approximate likelihood for large irregularly spaced spatial data likelihood approaches for large irregularly spaced spatial datasets are often very difficult if not infeasible to implement due to computational limitations even when we can assume normality exact calculations of the likelihood for a gaussian spatial process observed at n locations requires o n3 operations we present a version of whittle s approximation to the gaussian log likelihood for spatial regular lattices with missing values and for irregularly spaced datasets this method requires o nlog2n operations and does not involve calculating determinants we present simulations and theoretical results to show the benefits and the performance of the spatial likelihood approximation method presented here for spatial irregularly spaced datasets and lattices with missing values we apply these methods to estimate the spatial structure of sea surface temperatures using satellite data with missing values

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

confidence sets for optimal factor levels of a response surface construction of confidence sets for the optimal factor levels is an important topic in response surfaces methodology in wan et al 2015 an exact 1 confidence set has been provided for a maximum or minimum point i e an optimal factor level of a univariate polynomial function in a given interval in this article the method has been extended to construct an exact 1 confidence set for the optimal factor levels of response surfaces the construction method is readily applied to many parametric and semiparametric regression models involving a quadratic function a conservative confidence set has been provided as an intermediate step in the construction of the exact confidence set two examples are given to illustrate the application of the confidence sets the comparison between confidence sets indicates that our exact confidence set is better than the only other confidence set available in the statistical literature that guarantees the 1 confidence level

efficient recursions for general factorisable models let n s valued categorical variables be jointly distributed according to a distribution known only up to an unknown normalising constant for an unnormalised joint likelihood expressible as a product of factors we give an algebraic recursion which can be used for computing the normalising constant and other summations a saving in computation is achieved when each factor contains a lagged subset of the components combining in the joint distribution with maximum computational efficiency as the subsets attain their minimum size if each subset contains at most r 1 of the n components in the joint distribution we term this a lag r model whose normalising constant can be computed using a forward recursion in o sr 1 computations as opposed to o sn for the direct computation we show how a lag r model represents a markov random field and allows a neighbourhood structure to be related to the unnormalised joint likelihood we illustrate the method by showing how the normalising constant of the ising or autologistic model can be computed

recursive computing and simulation free inference for general factorizable models summary we illustrate how the recursive algorithm of reeves pettitt 2004 for general factorizable models can be extended to allow exact sampling maximization of distributions and computation of marginal distributions all of the methods we describe apply to discrete valued markov random fields with nearest neighbour integrations defined on regular lattices in particular we illustrate that exact inference can be performed for hidden autologistic models defined on moderately sized lattices in this context we offer an extension of this methodology which allows approximate inference to be carried out for larger lattices without resorting to simulation techniques such as markov chain monte carlo in particular our work offers the basis for an automatic inference machine for such models

predictive model assessment for count data we discuss tools for the evaluation of probabilistic forecasts and the critique of statistical models for count data our proposals include a nonrandomized version of the probability integral transform marginal calibration diagrams and proper scoring rules such as the predictive deviance in case studies we critique count regression models for patent data and assess the predictive performance of bayesian age period cohort models for larynx cancer counts in germany the toolbox applies in bayesian or classical and parametric or nonparametric settings and to any type of ordered discrete outcomes

hierarchical generalized linear models we consider hierarchical generalized linear models which allow extra error components in the linear predictors of generalized linear models the distribution of these components is not restricted to be normal this allows a broader class of models which includes generalized linear mixed models we use a generalization of henderson s joint likelihood called a hierarchical or h likelihood for inferences from hierarchical generalized linear models this avoids the integration that is necessary when marginal likelihood is used under appropriate conditions maximizing the h likelihood gives fixed effect estimators that are asymptotically equivalent to those obtained from the use of marginal likelihood at the same time we obtain the random effect estimates that are asymptotically best unbiased predictors an adjusted profile h likelihood is shown to give the required generalization of restricted maximum likelihood for the estimation of dispersion components a scaled deviance test for the goodness of fit a model selection criterion for choosing between various dispersion models and a graphical method for checking the distributional assumption of random effects are proposed the ideas of quasi likelihood and extended quasi likelihood are generalized to the new class we give examples of the poisson gamma binomial beta and gamma inverse gamma hierarchical generalized linear models a resolution is proposed for the apparent difference between population averaged and subject specific models a unified framework is provided for viewing and extending many existing methods

auxiliary mixture sampling for parameter driven models of time series of counts with applications to state space modelling we consider parameter driven models of time series of counts where the observations are assumed to arise from a poisson distribution with a mean changing over time according to a latent process estimation of these models is carried out within a bayesian framework using data augmentation and markov chain monte carlo methods we suggest a new auxiliary mixture sampler which possesses a gibbsian transition kernel where we draw from full conditional distributions belonging to standard distribution families only emphasis lies on application to state space modelling of time series of counts but we show that auxiliary mixture sampling may be applied to a wider range of parameter driven models including random effects models and panel data models based on the poisson distribution

theta duality on prym varieties and a torelli theorem let c c be an unramified double covering of irreducible smooth curves and let p be the attached prym variety we prove the schemetheoretic theta dual equalities in the prym variety t c v 2 and t v 2 c where v 2 is the brill noether locus of p associated to considered by welters as an application we prove a torelli theorem analogous to the fact that the symmetric product d g of a curve d of genus g determines the curve

seshadri constants on jacobian of curves we compute the seshadri constants on the jacobian of hyperelliptic curves as well as of curves with genus three and four for higher genus curves we conclude that if the seshadri constants of their jacobian are less than 2 then the curves must be hyperelliptic

monte carlo maximum likelihood estimation for non gaussian state space models state space models are considered for observations which have non gaussian distributions we obtain accurate approximations to the loglikelihood for such models by monte carlo simulation devices are introduced which improve the accuracy of the approximations and which increase computational efficiency the loglikelihood function is maximised numerically to obtain estimates of the unknown hyperparameters standard errors of the estimates due to simulation are calculated details are given for the important special cases where the observations come from an exponential family distribution and where the observation equation is linear but the observation errors are non gaussian the techniques are illustrated with a series for which the observations have a poisson distribution and a series for which the observation errors have a t distribution

rotating flow of a third grade fluid by homotopy analysis method the steady flow of a rotating third grade fluid past a porous plate has been analyzed the resulting nonlinear boundary value problem has been solved using homotopy analysis method explicit expression for the velocity field has been obtained the variations of velocity with respect to rotation suction blowing and non newtonian parameters are shown and discussed

an explicit analytic solution for free convection about a vertical flat plate embedded in a porous medium by means of homotopy analysis method an analytic technique namely the homotopy analysis method is applied to free convection about a vertical flat embedded in a saturated porous medium at high rayleigh numbers within the framework of boundary layer approximations the explicit totally analytic and uniformly valid solutions governed by a set of two fully coupled non linear equations are obtained which agree well with numerical results

advanced distribution theory for sizer sizer is a powerful method for exploratory data analysis in this article approximations to the distributions underlying the simultaneous statistical inference are investigated and large improvements are made in the approximation using extreme value theory this results in improved size and also in an improved global inference version of sizer the main points are illustrated with real data and simulated examples

fixed rank kriging for very large spatial data sets summary spatial statistics for very large spatial data sets is challenging the size of the data set n causes problems in computing optimal spatial predictors such as kriging since its computa tional cost is of order a73 in addition a large data set is often defined on a large spatial domain so the spatial process of interest typically exhibits non stationary behaviour over that domain a flexible family of non stationary covariance functions is defined by using a set of basis functions that is fixed in number which leads to a spatial prediction method that we call fixed rank kriging specifically fixed rank kriging is kriging within this class of non stationary covariance functions it relies on computational simplifications when n is very large for obtaining the spatial best linear unbiased predictor and its mean squared prediction error for a hidden spatial process a method based on minimizing a weighted frobenius norm yields best estimators of the covari ance function parameters which are then substituted into the fixed rank kriging equations the new methodology is applied to a very large data set of total column ozone data observed over the entire globe where n is of the order of hundreds of thousands

estimation and model identification for continuous spatial processes summary formal parameter estimation and model identification procedures for continuous domain spatial processes are introduced the processes are assumed to be adequately described by a linear model with residuals that follow a second order stationary gaussian random field and data are assumed to consist of noisy observations of the process at arbitrary sampling locations a general class of two dimensional rational spectral density functions with elliptic contours is used to model the spatial covariance function an iterative estimation procedure alleviates many of the computational difficulties of conventional maximum likelihood estimation for non lattice data the procedure is applied to several generated data sets and to an actual ground water data set

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

approximate bayesian inference for latent gaussian models by using integrated nested laplace approximations summary structured additive regression models are perhaps the most commonly used class of models in statistical applications it includes among others generalized linear models generalized additive models smoothing spline models state space models semiparametric regression spatial and spatiotemporal models log gaussian cox processes and geostatistical and geoadditive models we consider approximate bayesian inference in a popular subset of structured additive regression models latent gaussian models where the latent field is gaussian controlled by a few hyperparameters and with non gaussian response variables the posterior marginals are not available in closed form owing to the non gaussian response variables for such models markov chain monte carlo methods can be implemented but they are not without problems in terms of both convergence and computational time in some practical applications the extent of these problems is such that markov chain monte carlo sampling is simply not an appropriate tool for routine analysis we show that by using an integrated nested laplace approximation and its simplified version we can directly compute very accurate approximations to the posterior marginals the main benefit of these approximations is computational where markov chain monte carlo algorithms need hours or days to run our approximations provide more precise estimates in seconds or minutes another advantage with our approach is its generality which makes it possible to perform bayesian analysis in an automatic streamlined way and to compute model comparison criteria and various predictive measures so that models can be compared and the model under study can be challenged

julian j faraway extending the linear model with r generalized linear mixed effects and nonparametric regression models 2nd edition boca raton crc press

parameter orthogonality and approximate conditional inference on propose une statistique du rapport de vraisemblance construite a partir de la distribution conditionnelle des observations etant donne les estimateurs du maximum de vraisemblance pour les parametres de nuisance

algebraic cycles on prym varieties this article proposes a generalization of tautological rings introduced by beauville and moonen for jacobians the main result is that under certain hypotheses the special subvarieties of prym varieties are algebraically equivalent and their classes belong to the tautological ring

constrained monte carlo maximum likelihood for dependent data maximum likelihood estimates mles in autologistic models and other exponential family models for dependent data can be calculated with markov chain monte carlo methods the metropolis algorithm or the gibbs sampler which simulate ergodic markov chains having equilibrium distributions in the model from one realization of such a markov chain a monte carlo approximant to the whole likelihood function can be constructed the parameter value if any maximizing this function approximates the mle

solving the klein gordon equation by means of the homotopy analysis method an analytic technique namely the homotopy analysis method is applied to solve the nonlinear travelling waves governed by the klein gordon equation the phase speed and the solution which are dependent on the amplitude a are given and valid in the whole region 0