bayesian reconstructions from emission tomography data using a modified em algorithm a novel method of reconstruction from single photon emission computerized tomography data is proposed this method builds on the expectation maximization em approach to maximum likelihood reconstruction from emission tomography data but aims instead at maximum posterior probability estimation which takes account of prior belief about smoothness in the isotope concentration a novel modification to the em algorithm yields a practical method the method is illustrated by an application to data from brain scans

computational methods for inverse finite elastostatics abstract in the inverse motion problem in finite hyper elasticity the classical formulation relies on conservation laws based on eshelby s energy momentum tensor this formulation is shown to be lacking in several regards for a particular class of inverse motion problems where the deformed configuration and cauchy traction are given and the undeformed configuration must be calculated it is shown that for finite element calculations a simple re examination of the equilibrium equations provides a more suitable finite element formulation this formulation is also shown to involve only minor changes to existing elements designed for forward motion calculations examples illustrating the method in simple and complex situations involving a neo hookean material are presented

structural image restoration through deformable templates abstract prior knowledge on the space of possible images is given in the form of a function or template in some domain the set of all possible true images is assumed to be formed by a composition of that function with continuous mappings of the domain into itself a prior gaussian distribution is given on the set of continuous mappings the observed image is assumed to be a degradation of the true image with additive noise given the observed image a posterior distribution is then obtained and has the form of a nonlinear perturbation of the gaussian measure on the space of mappings we present simulations of the posterior distribution that lead to structural reconstructions of the true image in the sense that it enables us to determine landmarks and other characteristic features of the image as well as to spot pathologies in it moreover we show that the reconstruction algorithm is relatively robust when the images are degraded by noise that is not necessarily additive

bayesian phylogenetic inference via markov chain monte carlo methods we derive a markov chain to sample from the posterior distribution for a phylogenetic tree given sequence information from the corresponding set of organisms a stochastic model for these data and a prior distribution on the space of trees a transformation of the tree into a canonical cophenetic matrix form suggests a simple and effective proposal distribution for selecting candidate trees close to the current tree in the chain we illustrate the algorithm with restriction site data on 9 plant species then extend to dna sequences from 32 species of fish the algorithm mixes well in both examples from random starting trees generating reproducible estimates and credible sets for the path of evolution

generalized monte carlo significance tests summary simple monte carlo significance testing has many applications particularly in the preliminary analysis of spatial data the method requires the value of the test statistic to be ranked among a random sample of values generated according to the null hypothesis however there are situations in which a sample of values can only be conveniently generated using a markov chain initiated by the observed data so that independence is violated this paper describes two methods that overcome the problem of dependence and allow exact tests to be carried out the methods are applied to the rasch model to the finite lattice ising model and to the testing of association between spatial processes power is discussed in a simple case

hydrodynamical limit for a nongradient system the generalized symmetric exclusion process we consider a symmetric simple exclusion process where at most two particles per site are permitted this model turns out to be nongradient we prove that the particles densities under a diffusive rescaling of space and time converge to the solution of a diffusion equation we give a variational characterization of the diffusion coefficent we also prove for the generator of the process in finite volume a lower bound on the spectral gap uniform in the volume 1994 john wiley sons inc

bayesian computation via the gibbs sampler and related markov chain monte carlo methods the use of the gibbs sampler for bayesian computation is reviewed and illustrated in the context of some canonical examples other markov chain monte carlo simulation methods are also briefly described and comments are made on the advantages of sample based approaches for bayesian inference summaries

fluctuations of one dimensional ginzburg landau models in nonequilibrium we study the fluctuation of one dimensional ginzburg landau models in nonequilibrium along the hydrodynamic diffusion limit the hydrodynamic limit has been proved to be a nonlinear diffusion equation by fritz guo papanicolaou varadhan etc we proved that if the potential is uniformly convex then the fluctuation process is governed by an ornstein uhlenbeck process whose drift term is obtained by formally linearizing the hydrodynamic equation

statistical analysis of field experiments using neighbouring plots the paper describes and provides examples of four different applications of the use of neighbouring plot values in the analysis of agricultural field experiments the topics include the use of check plots to control environmental variation in large unreplicated variety trials spatial models based on first differences to accommodate fertility effects in trials that have some degree of replication adjustment for interplot competition using a simultaneous equations formulation and the analysis of trials in which plot values are affected by the particular treatments on neighbouring plots

bootstrapping phylogenies large deviations and dispersion effects summary a large deviation result is established for the bootstrap empirical distribution in a finite sample space thereby validating both nonparametric and parametric bootstrapping in certain phylogenetic inference problems the bias previously observed in the bootstrap distribution of the estimated tree topology is shown to stem from dispersion effects in the joint distribution of sample and bootstrap empirical distributions both results are examined for maximum likelihood estimation in a three taxon model having particularly simple geometry they are also applicable to discrete parameter problems outside of phylogenetic inference

absence of mass gap for a class of stochastic contour models we study a class of markovian stochastic processes in which the state space is a space of lattice contours and the elementary motions are local deformations we show under suitable hypotheses on the jump rates that the infinitesimal generator has zero mass gap this result covers among others the bfacf dynamics for fixed endpoint self avoiding walks and the sterling greensite dynamics for fixed boundary self avoiding surfaces our models also mimic the glauber dynamics for the low temperature ising model the proofs are based on two new general principles the minimum hitting time argument and the mean or mean exponential hitting time argument

markov chains for exploring posterior distributions several markov chain methods are available for sampling from a posterior distribution two important examples are the gibbs sampler and the metropolis algorithm in addition several strategies are available for constructing hybrid algorithms this paper outlines some of the basic methods and strategies and discusses some related theoretical and practical issues on the theoretical side results from the theory of general state space markov chains can be used to obtain convergence rates laws of large numbers and central limit theorems for estimates obtained from markov chain methods these theoretical results can be used to guide the construction of more efficient algorithms for the practical use of markov chain methods standard simulation methodology provides several variance reduction techniques and also give guidance on the choice of sample size and allocation

a computational method to assess the in vivo stresses and unloaded configuration of patient specific blood vessels in the modelling process of cardiovascular diseases one often comes across the numerical simulation of the blood vessel wall when the vessel geometry is patient specific and is obtained in vivo via medical imaging the stress distribution throughout the vessel wall is unknown however simulating the full physiological pressure load inside the blood vessel without incorporating the in vivo stresses will result in an inaccurate stress distribution and an incorrect deformation of the vessel wall in this work a computational method is formulated to restore the zero pressure geometry of patient specific blood vessels and to recover the in vivo stress field of the loaded structures at the moment of imaging the proposed backward displacement method is able to solve the inverse problem iteratively using fixed point iterations as only an update of the mesh is required the formulation of this method allows for a straightforward implementation in combination with existing structural solvers even if the structural solver is a black box

markov chain monte carlo convergence diagnostics a comparative review abstract a critical issue for users of markov chain monte carlo mcmc methods in applications is how to determine when it is safe to stop sampling and use the samples to estimate characteristics of the distribution of interest research into methods of computing theoretical convergence bounds holds promise for the future but to date has yielded relatively little of practical use in applied work consequently most mcmc users address the convergence problem by applying diagnostic tools to the output produced by running their samplers after giving a brief overview of the area we provide an expository review of 13 convergence diagnostics describing the theoretical basis and practical implementation of each we then compare their performance in two simple models and conclude that all of the methods can fail to detect the sorts of convergence failure that they were designed to identify we thus recommend a combination of strategies aimed at evaluating and accelerating mcmc sampler convergence including ap

a coupling regeneration scheme for diagnosing convergence in markov chain monte carlo algorithms abstract here i propose a convergence diagnostic for markov chain monte carlo mcmc algorithms based on couplings of a markov chain with an auxiliary chain that is periodically restarted from a fixed parameter value the diagnostic provides a mechanism for estimating the specific constants governing the rate of convergence of geometrically and uniformly ergodic chains and provides a lower bound on the effective sample size of a mcmc run it also provides a simple procedure for obtaining what is with high probability an independent sample from the stationary distribution

hydrodynamics and large deviation for simple exclusion processes we prove the hydrodynamical limit for weakly asymmetric simple exclusion processes a large deviation property with respect to this limit is established for the symmetric case we treat also the situation where a slow reaction creation and annihilation of particles is present

iterative simulation methods abstract the standard methods of generating sample from univariate distributions often become hopelessly inefficient when applied to realizations of stochastic processes iterative methods are not widely known amongst statisticians but some are standard practice in statistical physics and chemistry the methods are surveyed and compared with particular reference to their convergence properties

bayesian phylogenetic inference from animal mitochondrial genome arrangements summary the determination of evolutionary relationships is a fundamental problem in evolutionary biology genome arrangement data are potentially more informative than deoxyribonucleic acid sequence data for inferring evolutionary relationships between distantly related taxa we describe a bayesian framework for phylogenetic inference from mitochondrial genome arrangement data using markov chain monte carlo methods we apply the method to assess evolutionary relationships between eight animal phyla

scaling limits for gradient systems in random environment it is well known that the hydrodynamic limit of an interacting particle system satisfying a gradient condition such as the zero range process or the symmetric simple exclusion process is given by a possibly non linear parabolic equation and the equilibrium fluctuations from this limit are given by a generalized ornstein uhlenbeck process we prove that in the presence of a symmetric random environment these scaling limits also hold for almost every choice of the random environment with an homogenized diffusion coefficient that does not depend on the realization of the random environment

equilibrium fluctuations for zero range exclusion processes we introduce a markovian particle system which is a kind of lattice gas on z consisting of particles carrying energy and whose dynamics is a combination of those of an exclusion process for particles and a zero range process for energy it has two conserved quantities the number of particles and the total energy the process is reversible relative to certain product probability measures but of non gradient type it is proved that under hydrodynamic scaling the equilibrium fluctuation fields of two conserved quantities converge in law to an infinite dimensional ornstein uhlenbeck process

the empirical efficiency and validity of two neighbour models the validity and efficiency of two neighbour models the first difference model of besag and kempton 1986 biometrics 42 231 251 and their extended error in variables model were studied for a variety of simulated yield models the extended error in variables model is equivalent to the linear variance neighbour model of williams 1986 biometrika 73 279 287 the parameters of the linear variance model were estimated using the method of restricted maximum likelihood estimation since the method of maximum likelihood used by besag and kempton was found to be biased the efficiencies of the two neighbour models were compared with those of two classical analyses a randomized block analysis and an incomplete block analysis in general the neighbour analyses were more efficient than the classical analyses where the simulated yield model contained a trend component the exceptions were when the trend was effectively eliminated by replicate blocks where the incomplete block analysis made gains over the randomized block analysis the neighbour models made proportionately greater gains the linear variance analysis was the best overall in efficiency of those examined being in all cases either the most efficient analysis or close in efficiency to the best analysis although the first difference model is a special case of the linear variance model besag and kempton recommended a different estimator of treatment precision for the first difference model from that recommended for the linear variance model for both neighbour models the recommended estimators of treatment precision were judged to be empirically valid for all simulated yield models

equilibrium fluctuations of a one dimensional nongradient ginzburg landau model we study equilibrium fluctuations for hydrodynamic limits of a nongradient ginzburg landau model we prove that the limit fluctuation process is governed by a generalized stationary ornstein uhlenbeck process

boundary detection by constrained optimization a statistical framework is used for finding boundaries and for partitioning scenes into homogeneous regions the model is a joint probability distribution for the array of pixel gray levels and an array of labels in boundary finding the labels are binary zero or one representing the absence or presence of boundary elements in partitioning the label values are generic two labels are the same when the corresponding scene locations are considered to belong to the same region the distribution incorporates a measure of disparity between certain spatial features of block pairs of pixel gray levels using the kolmogorov smirnov nonparametric measures of difference between the distributions of these features the number of model parameters is minimized by forbidding label configurations which are assigned probability zero the maximum a posteriori estimator of boundary placements and partitionings is examined the forbidden states introduce constraints into the calculation of these configurations stochastic relaxation methods are extended to accommodate constrained optimization

equilibrium fluctuations for interacting ornstein uhlenbeck particles we study the hydrodynamic density fluctuations of an infinite system of interacting particles on d the particles interact between them through a two body superstable potential and with a surrounding fluid in equilibrium through a random viscous force of ornstein uhlenbeck type the stationary initial distribution is the gibbs measure associated with the potential and with a given temperature and fugacity we prove that the time dependent density fluctuation field converges in law under diffusive scaling of space and time to the solution of a linear stochastic partial differential equation driven by white noise

topology optimization utilizing inverse motion based form finding topology optimization at finite strain setting using the concept of inverse motion based form finding is introduced this novel procedure allows boundary conditions and shape of the structure in the operating deformed state to be prescribed the outcome of the optimization algorithm will be the shape of the undeformed structure i e the state in which the structure should be manufactured the objective of the optimization considered is to find the stiffest structure for a given amount of material the problem is regularized using a helmholtz filter which is formulated in the deformed configuration both the elastic boundary value problem and the partial differential equation associated with the helmholtz filter are solved using the finite element method the optimization problem is solved using a sequence of convex separable approximations the paper is closed by 2d as well as 3d numerical examples that clearly illustrates that the method is able to find optimal solutions for inverse motion finite strain topology optimization problems

phylogenetic inference linear invariants and maximum likelihood we develop a new statistical method for inferring phylogenies based on a likelihood ratio test this method does not require parameter constraints but does require identical evolutionary processes in the sites considered another method of phylogenetic inference is the method of linear invariants described by cavender 1989 molecular biology and evolution 6 301 316 based on a notion of lake 1987 molecular biology and evolution 4 167 191 we describe a sound mathematical basis for the use of linear invariants we show that the validity of the method requires parameter constraints but does not require that the evolutionary processes in differing sites be identical we show that the method of linear invariants is asymptotically equivalent to a less powerful version of our likelihood ratio test and is thus essentially a maximum likelihood technique

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

a variational r adaption and shape optimization method for finite deformation elasticity this paper is concerned with the formulation of a variational r adaption method for finite deformation elastostatic problems the distinguishing characteristic of the method is that the variational principle simultaneously supplies the solution the optimal mesh and in problems of shape optimization the equilibrium shapes of the system this is accomplished by minimizing the energy functional with respect to the nodal field values as well as with respect to the triangulation of the domain of analysis energy minimization with respect to the referential nodal positions has the effect of equilibrating the energetic or configurational forces acting on the nodes we derive general expressions for the configuration forces for isoparametric elements and nonlinear possibly anisotropic materials under general loading we illustrate the versatility and convergence characteristics of the method by way of selected numerical tests and applications including the problem of a semi infinite crack in linear and nonlinear elastic bodies and the optimization of the shape of elastic inclusions

inference in molecular population genetics full likelihood based inference for modern population genetics data presents methodological and computational challenges the problem is of considerable practical importance and has attracted recent attention with the development of algorithms based on importance sampling is and markov chain monte carlo mcmc sampling here we introduce a new is algorithm the optimal proposal distribution for these problems can be characterized and we exploit a detailed analysis of genealogical processes to develop a practicable approximation to it we compare the new method with existing algorithms on a variety of genetic examples our approach substantially outperforms existing is algorithms with efficiency typically improved by several orders of magnitude the new method also compares favourably with existing mcmc methods in some problems and less favourably in others suggesting that both is and mcmc methods have a continuing role to play in this area we offer insights into the relative advantages of each approach and we discuss diagnostics in the is framework

a tabu search algorithm for maximum parsimony phylogeny inference abstract phylogeny reconstruction is too complex a combinatorial problem for an exhaustive search because the number of possible solutions increases exponentially with the number of taxa involved in this paper we adopt the parsimony principle and design a tabu search algorithm for finding a most parsimonious phylogeny tree a special array structure is employed to represent the topology of trees and to generate the neighboring trees we test the proposed tabu search algorithm on randomly selected data sets obtained from nuclear ribosomal dna sequence data the experiments show that our algorithm explores fewer trees to reach the optimal one than the commonly used program dnapenny branch and bound based while it generates much more accurate results than the default options of the program dnapars heuristic search based the percentage of search space needed to find the best solution for our algorithm decreased rapidly as the number of taxa increased for a 20 taxon phylogeny problem it needs on average to examine only 3 92 10 15 of the sample space

computational methods for inverse deformations in quasi incompressible finite elasticity this paper presents a formulation for incorporating quasi incompressibility in inverse design problems for finite elastostatics where deformed configurations and cauchy tractions are known in the recent paper of govindjee and mihalic 1996 comput methods appl mech engng 136 47 57 a method for solving this class of inverse problems was presented for compressible materials here we extend this work to the important case of nearly incompressible materials a displacement pressure mixed formulation is combined with a penalty method to enforce the quasi incompressible constraint without locking numerical examples are presented and compared to known solutions further examples present practical applications of this research to active problems in elastomeric component design 1998 john wiley sons ltd

phylogenetic tree construction using markov chain monte carlo abstract we describe a bayesian method based on markov chain simulation to study the phylogenetic relationship in a group of dna sequences under simple models of mutational events our method produces a markov chain whose stationary distribution is the conditional distribution of the phylogeny given the observed sequences our algorithm strikes a reasonable balance between the desire to move globally through the space of phylogenies and the need to make computationally feasible moves in areas of high probability because phylogenetic information is described by a tree we have created new diagnostics to handle this type of data structure an important byproduct of the markov chain monte carlo phylogeny building technique is that it provides estimates and corresponding measures of variability for any aspect of the phylogeny under study

nonlinear diffusion limit for a system with nearest neighbor interactions we consider a system of interacting diffusions the variables are to be thought of as charges at sites indexed by a periodic one dimensional lattice the diffusion preserves the total charge and the interaction is of nearest neighbor type with the appropriate scaling of lattice spacing and time a nonlinear diffusion equation is derived for the time evolution of the macroscopic charge density

equilibrium fluctuations for a model of coagulating fragmenting planar brownian particles we study a model of mass bearing coagulating fragmenting planar brownian particles coagulation occurs when two particles are within a distance of order e our model is macroscopically described by an inhomogeneous smoluchowski s equation in the low e limit provided that the initial number of particles n is of order log e when a detailed balance condition is satisfied we establish a central limit theorem by showing that in the low e limit the particle density fluctuation fields obey an ornstein uhlenbeck stochastic differential equation

equilibrium fluctuations of nongradient reversible particle systems by taking the generalized symmetric exclusion process as an example we present a unified martingale approach to study the equilibrium fluctuations of nongradient reversible interacting particle systems the hydrodynamic limit of the generalized symmetric exclusion process has been derived by kipnis landim and 011a we show that the limit of the density fluctuation fields of this process is an infinite dimensional ornstein uhlenbeck process

coupled fluid structure interaction hemodynamics in a zero pressure state corrected arterial geometry abstract hemodynamic conditions in large arteries are significantly affected by the interaction of the pulsatile blood flow with the distensible arterial wall a numerical procedure for solving the fluid structure interaction problem encountered in cardiovascular flows is presented we consider a patient specific carotid bifurcation geometry obtained from 3d reconstruction of in vivo acquired tomography images which yields a geometrical representation of the artery corresponding to its pressurized state to recover the geometry of the artery in its zero pressure state which is required for a fluid structure interaction simulation we utilize inverse finite elastostatics time dependent flow simulations with in vivo measured inflow volume flow rate in the 3d undeformed artery are performed through the finite element method the coupled momentum method for fluid structure interaction is adopted to incorporate the influence of wall compliance in the numerical computation of the time varying flow domain to demonstrate the importance in recovering the zero pressure state of the artery in hemodynamic simulations we compute the time varying flow field with compliant walls for the original and the zero pressure state corrected geometric configurations of the carotid bifurcation the most important resulting effects in the hemodynamic environment are evaluated our results show a significant change in the wall shear stress distribution and the spatiotemporal extent of the recirculation regions

evolutionary similarity among genes an evolutionary history of a set of organisms is a family tree or topology with branches of various lengths between vertices that describe how closely the organisms are related to each other we

analysis of field experiments by least squares smoothing summary assuming a smooth trend plus independent error model for the environmental effects in the yields of a field plot experiment least squares smoothing methods are developed to estimate both the treatment effects and the unknown trend treatment estimates are closely related to those resulting from a generalized least squares analysis in which the covariance structure for the environmental effects has a particular form however the main emphases are on the accuracy of treatment estimates under a fixed smooth trend plus error model and the exploratory power of the basic method to isolate trend effects of unknown form although the detailed development is for the one dimensional case generalizations of the smoothness concept and extensions to two dimensions are also discussed application of the basic method is illustrated on three data sets and the results compared with other analyses

exponential convergence to equilibrium for a class of random walk models we prove exponential convergence to equilibrium l 2 geometric ergodicity for a random walk with inward drift on a sub cayley rooted tree this randomwalk model generalizes a monte carlo algorithm for the self avoiding walk proposed by berretti and sokal if the number of vertices of leveln in the tree grows asc n n n 1 we prove that the autocorrelation time satisfies n 2 n 1

finite element modelling of inverse design problems in large deformations anisotropic hyperelasticity this paper introduces a finite element model for the inverse design of pieces with large displacements in the elastic range the problem consists in determining the initial shape of the piece such that it attains the designed shape under the effect of service loads the model is particularly focused on the design of parts with a markedly anisotropic behavior like laminated turbine blades although the formulation expresses equilibrium on the distorted configuration it uses a standard constitutive equations library that is expressed as usual for measures attached to the undistorted configuration in this way the modifications to a standard finite elements code are limited to the routines for the computation of the finite element internal forces and tangent matrix two examples are given the first one for validation purposes while the second is an application which has industrial interest for the design of turbine blades copyright 2007 john wiley sons ltd

nonlinear fluctuations of weakly asymmetric interacting particle systems we introduce what we call the second order boltzmann gibbs principle which allows one to replace local functionals of a conservative one dimensional stochastic process by a possibly nonlinear function of the conserved quantity this replacement opens the way to obtain nonlinear stochastic evolutions as the limit of the fluctuations of the conserved quantity around stationary states as an application of this second order boltzmann gibbs principle we introduce the notion of energy solutions of the kpz and stochastic burgers equations under minimal assumptions we prove that the density fluctuations of one dimensional stationary weakly asymmetric conservative particle systems are sequentially compact and that any limit point is given by energy solutions of the stochastic burgers equation we also show that the fluctuations of the height function associated to these models are given by energy solutions of the kpz equation in this sense unfortunately we lack a uniqueness result for these energy solutions we conjecture these solutions to be unique and we show some regularity results for energy solutions of the kpz burgers equation supporting this conjecture

on referential and spatial formulations of inverse elastostatic analysis abstract there are two families of element formulation for inverse elastostatic analysis in the literature they employ different computation procedures at the element and material levels it has been suggested that one of them can preserve material library while the other requires redeveloping the material functions in this article we show that these two formulations are completely equivalent under certain conditions both can preserve the material library while under other conditions neither can we show that the modification of material functions is caused by the need of updating material symmetry in the inverse solution process several theoretical results were obtained while establishing the equivalence including an identity relating the inverse and forward tangent tensors for isotropic materials a comprehensive documentation of these two formulations is provided

on the irreducibility of a markov chain defined on a space of genotype configurations by a sampling scheme techniques from image processing are now being considered for use in pedigree analysis although the method that we develop here was motivated by considering it as an analogue to the gibbs sampler we justify it independently using the ergodic theorem for aperiodic irreducible finite markov chains while it is trivial to show that aperiodicity holds irreducibility is a more interesting condition proofs of irreducibility are provided for some special cases and counterexamples are provided for others where irreducibility does not hold an alternative method using relaxed genetic parameters and rejection is recommended and justified

equilibrium fluctuations of asymmetric simple exclusion processes in dimension d 3 we consider an asymmetric exclusion process in dimension d 3 under diffu sive rescaling starting from the bernoulli product measure with density 0 1 we prove that the density fluctuation field y n t converges to a generalized ornstein uhlenbeck process which is formally the solution of the stochastic differential equation dyt ayt dt db where a is a second order differential operator and b t is a mean zero gaussian field with known covariances

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

sequential monte carlo p values summary the assessment of statistical significance by monte carlo simulation may be costly in computer time this paper looks at a number of ways of calculating exact monte carlo p values by sequential sampling such p values are shown to have properties similar to those obtained by sampling with a fixed sample size both standard and generalized monte carlo procedures are discussed and in particular a sequential method is proposed for dealing with situations in which values can only be conveniently generated using a markov chain conditioned to pass through the observed data

spatial statistics and bayesian computation on wednesday may 6th 1992 professor b w silverman in the chair summary markov chain monte carlo mcmc algorithms such as the gibbs sampler have provided a bayesian inference machine in image analysis and in other areas of spatial statistics for several years founded on the pioneering ideas of ulf grenander more recently the observation that hyperparameters can be included as part of the updating schedule and the fact that almost any multivariate distribution is equivalently a markov random field has opened the way to the use of mcmc in general bayesian computation in this paper we trace the early development of mcmc in bayesian inference review some recent computational progress in statistical physics based on the introduction of auxiliary variables and discuss its current and future relevance in bayesian applications we briefly describe a simple mcmc implementation for the bayesian analysis of agricultural field experiments with which we have some practical experience

scaling limits of additive functionals of interacting particle systems using the renormalization method introduced in 17 we prove what we call the local boltzmann gibbs principle for conservative stationary interacting particle systems in dimension d 1 as applications of this result we obtain various scaling limits of additive functionals of particle systems like the occupation time of a given site or extensive additive fields of the dynamics as a by product of these results we also construct a novel process related to the stationary solution of the stochastic burgers equation