficient since it does not require a numerical procedure to calculate the inverse of the estimate furthermore our approach allows non gaussian input signals and the presence of additive measurement noise however only linear systems with a finite memory are admissible the conditions for the convergence of the proposed estimates are given computer simulations are included to verify the basic theory

efficient estimation for a subclass of shape invariant models in this paper we observe a fixed number of unknown 2 periodic func tions differing from each other by both phases and amplitude this semipara metric model appears in literature under the name shape invariant model while the common shape is unknown we introduce an asymptotically effi cient estimator of the finite dimensional parameter phases and amplitude using the profile likelihood and the fourier basis moreover this estimation method leads to a consistent and asymptotically linear estimator for the com mon shape

monotone smoothing with application to dose response curves and the assessment of synergism a spline based procedure for monotone curve smoothing is proposed and is illustrated by application to dose response curves it is then shown how such smoothing can be applied to assess possible synergism or antagonism of two drugs

searching for structure in curve samples abstract the shape of a regression curve can to a large extent be characterized by the succession of structural features like extrema inflection points and so on when analyzing a sample of regression curves it is often important to know at an early stage of data analysis which structural features are occurring consistently in each curve of the sample such a definition is usually not easy due to substantial interindividual variation both in the x and the y axis and due to the influence of noise a method is proposed for identifying typical features without relying on an a priori specified functional model for the curves the approach is based on the frequencies of occurrence of structural features as for example maxima in the curve sample along the x axis important tools are nonparametric regression and differentiation and kernel density estimation apart from a theoretical foundation the usefulness of the method is documented by application to two interesting biomedical areas growth and develop

monotone b spline smoothing abstract estimation of growth curves or item response curves often involves monotone data smoothing methods that have been studied in the literature tend to be either less flexible or more difficult to compute when constraints such as monotonicity are incorporated built on the ideas of koenker ng and portnoy and ramsay we propose monotone b spline smoothing based on l 1 optimization this method inherits the desirable properties of spline approximations and the computational efficiency of linear programs the constrained fit is similar to the unconstrained estimate in terms of computational complexity and asymptotic rate of convergence through applications to some real and simulated data we show that the method is useful in a variety of applications the basic ideas utilized in monotone smoothing can be useful in some other constrained function estimation problems

statistical tools to analyze data representing a sample of curves the paper is concerned with data representing a sample of smooth curves which can be considered as independent realizations of an underlying biological chemical ldots process such samples of curves often possess the following features there is a typical structural pattern common to all curves of the sample on the other hand individual realizations of the typical shape show different dynamics and intensity in particular typical peaks are shifted from individual to individual differences in dynamics complicate the analysis of samples of curves for example the cross sectional average usually does not reflect an average pattern due to shifts structure is smeared or might even disappear our approach consists in synchronizing the individual curves before determining the average or any further statistics pointwise averaging of the synchronized curves then leads to an average curve which represents the common structure with average dynamics and average intensity the method requires the introduction of new statistical objects they are defined mathematically their properties are discussed and possible estimators are proposed the asymptotic bias and variance of the estimators are derived an application to visually evoked brain potentials illustrates the approach

generalized arma models with martingale difference errors the analysis of non gaussian time series has been studied extensively and has many applications many successful models can be viewed as special cases or variations of the generalized autoregressive moving average garma models of benjamin et al 2003 where a link function similar to that used in generalized linear models is introduced and the conditional mean under the link function assumes an arma structure under such a model the transformed time series under the same link function assumes an arma form as well unfortunately unless the link function is an identity function the error sequence defined in the transformed arma model is usually not a martingale difference sequence in this paper we extend the garma model in such a way that the resulting arma model in the transformed space has a martingale difference sequence as its error sequence the benefit of such an extension are four folds it has easily verifiable conditions for stationarity and ergodicity its gaussian pseudo likelihood estimator is consistent standard time series model building tools are ready to use and its mle s asymptotic distribution can be established we also proposes two new classes of non gaussian time series models under the new framework the performance of the proposed models is demonstrated with simulated and real examples

a functional data analytic approach to signal discrimination motivated by specific problems involving radar range profiles we suggest techniques for real time discrimination in the context of signal analysis the key to our approach is to regard the signals as curves in the continuum and employ a functional data analytic fda method for dimension reduction based on the fda technique for principal coordinates analysis this has the advantage relative to competing methods such as canonical variates analysis of providing a signal approximation that is best possible in an l2 sense for a given dimension as a result it produces particularly good discrimination we explore the use of both nonparametric and gaussian based discriminators applied to the dimensionreduced data

volume preserving algorithms for source free dynamical systems in this paper we first expound why the volume preserving algorithms are proper for numerically solving source free systems and then prove all the conventional methods are not volume preserving secondly we give a general method of constructing volume preserving difference schemes for source free systems on the basis of decomposing a source free vector field as a finite sum of essentially 2 dimensional hamiltonian fields and of composing the corresponding essentially symplectic schemes into a volume preserving one lastly we make some special discussions for so called separable source free systems for which arbitrarily high order explicit revertible volume preserving schemes can be constructed

inference for monotone functions under short and long range dependence confidence intervals and new universal limits abstractwe introduce new point wise confidence interval estimates for monotone functions observed with additive dependent noise our methodology applies to both short and long range dependence regimes for the errors the interval estimates are obtained via the method of inversion of certain discrepancy statistics this approach avoids the estimation of nuisance parameters such as the derivative of the unknown function which previous methods are forced to deal with the resulting estimates are therefore more accurate stable and widely applicable in practice under minimal assumptions on the trend and error structure the dependence of the errors especially long range dependence leads to new phenomena where new universal limits based on convex minorant functionals of drifted fractional brownian motion emerge some extensions to uniform confidence bands are also developed supplementary materials for this article are available online

functional components of variation in handwriting abstract functional data analysis techniques are used to analyze a sample of handwriting in chinese the goals are a to identify a differential equation that satisfactorily models the data s dynamics and b to use the model to classify handwriting samples taken from differential individuals after preliminary smoothing and registration steps a second order linear differential equation for which the forcing function is small is found to provide a good reconstruction of the original script records the equation is also able to capture a substantial amount of the variation in the scripts across replication the cross validated classification process is 100 effective for the samples analyzed

a brief survey of bandwidth selection for density estimation abstract there has been major progress in recent years in data based bandwidth selection for kernel density estimation some second generation methods including plug in and smoothed bootstrap techniques have been developed that are far superior to well known first generation methods such as rules of thumb least squares cross validation and biased cross validation we recommend a solve the equation plug in bandwidth selector as being most reliable in terms of overall performance this article is intended to provide easy accessibility to the main ideas for nonexperts

bayesian spatial monotonic multiple regression we consider monotonic multiple regression for contiguous regions the regression functions vary regionally and may exhibit spatial structure we develop bayesian nonparametric methodology that permits estimation of both continuous and discontinuous functional shapes using marked point process and reversible jump markov chain monte carlo techniques spatial dependence is incorporated by a flexible prior distribution which is tuned using cross validation and bayesian optimization we derive the mean and variance of the prior induced by the marked point process approach asymptotic results show consistency of the estimated functions posterior realizations enable variable selection the detection of discontinuities and prediction in simulations and in an application to a norwegian insurance data set our methodology shows better performance than existing approaches

calculating effective diffusivities in the limit of vanishing molecular diffusion in this paper we study the problem of the numerical calculation by monte carlo methods of the effective diffusivity for a particle moving in a periodic divergent free velocity field in the limit of vanishing molecular diffusion in this limit traditional numerical methods typically fail since they do not represent accurately the geometry of the underlying deterministic dynamics we propose a stochastic splitting method that takes into account the volume preserving property of the equations of motion in the absence of noise and when inertial effects can be neglected an extension of the method is then proposed for the cases where the noise has a non trivial time correlation structure and when inertial effects cannot be neglected the method of modified equations is used to explain failings of euler based methods the new stochastic geometric integrators are shown to outperform standard euler based integrators various asymptotic limits of physical interest are investigated by means of numerical experiments using the new integrators

nonparametric state price density estimation using constrained least squares and the bootstrap the economic theory of option pricing imposes constraints on the structure of call functions and state price densities except in a few polar cases it does not prescribe functional forms this paper proposes a nonparametric estimator of option pricing models which incorporates various restrictions such as monotonicity and convexity within a single least squares procedure the bootstrap is used to produce confidence intervals for the call function and its first two derivatives and to calibrate a residual regression test of shape constraints we apply the techniques to option pricing data on the dax

nonparametric conditional density estimation using piecewise linear solution path of kernel quantile regression the goal of regression analysis is to describe the stochastic relationship between an input vector x and a scalar output y this can be achieved by estimating the entire conditional density p y x in this letter we present a new approach for nonparametric conditional density estimation we develop a piecewise linear path following method for kernel based quantile regression it enables us to estimate the cumulative distribution function of p y x in piecewise linear form for all x in the input domain theoretical analyses and experimental results are presented to show the effectiveness of the approach

inference for density families using functional principal component analysis we consider t 1 t samples of iid observations x1t xntt from unknown population densities ft to characterize differences and similarities of ft we assume their expansions into the first l principal components from the given observations xit we study inference on the components and on their required number l a detailed asymptotic theory is presented our method is applied in the analysis of yearly cross sectional samples of british households interpretation of the estimated principal components and their scores provides new insights into the evolution and interplay of household income and age distributions from 1968 1988 from estimating their required numbersl we draw conclusions on the dimensionality of mixture models for describing the densities

the prime factors of wendt s binomial circulant determinant wendt s binomial circulant determinant w is the determinant of an m by m circulant matrix of integers with i j th entry i i whenever 2 divides m but 3 does not we explain how we found the prime factors of wm for each even m 200 by implementing a new method for computations in algebraic number fields that uses only modular arithmetic as a consequence we prove that if p and q mp l are odd primes 3 does not divide m and m 200 then the first case of fermat s last theorem is true for exponent p 1991 american mathematical society

monotonic calibrated interpolated look up tables real world machine learning applications may have requirements beyond accuracy such as fast evaluation times and interpretability in particular guaranteed monotonicity of the learned function with respect to some of the inputs can be critical for user confidence we propose meeting these goals for low dimensional machine learning problems by learning flexible monotonic functions using calibrated interpolated look up tables we extend the structural risk minimization framework of lattice regression to monotonic functions by adding linear inequality constraints in addition we propose jointly learning interpretable calibrations of each feature to normalize continuous features and handle categorical or missing data at the cost of making the objective non convex we address large scale learning through parallelization mini batching and random sampling of additive regularizer terms case studies on real world problems with up to sixteen features and up to hundreds of millions of training samples demonstrate the proposed monotonic functions can achieve state of the art accuracy in practice while providing greater transparency to users

discrete gradient methods for solving odes numerically while preserving a first integral we show that all direct methods for preserving a first integral during the numerical integration of an ordinary differential equation fit into the unified framework of discrete gradient methods using this framework we construct several new integral preserving schemes

semiparametric curve alignment and shift density estimation for biological data we observe a large number of signals all of them with identical although unknown shape but with a different random shift the objective is to estimate the individual time shifts and their distribution such an objective appears in several biological applications like neuroscience or ecg signal processing in which the estimation of the distribution of the elapsed time between repetitive pulses with a possibly low signal noise ratio and without a knowledge of the pulse shape is of interest we suggest an m estimator leading to a three stage algorithm we first split our data set in blocks then the shift estimation in each block is done by minimizing a cost function based on the periodogram the estimated shifts are eventually plugged into a standard density estimator we show that under mild regularity assumptions the density estimate converges weakly to the true shift distribution the theory is applied both to simulations and to alignment of real ecg signals the proposed approach outperforms the standard methods for curve alignment and shift density estimation even in the case of low signal to noise ratio and is robust to numerous perturbations common in ecg signals

on the numerical integration of ordinary differential equations by symmetric composition methods differential equations of the form dot x x a b are considered where the vector fields a and b can be integrated exactly enabling numerical integration of x by composition of the flows of a and b various symmetric compositions are investigated for order complexity and reversibility free lie algebra theory gives simple formulae for the number of determining equations for a method to have a particular order a new more accurate way of applying the methods thus obtained to compositions of an arbitrary first order integrator is described and tested the determining equations are explored and new methods up to 100 times more accurate at constant work than those previously known are given

cyclotomic invariants for primes to one million our recent computation of cyclotomic invariants for primes between 125000 and 150000 was extended to one million no new phenomena appear this note is a sequel to our recent report 2 on the computation of certain cyclotomic invariants for primes p between 125000 and 150000 that work was based on the table of irregular primes supplied by tanner and wagstaff see 4 meanwhile the extension of this table to p 0 let hn and an denote the class number and p class group respectively of the cyclotomic field kn generated by the pn lth roots of 1 and let h and anstand for their minus parts denote by rp the index of irregularity of p that is the number of p divisible bernoulli numbers bt with t e i 2 4 p 3 1 our computations now allow us to state that 1 an z pn lz rp n 0 1 ordp hj ordp b2b4 bp 3 for all p 106 where ordp a denotes the exponent of p in the canonical decomposition of a note that the computations of 1 together with earlier computations by wagstaff et al imply that anan for these p from this and 1 it follows among other things that the a invariant of the 7p extension u 0 kn over ko equals rp in this range it is worth pointing out that the results in 1 also imply the truth of fermat s last theorem for all prime exponents up to one million we now describe briefly the contents of our computations let p t be an irregular pair i e a pair with t e i and p i bt as in 2 put si e at1 qa s2 e atqa2 o a p 2 o a p 2 received by the editor april 15 1991 1991 mathematics subject classification primary 1 r18 1 1b68 1 1r23 1 1r29 1 y40

irregular primes to one million using fast algorithms for power series inversion based on the fast fourier transform and multisectioning of power series we have calculated all irregular primes up to one million including their indices of irregularity and associated irregular pairs using this data we verified that fermat s last theorem and vandiver s conjecture are true for these primes two primes with index of irregularity five were already known we find that there are nine other primes less than one million with index five and that the prime 527377 is the unique prime less than one million with index six a pair of integers p k is said to be an irregular pair if p is a prime k is an even integer satisfying 2 p are known see 8 our calculations show that vandiver s conjecture is true for all p 106 the table of irregular pairs could also be used to calculate iwasawa invariants for the corresponding primes we did not do this as part of our calculations see 9 or 4 for a discussion of this problem previous computations of irregular pairs have used algorithms that take 0 p2 arithmetic operations for each prime p the bernoulli numbers are defined in received by the editor april 30 1991 and in revised form september 10 1991 1991 mathematics subject classification primary 11b68 secondary 1 1d41 65t20 1 1y99 the first author was partially supported by national science foundation grant dms 9012989 d 1992 american mathematical society 0025 5718 92 1 00 25 per page

new congruences for the bernoulli numbers on etablit une nouvelle congruence pour calculer les nombres de bernoulli modulo un nombre premier on developpe un programme d ordinateur fonctionnant sur le systeme cyber205 on verifie le grand theoreme de fermat pour tous les exposants jusqu a 150000

the monotone smoothing of scatterplots we consider the problem of summarizing a scatterplot with a smooth monotone curve a solution that combines local averaging and isotonic regression is proposed and we demonstrate its use with two examples in the second example the procedure is applied in a regression setting to some data from box and cox 1964 and it is shown how this new procedure generalizes box and cox s well known family of transformations in the same example the bootstrap is applied to obtain a measure of the variability of the procedure

modeling and testing differential item functioning in unidimensional binary item response models with a single continuous covariate a functional data analysis approach differential item functioning dif referring to between group variation in item characteristics above and beyond the group level disparity in the latent variable of interest has long been regarded as an important item level diagnostic the presence of dif impairs the fit of the single group item response model being used and calls for either model modification or item deletion in practice depending on the mode of analysis methods for testing dif with continuous covariates rather than categorical grouping variables have been developed however they are restrictive in parametric forms and thus are not sufficiently flexible to describe complex interaction among latent variables and covariates in the current study we formulate the probability of endorsing each test item as a general bivariate function of a unidimensional latent trait and a single covariate which is then approximated by a two dimensional smoothing spline the accuracy and precision of the proposed procedure is evaluated via monte carlo simulations if anchor items are available we proposed an extended model that simultaneously estimates item characteristic functions icfs for anchor items icfs conditional on the covariate for non anchor items and the latent variable density conditional on the covariate all using regression splines a permutation dif test is developed and its performance is compared to the conventional parametric approach in a simulation study we also illustrate the proposed semiparametric dif testing procedure with an empirical example

generating functions for dynamical systems with symmetries integrals and differential invariants abstract we give a survey and some new examples of generating functions for systems with symplectic structure systems with a first integral systems that preserve volume and systems with symmetries and or time reversing symmetries both odes and maps are treated and we discuss how generating functions may be used in the structure preserving numerical integration of odes with the above properties

tests for monotonicity of a regression mean with guaranteed level in this paper a nonparametric procedure for testing for monotonicity of a regression mean with guaranteed level is proposed the procedure is based on signs of differences of observations from the response variable the test is calibrated against the most difficult null hypothesis when the regression function is constant and produces an exact test in this context in general the test is conservative the power of the test is good and comparable with that of other nonparametric tests it is shown that the testing procedure has asymptotic power 1 against certain local alternatives the method is also robust against heavy tailed error distributions and even maintains good power when the errors are for example cauchy distributed a simulation study is provided to demonstrate finite sample behaviour of the testing procedure

bayesian multivariate isotonic regression splines in many applications interest focuses on assessing the relationship between a predictor and a multivariate outcome variable and there may be prior knowledge about the shape of the regression curves for example regression functions that relate dose of a possible risk factor to different adverse outcomes can often be assumed to be nondecreasing in such cases interest focuses on 1 assessing evidence of an overall adverse effect 2 determining which outcomes are most affected and 3 estimating outcome specific regression curves this article proposes a bayesian approach for addressing this problem motivated by multisite tumor data from carcinogenicity experiments a multivariate smoothing spline model is specified that accommodates dependency in the multiple curves through a hierarchical markov random field prior for the basis coefficients while also allowing for residual correlation a gibbs sampler is proposed for posterior computation and the approach is applied to data on body weight and t

time normalization of voice signals using functional data analysis the harmonics to noise ratio hnr has been used to quantify the waveform irregularity of voice signals yumoto et al j acoust soc am 71 1544 1550 1982 this measure assumes that the signal consists of two components a harmonic component which is the common pattern that repeats from cycle to cycle and an additive noise component which produces the cycle to cycle irregularity it has been shown j qi j acoust soc am 92 2569 2576 1992 that a valid computation of the hnr requires a nonlinear time normalization of the cycle wavelets to remove phase differences between them this paper shows the application of functional data analysis to perform an optimal nonlinear normalization and compute the hnr of voice signals results obtained for the same signals using zero padding linear normalization and dynamic programming algorithms are presented for comparison functional data analysis offers certain advantages over other approaches it preserves meaningful features of signal shape produces differentiable results and allows flexibility in selecting the optimization criteria for the wavelet alignment an extension of the technique for the time normalization of simultaneous voice signals such as acoustic egg and airflow signals is also shown the general purpose of this article is to illustrate the potential of functional data analysis as a powerful analytical tool for studying aspects of the voice production process