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Inference in state-space models usually relies on recursive forms for filtering and smoothing of the state vectors regarding the temporal structure of the observations, an assumption that is, from our view point, unnecessary if the dataset is fixed, that is, completely available before analysis. In this paper, we propose a computational framework to perform approximate full Bayesian inference in linear and generalized dynamic linear models based on the Integrated Nested Laplace Approximation (INLA) approach. The proposed framework directly approximates the posterior marginals of interest disregarding the assumption of recursive updating/estimation of the states and hyperparameters in the case of fixed datasets and, therefore, enable us to do fully Bayesian analysis of complex state-space models more easily and in a short computational time. The proposed framework overcomes some limitations of current tools in the dynamic modeling literature and is vastly illustrated with a series of simulated as well as well known real-life examples from the literature, including realistically complex models with correlated error structures and models with more than one state vector, being mutually dependent on each other. R code is available online for all the examples presented.

Summary1. Spatial analysis of ecological data is central to many interesting questions in ecology. Bayesianimplementation of spatially explicit models has received increasing attention from ecologists asMonteCarloMarkovChain(MCMC)methodshavebecomefreelyaccessible.MCMCsimulationsoffer a flexible framework for modelling extensive ecological data, but they also come with a widerangeofproblemsregardingconvergence,processingtimeandimplementation.2. WeintroducetoecologistsanalternativeprocedureforfittingBayesianhierarchicalspatialmod-els (BHSM) with quite general spatial covariance structures. This procedure uses integrated nestedLaplaceapproximations(INLA)asanalternativetoMCMC.3. We show, using a case study of species distribution model with binary areal data, that imple-menting BHSM with INLA does not require advanced programming skills, yields accurate resultscompared with MCMC and is rapid (e.g. a few seconds with small to moderate data sets). BHSMsefficiently removed spatial autocorrelation in the residuals and fairly evaluated uncertainty inparameterestimatesandpredictions.4. The rapidity of INLA significantly decreased the processing time and allowed both sensitivityanalyses on priors and cross-validation tests to be performed within a reasonable amount of time,whichultimatelyincreasedmodeltransparency.Key-words: Bayesian hierarchical spatial models, CAR model, Mate´rn, MCMC, spatialautocorrelation, species distribution modelIntroduction

This article presents a methodology for modeling aggregated disease incidence data with the spatially continuous log-Gaussian Cox process. Statistical models for spatially aggregated disease incidence data usually assign the same relative risk to all individuals in the same reporting region (census areas or postal regions). A further assumption that the relative risks in two regions are independent given their neighbor's risks (the Markov assumption) makes the commonly used Besag–York–Mollié model computationally simple. The continuous model proposed here uses a data augmentation step to sample from the posterior distribution of the exact locations at each step of an Markov chain Monte Carlo algorithm, and models the exact locations with an log-Gaussian Cox process. A simulation study shows the log-Gaussian Cox process model consistently outperforming the Besag–York–Mollié model. The method is illustrated by making inference on the spatial distribution of syphilis risk in North Carolina. The effect of several known social risk factors are estimated, and areas with risk well in excess of that expected given these risk factors are identified.

A Bayesian multiscale technique for the detection of statistically significant features in noisy images is proposed. The prior is defined as a stationary intrinsic Gaussian Markov random field on a toroidal graph, which enables efficient computation of the relevant posterior marginals. Hence the method is applicable to large images produced by modern digital cameras. The technique is demonstrated in two examples from medical imaging. We model digital images as intrinsic Gaussian Markov random fields. This Bayesian scale-space method detects significant gradient and curvature. Efficient computation is achieved by defining images on a toroidal graph. The technique is successfully demonstrated in two examples from medical imaging.

Summary Clinical data on the location of residence at the time of diagnosis of new lupus cases in Toronto, Canada, for the 40 years to 2007 are modelled with the aim of finding areas of abnormally high risk. Inference is complicated by numerous irregular changes in the census regions on which population is reported. A model is introduced consisting of a continuous random spatial surface and fixed effects for time and ages of individuals. The process is modelled on a fine grid and Bayesian inference performed by using integrated nested Laplace approximations. Predicted risk surfaces and posterior probabilities of exceedance are produced for lupus and, for comparison, psoriatic arthritis data from the same clinic. Simulations studies are also carried out to understand better the performance of the model proposed as well as to compare with existing methods.

Gaussian random fields (GRFs) are the most common way of modeling structured spatial random effects in spatial statistics. Unfortunately, their high computational cost renders the direct use of GRFs impractical for large problems and approximations are commonly used. In this paper, we compare two approximations to GRFs with Matern covariance functions: the kernel convolution approximation and the Gaussian Markov random field representation of an associated stochastic partial differential equation. We show that the second approach is a natural way to tackle the problem and is better than methods based on approximating the kernel convolution. Furthermore, we show that kernel methods, as described in the literature, do not work when the random field is not smooth. Copyright © 2011 John Wiley & Sons, Ltd.

Summary Suicide has become one of the leading causes of death of Swiss males aged between 15 and 44 years, whose age-standardized rates are about three times higher than those for females. We compared age-stratified suicide rates of Swiss men and women aged 15–79 years and analysed gender-specific differences from 1950 to 2007. Furthermore, we explored whether changes in measures of family integration can explain changes in suicide trends. The use of multivariate age–period–cohort models avoids age aggregation and allows the exploration of heterogeneous time trends across age, period and birth cohort. In addition, explanatory variables can be included. We found strong gender-specific differences in suicide mortality. Although the same risk factors may act on age and overdispersion, there was no significant correlation between gender-specific cohort effects. Family integration had an effect on Swiss suicide risk but only partially explained the underlying trends over time.

Volatility in financial time series is mainly analysed through two classes of models; the generalized autoregressive conditional heteroscedasticity (GARCH) models and the stochastic volatility (SV) ones. GARCH models are straightforward to estimate using maximum-likelihood techniques, while SV models require more complex inferential and computational tools, such as Markov Chain Monte Carlo (MCMC). Hence, although provided with a series of theoretical advantages, SV models are in practice much less popular than GARCH ones. In this paper, we solve the problem of inference for some SV models by applying a new inferential tool, integrated nested Laplace approximations (INLAs). INLA substitutes MCMC simulations with accurate deterministic approximations, making a full Bayesian analysis of many kinds of SV models extremely fast and accurate. Our hope is that the use of INLA will help SV models to become more appealing to the financial industry, where, due to their complexity, they are rarely used in practice.

Deterministic Bayesian inference for latent Gaussian models has recently become available using integrated nested Laplace approximations (INLA). Applying the INLA-methodology, marginal estimates for elements of the latent field can be computed efficiently, providing relevant summary statistics like posterior means, variances and pointwise credible intervals. In this article, we extend the use of INLA to joint inference and present an algorithm to derive analytical simultaneous credible bands for subsets of the latent field. The algorithm is based on approximating the joint distribution of the subsets by multivariate Gaussian mixtures. Additionally, we present a saddlepoint approximation to compute Bayesian contour probabilities, representing the posterior support of fixed parameter vectors of interest. We perform a simulation study and apply the given methods to two real examples.

The data cloning method is a new computational tool for computing maximum likelihood estimates in complex statistical models such as mixed models. This method is synthesized with integrated nested Laplace approximation to compute maximum likelihood estimates efficiently via a fast implementation in generalized linear mixed models. Asymptotic behavior of the hybrid data cloning method is discussed. The performance of the proposed method is illustrated through a simulation study and real examples. It is shown that the proposed method performs well and rightly justifies the theory. Supplemental materials for this article are available online.

Quantile regression problems in practice may require flexible semiparametric forms of the predictor for modeling the dependence of responses on covariates. Furthermore, it is often necessary to add random effects accounting for overdispersion caused by unobserved heterogeneity or for correlation in longitudinal data. We present a unified approach for Bayesian quantile inference on continuous response via Markov chain Monte Carlo (MCMC) simulation and approximate inference using integrated nested Laplace approximations (INLA) in additive mixed models. Different types of covariate are all treated within the same general framework by assigning appropriate Gaussian Markov random field (GMRF) priors with different forms and degrees of smoothness. We applied the approach to extensive simulation studies and a Munich rental dataset, showing that the methods are also computationally efficient in problems with many covariates and large datasets.

A parametric model for the ultrasound signals from blood and tissue is developed and a new imaging method, knowledge-based imaging, is defined. This method utilizes the likelihood ratio function to classify blood and tissue signals. The method separates blood and tissue signals by the difference in movement patterns in addition to the difference in powers. The prior information about the levels of expected system white noise and clutter noise are utilized to enhance the image quality. The implementation of knowledge-based imaging is outlined, and some knowledge-based images with different parameter settings are visually compared with a second-harmonic image, a fundamental image and a bandwidth image. In order to understand the parameter estimation process a computer simulation is introduced to outline the differences between the imaging methods. The apparent error rates are calculated in any reasonable tissue to blood signal ratio, tissue to white noise ratio and clutter to white noise ratio. A discussion of further development of knowledge-based imaging is also described in this paper.

A fully-automatic Bayesian visualization tool to identify periodic components of evenly sampled stationary time series, is presented. The given method applies the multiscale ideas of the SiZer-methodology to the log-spectral density of a given series. The idea is to detect significant peaks in the true underlying curve viewed at different resolutions or scales. The results are displayed in significance maps, illustrating for which scales and for which frequencies, peaks in the log-spectral density are detected as significant. The inference involved in producing the significance maps is performed using the recently developed simplified Laplace approximation. This is a Bayesian deterministic approach used to get accurate estimates of posterior marginals for latent Gaussian Markov random fields at a low computational cost, avoiding the use of Markov chain Monte Carlo techniques. Application of the given exploratory tool is illustrated analyzing both synthetic and real time series.

The article considers Bayesian analysis of hierarchical models for count, binomial and multinomial data using efficient MCMC sampling procedures. To this end, an improved method of auxiliary mixture sampling is proposed. In contrast to previously proposed samplers the method uses a bounded number of latent variables per observation, independent of the intensity of the underlying Poisson process in the case of count data, or of the number of experiments in the case of binomial and multinomial data. The bounded number of latent variables results in a more general error distribution, which is a negative log-Gamma distribution with arbitrary integer shape parameter. The required approximations of these distributions by Gaussian mixtures have been computed. Overall, the improvement leads to a substantial increase in efficiency of auxiliary mixture sampling for highly structured models. The method is illustrated for finite mixtures of generalized linear models and an epidemiological case study.

The second-order random walk (RW2) model is commonly used for smoothing data and for modelling response functions. It is computationally efficient due to the Markov properties of the joint (intrinsic) Gaussian density. For evenly spaced locations the RW2 model is well established, whereas for irregularly spaced locations there is no well established construction in the literature. By considering the RW2 model as the solution of a stochastic differential equation (SDE), a dis- cretely observed integrated Wiener process, it is possible to derive the density preserving the Markov properties by augmenting the state-space with the velocities. Here, we derive a computationally more efficient RW2 model for irregular locations using a Galerkin approximation to the solution of the SDE without the need of augmenting the state-space. Numerical comparison with the exact solution demonstrates that the error in the Galerkin approximation is small and negligible in applications.

Many commonly used models in statistics can be formulated as (Bayesian) hierarchical Gaussian Markov random field models. These are characterised by assuming a (often large) Gaussian Markov random field (GMRF) as the second stage in the hierarchical structure and a few hyperparameters at the third stage. Markov chain Monte Carlo is the common approach for Bayesian inference in such models. The variance of the Monte Carlo estimates is Op(M 1/2 ) where M is the number of samples in the chain so, in order to obtain precise estimates of marginal densities, say, we need M to be very large. Inspired by the fact that often one-block and independence samplers can be constructed for hierarchical GMRF models, we will in this work investigate whether MCMC is really needed to estimate marginal densities, which often is the goal of the analysis. By making use of GMRFapproximations, we show by typical examples that marginal densities can indeed be very precisely estimated by deterministic schemes. The methodological and practical consequence of these findings are indeed positive. We conjecture that for many hierarchical GMRF-models there is really no need for MCMC based inference to estimate marginal densities. Further, by making use of numerical methods for sparse matrices the computational costs of these deterministic schemes are nearly instant compared to the MCMC alternative. In particular, we discuss in detail the issue of computing marginal variances for GMRFs.

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. Copyright 2007, Oxford University Press.

An approach by which the scour depth around a spherical body and the self-burial depth of such a body in random waves can be derived is presented. Here the formulas for scour and self-burial depths of a spherical body by Truelsen et al. [Truelsen C, Sumer BM, Fredsoe J. Scour around spherical bodies and self- burial. ASCE J Waterway Port Coast Ocean Eng 2005;131(1):1–13] for regular waves are used. They are combined with describing the waves as a stationary Gaussian narrow-band random process to derive the scour and self-burial depths in random waves.

In a bivariate meta-analysis, the number of diagnostic studies involved is often very low so that frequentist methods may result in problems. Using Bayesian inference is particularly attractive as informative priors that add a small amount of information can stabilise the analysis without overwhelming the data. However, Bayesian analysis is often computationally demanding and the selection of the prior for the covariance matrix of the bivariate structure is crucial with little data. The integrated nested Laplace approximations method provides an efficient solution to the computational issues by avoiding any sampling, but the important question of priors remain. We explore the penalised complexity (PC) prior framework for specifying informative priors for the variance parameters and the correlation parameter. PC priors facilitate model interpretation and hyperparameter specification as expert knowledge can be incorporated intuitively. We conduct a simulation study to compare the properties and behaviour of differently defined PC priors to currently used priors in the field. The simulation study shows that the PC prior seems beneficial for the variance parameters. The use of PC priors for the correlation parameter results in more precise estimates when specified in a sensible neighbourhood around the truth. To investigate the usage of PC priors in practice, we reanalyse a meta-analysis using the telomerase marker for the diagnosis of bladder cancer and compare the results with those obtained by other commonly used modelling approaches. Copyright © 2017 John WileySons, Ltd.

Bayesian penalized splines (P-splines) assume an intrinsic Gaussian Markov random field prior on the spline coefficients, conditional on a precision hyper-parameter [Formula: see text]. Prior elicitation of [Formula: see text] is difficult. To overcome this issue, we aim to building priors on an interpretable property of the model, indicating the complexity of the smooth function to be estimated. Following this idea, we propose penalized complexity (PC) priors for the number of effective degrees of freedom. We present the general ideas behind the construction of these new PC priors, describe their properties and show how to implement them in P-splines for Gaussian data.

Discussion of "Cross-Covariance Functions for Multivariate Geostatistics" by Genton and Kleiber [arXiv:1507.08017]., Comment: Published at http://dx.doi.org/10.1214/15-STS515 in the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org)

Weintroduceanewcopula-basedcorrectionforgeneralizedlinearmixedmodels(GLMMs)within the integrated nested Laplace approximation (INLA) approach for approximateBayesian inference for latent Gaussian models. GLMMs for Binomial and Poisson datawith many zeroes and low counts have been a somewhat difficult case for INLA, and thecase of binary data has been particularly problematic. Our new correction has been im-plemented as part of the R-INLA package, and adds only negligible computational cost.Empiricalevaluationsonbothrealandsimulateddataindicatethatthemethodworkswell.Keywords: Bayesian computation; copulas; generalized linear mixed models; integratednestedLaplaceapproximation;latentGaussianmodels 1 Introduction IntegratedNestedLaplaceApproximations(INLA)wereintroducedbyRue,MartinoCMcCulloch,SearleN2;:::;n,letProb(y

http://www.jstatsoft.org/v63/i20 The integrated nested Laplace approximation (INLA) provides an interesting way of approximating the posterior marginals of a wide range of Bayesian hierarchical models. This approximation is based on conducting a Laplace approximation of certain functions and numerical integration is extensively used to integrate some of the models parameters out. The R - INLA package o ers an interface to INLA, providing a suitable framework for data analysis. Although the INLA methodology can deal with a large number of models, only the most relevant have been implemented within R - INLA . However, many other important models are not available for R - INLA yet. In this paper we show how to fit a number of spatial models with R - INLA , including its interaction with other R packages for data analysis. Secondly, we describe a novel method to extend the number of latent models available for the model parameters. Our approach is based on conditioning on one or several model parameters and fit these conditioned models with R-INLA. Then these models are combined using Bayesian model averaging to provide the final approximations to the posterior marginals of the model. Finally, we show some examples of the application of this technique in spatial statistics. It is worth noting that our approach can be extended to a number of other fields, and not only spatial statistics

Summary To account for measurement error (ME) in explanatory variables, Bayesian approaches provide a flexible framework, as expert knowledge can be incorporated in the prior distributions. Recently, integrated nested Laplace approximations have been proven to be a computationally convenient alternative to sampling approaches for Bayesian inference in latent Gaussian models. We show how the most common approaches to adjust for ME, the classical and the Berkson ME, fit into this framework. This is achieved through a reformulation with augmented pseudo-observations and a suitable extension of the latent Gaussian field. Two specific classes are described, which allow for a particularly simple implementation using integrated nested Laplace approximations. We present three applications within the framework of generalized linear (mixed) models with ME. To illustrate the practical feasibility, R code is provided in on-line supplementary material.

Space-varying regression models are generalizations of standard linear models where the regression coefficients are allowed to change in space. The spatial structure is specified by a multivariate extension of pairwise difference pri- ors thus enabling incorporation of neighboring structures and easy sampling schemes. Different sampling schemes are available and may be used in an MCMC algorithm. These schemes are compared in terms of chain autocor- relation and resulting inference. We also discuss different prior specifications that accommodate the spatial structure. Results are illustrated with simulated data and applied to a real dataset. Os modelos de regressão com parâmetros variando no espaço são uma generalização dos modelos lineares em que é permitido aos coeficientes da regressão mudarem ao longo do espaço. A estrutura espacial é especificada por uma extensão multivariada de uma distribuição a priori que considera as diferenças entre os coeficientes de regiões vizinhas. Isso permite a incorporação da informação da vizinhança espacial. Para estimar o modelo utilizamos a abordagem bayesiana e o algoritmo do MCMC considerando diferentes esquemas de amostragem. Esses esquemas foram comparados em termos da autocorrelação da cadeia de Markov, e em termos dos resultados obtidos. Foram discutidas diferentes especificações a priori que admitem estruturas espaciais semelhantes. Os resultados são ilustrados com dados simulados e com um conjunto real de informações.

A recently proposed Bayesian multiscale tool for exploratory analysis of time series data is reconsidered and umerous important improvements are suggested. The improvements are in the model itself, the algorithms to analyse it, and how to display the results. The consequence is that exact results can be obtained in real time using only a tiny fraction of the CPU time previously needed to get approximate results. Analysis of both real and synthetic data are given to illustrate our new approach. Multiscale analysis for time series data is a useful tool in applied time series analysis, and with the new model and algorithms, it is also possible to do such analysis in real time.

A systematic approach for predicting the mean erosion and mean deposition rates of mud beneath random waves is derived. This has been accomplished by applying formulas valid for regular waves and by describing the waves as a stationary Gaussian narrow-band random process. The present approach covers flow in the laminar, smooth turbulent and rough turbulent flow regimes. Examples are given, using data typical for field conditions representing laminar and smooth turbulent flow conditions, which are the most common flow regimes over mud beds.

This note discusses the approach of specifying a Gaussian Markov random field (GMRF) by the Cholesky triangle of the precision matrix. A such representation can be made extremely sparse using numerical techniques for incomplete sparse Cholesky factorization, and provide very computational efficient representation for simulating from the GMRF. However, we provide theoretical and empirical justification showing that the sparse Cholesky triangle representation is fragile when conditioning a GMRF on a subset of the variables or observed data, meaning that the computational cost increases.

An approach by which the scour depth around group of slender vertical piles in random waves can be derived is presented. Here, formulas based on data from laboratory tests for scour depth by Sumer and Fredsoe [Sumer BM, Fredsoe J. Wave scour around group of vertical piles. ASCE J Waterway, Port Coastal Ocean Eng. 1998; 124(5):248-255.] for group of slender vertical piles for regular waves are used. They are combined with describing the waves as a stationary Gaussian narrow-band random process to derive the scour depths in random waves.

This article discusses and extends statistical models to jointly analyse the spatial variation of rates of several diseases with common risk factors. We start with a review of methods for separate analyses of diseases, then move to ecological regression approaches, where the rates from one of the diseases enter as surrogate covariates for exposure. Finally, we propose a general framework for jointly modelling the variation of two or more diseases, some of which share latent spatial fields, but with possibly different risk gradients. In our application, we consider mortality data on oral, oesophagus, larynx and lung cancers for males in Germany, which all share smoking as a common risk factor. Furthermore, the first three cancers are also known to be related to excessive alcohol consumption. An empirical comparison of the different models based on a formal model criterion as well as on the posterior precision of the relative risk estimates strongly suggests that the joint modelling approach is a useful and valuable extension over individual analyses.

An approach by which the scour depth and protection layer width around the head of vertical-wall breakwaters, the scour and deposition depths as well as the protection layer widths at the round head of rubble-mound breakwaters in random waves can be derived is presented. Here the formulas for scour depth by Sumer and Fredsoe (1997) for vertical-wall breakwaters for regular waves and Fredsoe and Sumer (1997) for rubble-mound breakwaters for irregular waves are used. They are combined with describing the waves as a stationary Gaussian narrow-band random process to derive the scour and deposition depths as well as protection layer widths in random waves. Comparisons are made between the present approach and the Fredsoe and Sumer (1997) random wave scour data for rubble-mound breakwaters.

The effect of boundary layer streaming on sea bed shear stresses, as well as on the mean bedload sediment transport rate, beneath random waves, is investigated. Formulas for the bottom friction and bedload sediment transport under regular waves have been applied to obtain the mean bedload sediment transport rate caused by steady streaming under linear random waves. Friction factors for steady streaming under random waves are also provided. The effect of streaming and second order wave asymmetry on the mean bedload sediment transport rate is discussed.

An approach by which the scour depth and scour width below a fixed pipeline and scour depth around a circular vertical pile in random waves can be derived is presented. Here, the scour depth formulas by Sumer and Fredsoe [ASCE J. Waterw., Port, Coastal Ocean Eng. 116 (1990) 307] for pipelines and Sumer et al. [ASCE J. Waterw., Port, Coastal Ocean Eng. 114 (1992) 599] for vertical piles as well as the scour width formula by Sumer and Fredsoe [The Mechanics of Scour in the Marine Environment, World Scientific, Singapore, 2002] for pipelines combined with describing the waves as a stationary Gaussian narrow-band random process are used to derive the cumulative distribution functions of the scour depths and width. Comparisons are made between the present approach and random wave scour data. Tentative approaches to related random wave scour cases are also suggested.

The boundary layer under random waves alone, as well as under random waves plus current, has been examined using a dynamic turbulent boundary layer model; this is based upon the linearised boundary layer equations, with horizontally uniform forcing. The turbulence closure is provided by a high Reynolds number k − e model. The model appears to be verified, as far as data exists, i.e., for sinusoidal waves alone as well as for sinusoidal waves plus a mean current. The time and space variation of the velocity, the turbulent kinetic energy and the shear stress within the bottom boundary layer have been examined. Correlations between boundary layer quantities due to the grouping of the largest waves in a realistic sea state have also been examined. A wave friction factor for random waves is proposed. Estimates of probability density functions for individual bottom shear stress maxima are given, for random waves alone as well as for random waves plus current. Superposition of a mean current on the waves at the outer boundary induces a drift and an enhancement of the flow quantities within the boundary layer. The enhancement of the friction velocity has been demonstrated and quantified. For the case of a non-zero angle between the waves and the current, the time variation of the horizontal direction of the friction velocity vector has been quantified. Estimates of the apparent roughness experienced by the current, in the presence of waves, are given. The resulting mean bottom shear stress for random waves plus current has been shown to agree reasonably well with that obtained by an equivalent sinusoidal wave plus current. The bottom friction under random waves alone has been shown to be in good agreement with that obtained by Madsen (1994), based on an equivalent sinusoidal wave.

Joint distributions of successive wave crest heights and successive wave trough depths for nonlinear waves are presented. Two different approaches are used in order to derive the probability distributions. The first method includes the effect of second-order Stokes-type nonlinearity on successive wave statistics in finite water depth, and the second method is a parametric model only for crest heights based on second-order simulations. The theoretical distributions are compared with observed wave data obtained from field measurements in the central North Sea.

Exceedances over high thresholds are often modeled by fitting a generalized Pareto distribution (GPD) on R+. It is difficult to select the threshold, above which the GPD assumption is enough solid and enough data is available for inference. We suggest a new dynamically weighted mixture model, where one term of the mixture is the GPD, and the other is a light-tailed density distribution. The weight function varies on R+ in such a way that for large values the GPD component is predominant and thus takes the role of threshold selection. The full data set is used for inference on the parameters present in the two component distributions and in the weight function. Maximum likelihood provides estimates with approximate standard deviations. Our approach has been successfully applied to simulated data and to the (previously studied) Danish fire loss data set. We compare the new dynamic mixture method to Dupuis' robust thresholding approach in peaks-over-threshold inference. We discuss robustness with respect to the choice of the light-tailed component and the form of the weight function. We present encouraging simulation results that indicate that the new approach can be useful in unsupervised tail estimation, especially in heavy tailed situations and for small percentiles.

Local linear M-smoothing is proposed as a method for noise reduction in one-dimensional signals. It is more appropriate than conventional local linear smoothing, because it does not introduce blurring of jumps in the signal. It improves local constant M-smoothing, by avoiding boundary effects at edges and jumps. While the idea of local linear M-smoothing is straightforward, numerical issues are challenging, because of the local minima aspect that is crucial to good performance. We give an algorithm which is both fast and robust together with the theoretical properties of the local linear M-smoother. The new M-smoother gives a large improvement for some data sets compared to the local constant M-smoother and demonstrates elsewhere good performance on various artificial and magnetic resonance data sets.

In recent years, the availability of infectious disease counts in time and space has increased, and consequently, there has been renewed interest in model formulation for such data. In this paper, we describe a model that was motivated by the need to analyze hand, foot, and mouth disease surveillance data in China. The data are aggregated by geographical areas and by week, with the aims of the analysis being to gain insight into the space-time dynamics and to make short-term predictions, which will aid in the implementation of public health campaigns in those areas with a large predicted disease burden. The model we develop decomposes disease-risk into marginal spatial and temporal components and a space-time interaction piece. The latter is the crucial element, and we use a tensor product spline model with a Markov random field prior on the coefficients of the basis functions. The model can be formulated as a Gaussian Markov random field and so fast computation can be carried out using the integrated nested Laplace approximation approach. A simulation study shows that the model can pick up complex space-time structure and our analysis of hand, foot, and mouth disease data in the central north region of China provides new insights into the dynamics of the disease.

The smoothing spline is one of the most popular curve-fitting methods, partly because of empirical evidence supporting its effectiveness and partly because of its elegant mathematical formulation. However, there are two obstacles that restrict the use of the smoothing spline in practical statistical work. Firstly, it becomes computationally prohibitive for large data sets because the number of basis functions roughly equals the sample size. Secondly, its global smoothing parameter can only provide a constant amount of smoothing, which often results in poor performances when estimating inhomogeneous functions. In this work, we introduce a class of adaptive smoothing spline models that is derived by solving certain stochastic differential equations with finite element methods. The solution extends the smoothing parameter to a continuous data-driven function, which is able to capture the change of the smoothness of the underlying process. The new model is Markovian, which makes Bayesian computation fast. A simulation study and real data example are presented to demonstrate the effectiveness of our method.

In this paper, we introduce a new concept for constructing prior distributions. We exploit the natural nested structure inherent to many model components, which defines the model component to be a flexible extension of a base model. Proper priors are defined to penalise the complexity induced by deviating from the simpler base model and are formulated after the input of a user-defined scaling parameter for that model component, both in the univariate and the multivariate case. These priors are invariant to reparameterisations, have a natural connection to Jeffreys' priors, are designed to support Occam's razor and seem to have excellent robustness properties, all which are highly desirable and allow us to use this approach to define default prior distributions. Through examples and theoretical results, we demonstrate the appropriateness of this approach and how it can be applied in various situations., Major revision of previous version. Includes a beefed up literature review and new desiderata for hierarchical priors. Removes (for space) the Cox proportional hazard model and the section on hyperparameters for Gaussian random fields

O sitema da corrente de Humboldt do norete (NHCS) é um dos mais produtivos ecossisteas em termos de peixes do mundo. Em particular, a anchova peruana (Engraulis reingers) é a maior presa dos predadores superiores, como mamíferos, aves, peixes e pescadores. Nesse contexto, é importante compreender a dinâmica da distribuição de anchova paraa preservá-la,bem como para explorar sua capacidade econômica. Usando os dados recolhidos pelo "Instituto del Mar del Perú" (IMARPE), durante uma pesquisa cientifica em 2005, apresenta-se uma análise estatística que tem como objetivos principais:(i) se adaptar às características dos dados amostrados como: dependência espacial, altas proporções de zeros e grandes tamanhos de amostras, (ii) fornecxer informações importantes da dinâmica da população de anchovas e propor um modelo para estimação e previsão da biomassa da anchova no NHCS do Perú. Os dados são analisados em um contexto Bayesiano usando a metodologia Integrated Nested Laplace Approximation (INLA). Finalmente, usa-se critérios de comparações entre modelos para selecionar o modelo proposto de melhor ajuste. Também é feito um estudo do poder preditivo de cada modelo. Além disso, é realizado um diagnóstico de influência Bayesiana para o modelo preferido. The Northern Humboldt Current System (NHCS) is the world most productive ecosystem in terms of fish. In particular, Peruvian anchovy (Engraulis ringens) is the major prey of the principal top predators, like mammals, seabirds, fish and fishers. In this context, it is important to understand the dynamics of the anchovy distribution to preserve it as well as to explore its economical capacities. Using the data collected by the Instituto del Mar del Perú (IMARPE), during a scientific survey in 2005, we present a statistical analysis that has as main goals: (i) adapt to the characteristics of the sampled data, such as spatial dependence, high proportions of zeros and big samples size, (ii) provide important insights on the dynamics of the anchovy population and propose a model for estimation and prediction of anchovy biomass in the NHCS of Perú. These data are analyzed in a Bayesian framework using the Integrated Nested Laplace Approximation (INLA) methodology. Finally, model comparison is performed to select the best model and predictive checks to study the predictive power of each model. Moreover, a Bayesian spatial influence diagnostic is performed for the preferred model.

During the last three decades, Bayesian methods have developed greatly in the field of epidemiology. Their main challenge focusses around computation, but the advent of Markov Chain Monte Carlo methods (MCMC) and in particular of the WinBUGS software has opened the doors of Bayesian modelling to the wide research community. However model complexity and database dimension still remain a constraint. Recently the use of Gaussian random fields has become increasingly popular in epidemiology as very often epidemiological data are characterised by a spatial and/or temporal structure which needs to be taken into account in the inferential process. The Integrated Nested Laplace Approximation (INLA) approach has been developed as a computationally efficient alternative to MCMC and the availability of an R package (R-INLA) allows researchers to easily apply this method. In this paper we review the INLA approach and present some applications on spatial and spatio-temporal data.

A stationary spatial model is an idealization and we expect that the true dependence structures of physical phenomena are spatially varying, but how should we handle this non-stationarity in practice? We study the challenges involved in applying a flexible non-stationary model to a dataset of annual precipitation in the conterminous US, where exploratory data analysis shows strong evidence of a non-stationary covariance structure. The aim of this paper is to investigate the modelling pipeline once non-stationarity has been detected in spatial data. We show that there is a real danger of over-fitting the model and that careful modelling is necessary in order to properly account for varying second-order structure. In fact, the example shows that sometimes non-stationary Gaussian random fields are not necessary to model non-stationary spatial data., Comment: Minor change from previous version. arXiv admin note: text overlap with arXiv:1306.0408

In this paper we explore the use of the Integrated Laplace Approximation (INLA) for Bayesian inference in some widely used models in Spatial Econometrics. Bayesian inference often relies on computationally intensive simulation methods, such as Markov Chain Monte Carlo. When only marginal inference is needed, INLA provides a fast and accurate estimate of the posterior marginals of the parameters in the model.Furthermore, we have compared the results provided by these models to those obtained with a more general class of Generalised Linear Models with random effects. In these models, spatial autocorrelation is modelled by means of correlated Gaussian random effects. We also discuss a procedure to extend the class of models that the R-INLA software can fit. This approach is based on conditioning on one or more parameters so that the resulting models can be fitted with R-INLA across sets of values of the fixed parameters. The posterior marginals of these parameters of interest are then obtained by combining the marginal likelihoods (which are conditioned on the values of the parameters fixed) of the fitted models and a prior on these parameters. This approach can also be used to fit even more general models. Finally, we discuss the use of all these models on two datasets based on median housing prices for census tracts in Boston and the probability of business re-opening in New Orleans in the aftermath of hurricane Katrina. © 2014. This is the authors’ accepted and refereed manuscript to the article. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/

In recent years, a number of statistical models have been proposed for the purposes of high-level image analysis tasks such as object recognition. However, in general, these models remain hard to use in practice, partly as a result of their complexity, partly through lack of software. In this paper we concentrate on a particular deformable template model which has proved potentially useful for locating and labelling cells in microscope slides Rue and Hurn (1999). This model requires the specification of a number of rather non-intuitive parameters which control the shape variability of the deformed templates. Our goal is to arrange the estimation of these parameters in such a way that the microscope user's expertise is exploited to provide the necessary training data graphically by identifying a number of cells displayed on a computer screen, but that no additional statistical input is required. In this paper we use maximum likelihood estimation incorporating the error structure in the generation of our training data.

A common discussion subject for the male part of the population in particular is the prediction of the next week-end's soccer matches, especially for the local team. Knowledge of offensive and defensive skills is valuable in the decision process before making a bet at a bookmaker. We take an applied statistician's approach to the problem, suggesting a Bayesian dynamic generalized linear model to estimate the time-dependent skills of all teams in a league, and to predict the next week-end's soccer matches. The problem is more intricate than it may appear at first glance, as we need to estimate the skills of all teams simultaneously as they are dependent. It is now possible to deal with such inference problems by using the Markov chain Monte Carlo iterative simulation technique. We show various applications of the proposed model based on the English Premier League and division 1 in 1997–1998: prediction with application to betting, retrospective analysis of the final ranking, the detection of surprising matches and how each team's properties vary during the season.

Shear stresses on a rough seabed under irregular waves plus current are calculated. Parameterized models valid for regular waves plus current have been used in Monte Carlo simulations, assuming the wave amplitudes to be Rayleigh-distributed. Numerical estimates of the probability distribution functions are presented. For waves only, the shear stress maxima follow a Weibull distribution, while for waves plus current, both the maximum and time-averaged shear stresses are well represented by a three-parameter Weibull distribution. The behaviour of the maximum shear stresses under a wide range of wave-current conditions has been investigated, and it appears that under certain conditions, the current has a significant influence on the maximum shear stresses. Results of comparison between predictions and measurements of the maximum bottom shear stresses from laboratory and field experiments are presented.

This paper addresses the task of locating and identifying an unknown number of objects of different types in an image. Baddeley & Van Lieshout (1993) advocate marked point processes as object priors, whereas Grenander & Miller (1994) use deformable template models. In this paper elements of both approaches are combined to handle scenes containing variable numbers of objects of different types, using reversible jump Markov chain Monte Carlo methods for inference (Green, 1995). The naive application of these methods here leads to slow mixing and we adapt the model and algorithm in tandem in proposing three strategies to deal with this. The first two expand the model space by introducing an additional 'unknown' object type and the idea of a variable resolution template. The third strategy, utilising the first two, augments the algorithm with classes of updates which provide intuitive transitions between realisations containing different numbers of cells by splitting or merging nearby objects.

Markov chain Monte Carlo methods are widely used to study highly structured stochastic systems. However, when the system is subject to constraints, it is difficult to find irreducible proposal distributions. We suggest a “block-wise” approach for constrained sampling and optimisation.

A joint distribution of successive wave periods is presented. First, the analysis includes comparisons between observed wave data and an empirical as well as theoretical distributions of wave period. Secondly, a joint distribution of successive wave periods based on a best fit of a Weibull distribution to the wave period distribution is developed. Comparisons are made with observed wave data as well as with the previous approach of Myrhaug & Rue (1993). It appears that the revised approach is in better agreement with the data.