a composite likelihood approach to binary spatial data abstract conventional geostatistics addresses the problem of estimation and prediction for continuous observations but in many practical applications in public health environmental remediation or ecological research the most commonly available data are in the form of counts e g number of cases or indicator variables denoting above or below threshold values also in many situations it is less expensive to obtain an imprecise categorical observation than to obtain precise measurements of the variable of interest such as a contaminant this article proposes a computationally simple method for estimation and prediction using binary or indicator data in space the proposed method is based on pairwise likelihood contributions and the large sample properties of the estimators are obtained in a straightforward manner we illustrate the methodology through application to indicator data related to gypsy moth defoliation in massachusetts

on the synchronizability and detectability of random ppm sequences the problem of synchronization and detection of random pulse position modulation ppm sequences is investigated under the assumption of perfect slot synchronization maximum likelihood ppm symbol synchronization and receiver algorithms are derived that make decisions based on both soft and hard data these algorithms are seen to be easily implementable the author derives bounds on the symbol error probability and the probability of false synchronization that indicate the existence of a severe performance floor which can be the limiting factor in the overall system performance the performance floor is inherent in the ppm format and random data and becomes more serious as the ppm alphabet size q is increased a way to eliminate the performance floor is suggested by inserting special ppm symbols in the random data stream

robust and consistent estimates of autoregressive moving average parameters summary we aim at estimates of autoregressive moving average parameters which are simultaneously consistent at the nominal gaussian model and insensitive to outliers in the data the estimates may be viewed as a robust version of maximum likelihood estimates of order r and for purely autoregressive models reduce to a special case of generalized m estimates

pairwise likelihood methods for inference in image models summary we consider parameter estimation for certain random set models for image data for the spatial models considered here a full likelihood based approach to this problem is often difficult since the likelihood generally cannot be computed for images of typical size this has motivated the consideration of various less computationally demanding parameter estimation techniques we discuss one method based on likelihoods for small subsets of the data consideration of the basic technique within the framework of the theory of estimating functions leads to a weighted version of the basic approach results of a simulation study are reported for some variants of the boolean model and excursion sets of random fields the methods are illustrated for some data on the spatial incidence of heather

pruned enriched rosenbluth method simulations of θ polymers of chain length up to 1 000 000 we present an algorithm for simulating flexible chain polymers it combines the rosenbluth rosenbluth method with recursive enrichment although it can be applied also in more general situations it is most efficient for three dimensional theta polymers on the simple cubic lattice there it allows high statistics simulations of chains of length up to n 10 sup 6 for storage reasons this is feasable only for polymers in a finite volume for free theta polymers in infinite volume we present very high statistics runs with n 10000 these simulations fully agree with previous simulations made by hegger and grassberger j chem phys bold 102 6681 1995 with a similar but less efficient algorithm showing that logarithmic corrections to mean field behavior are much stronger than predicted by field theory but the finite volume simulations show that the density inside a collapsed globule scales with the distance from the theta point as predicted by mean field theory in contrast to claims in the work mentioned above in addition to the simple cubic lattice we also studied two versions of the bond fluctuation model but with much shorter chains finally we show that our method can be applied also to off lattice models and illustrate this with simulations of amore model studied in detail by freire ital et al macromolecules bold 19 452 1986 and later work copyright ital 1997 ital the american physical society less

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

join and cut algorithm for self avoiding walks with variable length and free endpoints we introduce a new monte carlo algorithm for generating self avoiding walks of variable length and free endpoints the algorithm works in the unorthodox ensemble consisting of all pairs of saws such that the total number of stepsntot in the two walks is fixed the elementary moves of the algorithm are fixed n e g pivot moves on the individual walks and a novel join and cut move that concatenates the two walks and then cuts them at a random location we analyze the dynamic critical behavior of the new algorithm using a combination of rigorous heuristic and numerical methods in two dimensions the autocorrelation time in cpu units grows as n 1 5 and the behavior improves in higher dimensions this algorithm allows high precision estimation of the critical exponent

weighted empirical adaptive variance estimators for correlated data regression estimating equations based on marginal generalized linear models are useful for regression modelling of correlated data but inference and testing require reliable estimates of standard errors we introduce a class of variance estimators based on the weighted empirical variance of the estimating functions and show that an adaptive choice of weights allows reliable estimation both asymptotically and by simulation in finite samples connections with previous bootstrap and jackknife methods are explored the effect of reliable variance estimation is illustrated in data on health effects of air pollution in king county washington

regression analysis with censored autocorrelated data abstract for many studies in which data are collected sequentially in time the sensitivity of the measurement is limited and an exact value can be recorded only if it falls within a specified range this gives rise to a censored time series in this article we present a methodology for regression analysis of censored time series data we fit autoregressive models to account for the time dependence two numerical methods for full likelihood estimation and an approximate method are discussed the methods are illustrated with air pollution data subject to lower limits of detection

towards a unification of second order theory for likelihood and marginal composite likelihood an adjustment for marginal composite likelihoods is derived to match the second order theory of the likelihood when inference is for a vector valued parameter in the absence of nuisance components the adjustment overcomes the failure of bartlett identities for marginal composite likelihoods and leads to a bartlett correctable marginal composite likelihood ratio statistic

a strongly consistent procedure for model selection in a regression problem summary we consider the multiple regression model yn xn en where yn and en are n vector random variables xn is an n x m matrix and 83 is an m vector of unknown regression parameters each component of 3 may be zero or nonzero which gives rise to 2 possible models for multiple regression we provide a decision rule for the choice of a model which is strongly consistent for the true model as n oo the result is proved under certain mild conditions for instance without assuming normality of the distribution of the components of en

large deviation properties of the extended moran model the distributions of the times to the first common ancestor t mrca is numerically studied for an ecological population model the extended moran model this model has a fixed population size n the number of descendants is drawn from a beta distribution beta alpha 2 alpha for various choices of alpha this includes also the classical moran model alpha 0 as well as the uniform distribution alpha 1 using a statistical mechanics based large deviation approach the distributions can be studied over an extended range of the support down to probabilities like 10 70 which allowed us to study the change of the tails of the distribution when varying the value of alpha in 0 2 we find exponential distributions p t mrca delta t mrca in all cases with systematically varying values for the base delta only for the cases alpha 0 and alpha 1 analytical results are known i e delta exp 2 n 2 and delta 2 3 respectively we recover these values confirming the validity of our approach finally we also study the correlations between t mrca and the number of descendants

accurate approximations for posterior moments and marginal densities abstract this article describes approximations to the posterior means and variances of positive functions of a real or vector valued parameter and to the marginal posterior densities of arbitrary i e not necessarily positive parameters these approximations can also be used to compute approximate predictive densities to apply the proposed method one only needs to be able to maximize slightly modified likelihood functions and to evaluate the observed information at the maxima nevertheless the resulting approximations are generally as accurate and in some cases more accurate than approximations based on third order expansions of the likelihood and requiring the evaluation of third derivatives the approximate marginal posterior densities behave very much like saddle point approximations for sampling distributions the principal regularity condition required is that the likelihood times prior be unimodal

tuning parameter selectors for the smoothly clipped absolute deviation method summary the penalized least squares approach with smoothly clipped absolute deviation penalty has been consistently demonstrated to be an attractive regression shrinkage and selection method it not only automatically and consistently selects the important variables but also produces estimators which are as efficient as the oracle estimator however these attractive features depend on appropriate choice of the tuning parameter we show that the commonly used generalized crossvalidation cannot select the tuning parameter satisfactorily with a nonignorable overfitting effect in the resulting model in addition we propose a bic tuning parameter selector which is shown to be able to identify the true model consistently simulation studies are presented to support theoretical findings and an empirical example is given to illustrate its use in the female labor supply data

sparse pairwise likelihood estimation for multivariate longitudinal mixed models abstractit is becoming increasingly common in longitudinal studies to collect and analyze data on multiple responses for example in the social sciences we may be interested in uncovering the factors driving mental health of individuals over time where mental health is measured using a set of questionnaire items one approach to analyzing such multi dimensional data is multivariate mixed models an extension of the standard univariate mixed model to handle multiple responses estimating multivariate mixed models presents a considerable challenge however let alone performing variable selection to uncover which covariates are important in driving each response motivated by composite likelihood ideas we propose a new approach for estimation and fixed effects selection in multivariate mixed models called approximate pairwise likelihood estimation and shrinkage aples the method works by constructing a quadratic approximation to each term in the pairwise likelihood function and then augmenting this ap

performance of pll based optical oppm communication systems the power spectral density psd of a direct detected optical signal with overlapping pulse position modulation oppm scheme is derived it is demonstrated that this spectrum contains a strong periodic component at the signal symbol frequency thereby enabling a simple pll device to provide joint symbol and slot synchronization the variance of the timing error for a linearized pll synchronizer is shown to be mainly dominated by and is inversely proportional to the product of the pll closed loop bandwidth and symbol duration of the oppm signal the performance of a shot noise limited pll based optical oppm communication system is then assessed in terms of the overall system symbol error rate

on sample reuse methods for dependent data we suggest a sample reuse method for dependent data based on a cross between the block bootstrap and richardson extrapolation instead of simulating a same size resample by resampling blocks and placing them end to end it analyses the blocks directly and employs a variant of richardson extrapolation to adjust for block size a simple empirical rule also based on richardson extrapolation is suggested for empirically selecting the block size performance in the contexts of distribution and bias estimation is discussed via theoretical analysis and numerical simulation

practical codes for photon communication in a recent paper pierce studied the problems of communicating at optical frequencies using photon counting techniques and concluded that at low temperatures we encounter insuperable problems of encoding long before we approach channel capacity in this paper it is shown that even assuming a noiseless model for photon communication for which capacity measured in nats photon is infinite it is unlikely that a signaling efficiency of even 10 nats photon could be achieved practically on the positive side it is shown that pulse position modulation plus reed solomon coding yields practical results in the range of 2 to 3 nats photon

computing bayes factors by combining simulation and asymptotic approximations abstract the bayes factor is a ratio of two posterior normalizing constants which may be difficult to compute we compare several methods of estimating bayes factors when it is possible to simulate observations from the posterior distributions via markov chain monte carlo or other techniques the methods that we study are all easily applied without consideration of special features of the problem provided that each posterior distribution is well behaved in the sense of having a single dominant mode we consider a simulated version of laplace s method a simulated version of bartlett correction importance sampling and a reciprocal importance sampling technique we also introduce local volume corrections for each of these in addition we apply the bridge sampling method of meng and wong we find that a simulated version of laplace s method with local volume correction furnishes an accurate approximation that is especially useful when likelihood function evaluations are costly a simple bridge sampli

semiparametric normal transformation models for spatially correlated survival data there is an emerging interest in modeling spatially correlated survival data in biomedical and epidemiologic studies in this article we propose a new class of semiparametric normal transformation models for right censored spatially correlated survival data this class of models assumes that survival outcomes marginally follow a cox proportional hazard model with unspecified baseline hazard and their joint distribution is obtained by transforming survival outcomes to normal random variables whose joint distribution is assumed to be multivariate normal with a spatial correlation structure a key feature of the class of semiparametric normal transformation models is that it provides a rich class of spatial survival models where regression coefficients have population average interpretation and the spatial dependence of survival times is conveniently modeled using the transformed variables by flexible normal random fields we study the relationship of the spatial correlation structure of the transformed no

a serially correlated gamma frailty model for longitudinal count data a poisson gamma model is introduced to account for between subjects heterogeneity and within subjects serial correlation occurring in longitudinal count data the model extends the usual time constant shared frailty approach to allow time varying serially correlated gamma frailty whilst retaining standard marginal assumptions a composite likelihood approach to estimation and testing for serial correlation is proposed the work is motivated by a clinical trial on patient controlled analgesia where the number of analgesic doses taken by hospital patients in successive time intervals following abdominal surgery is recorded

extended bayesian information criteria for model selection with large model spaces summary the ordinary bayesian information criterion is too liberal for model selection when the model space is large in this paper we re examine the bayesian paradigm for model selection and propose an extended family of bayesian information criteria which take into account both the number of unknown parameters and the complexity of the model space their consistency is established in particular allowing the number of covariates to increase to infinity with the sample size their performance in various situations is evaluated by simulation studies it is demonstrated that the extended bayesian information criteria incur a small loss in the positive selection rate but tightly control the false discovery rate a desirable property in many applications the extended bayesian information criteria are extremely useful for variable selection in problems with a moderate sample size but with a huge number of covariates especially in genome wide association studies which are now an active area in genetics research

a pairwise likelihood augmented cox estimator for left truncated data survival data collected from a prevalent cohort are subject to left truncation and the analysis is challenging conditional approaches for left truncated data could be inefficient as they ignore the information in the marginal likelihood of the truncation times length biased sampling methods may improve the estimation efficiency but only when the underlying truncation time is uniform otherwise they may generate biased estimates we propose a semiparametric method for left truncated data under the cox model with no parametric distributional assumption about the truncation times our approach is to make inference based on the conditional likelihood augmented with a pairwise likelihood which eliminates the truncation distribution yet retains the information about the regression coefficients and the baseline hazard function in the marginal likelihood an iterative algorithm is provided to solve for the regression coefficients and the baseline hazard function simultaneously by empirical process and u process theories it has been shown that the proposed estimator is consistent and asymptotically normal with a closed form consistent variance estimator simulation studies show substantial efficiency gain of our estimator in both the regression coefficients and the cumulative baseline hazard function over the conditional approach estimator when the uniform truncation assumption holds our estimator enjoys smaller biases and efficiency comparable to that of the full maximum likelihood estimator an application to the analysis of a chronic kidney disease cohort study illustrates the utility of the method

importance weighted marginal bayesian posterior density estimation abstract markov chain sampling schemes generate dependent observations i 0 i n from a full joint posterior distribution data frequently only certain marginals of this full posterior density are of interest thus an interesting problem is how to estimate the marginal posterior densities based on the dependent observations i 0 i n from data we propose a new importance weighted marginal density estimation iwmde method an iwmde is obtained by averaging many dependent observations of the ratio of the full joint posterior densities multiplied by a weighting conditional density w the asymptotic properties for the iwmde and the guidelines for choosing a weighting conditional density w are also considered a bivariate normal model and a constrained linear multiple regression model are used to illustrate how to derive the iwmde s for the marginal posterior densities

sequential imputations and bayesian missing data problems abstract for missing data problems tanner and wong have described a data augmentation procedure that approximates the actual posterior distribution of the parameter vector by a mixture of complete data posteriors their method of constructing the complete data sets is closely related to the gibbs sampler both required iterations and similar to the em algorithm convergence can be slow we introduce in this article an alternative procedure that involves imputing the missing data sequentially and computing appropriate importance sampling weights in many applications this new procedure works very well without the need for iterations sensitivity analysis influence analysis and updating with new data can be performed cheaply bayesian prediction and model selection can also be incorporated examples taken from a wide range of applications are used for illustration

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

approximate likelihood methods for estimating local recombination rates summary there is currently great interest in understanding the way in which recombination rates vary over short scales across the human genome aside from inherent interest an understanding of this local variation is essential for the sensible design and analysis of many studies aimed at elucidating the genetic basis of common diseases or of human population histories standard pedigree based approaches do not have the fine scale resolution that is needed to address this issue in contrast samples of deoxyribonucleic acid sequences from unrelated chromosomes in the population carry relevant information but inference from such data is extremely challenging although there has been much recent interest in the development of full likelihood inference methods for estimating local recombination rates from such data they are not currently practicable for data sets of the size being generated by modern experimental techniques we introduce and study two approximate likelihood methods the first a marginal likelihood ignores some of the data a careful choice of what to ignore results in substantial computational savings with virtually no loss of relevant information for larger sequences we introduce a composite likelihood which approximates the model of interest by ignoring certain long range dependences an informal asymptotic analysis and a simulation study suggest that inference based on the composite likelihood is practicable and performs well we combine both methods to reanalyse data from the lipoprotein lipase gene and the results seriously question conclusions from some earlier studies of these data

composite likelihood bayesian information criteria for model selection in high dimensional data for high dimensional data sets with complicated dependency structures the full likelihood approach often leads to intractable computational complexity this imposes difficulty on model selection given that most traditionally used information criteria require evaluation of the full likelihood we propose a composite likelihood version of the bayes information criterion bic and establish its consistency property for the selection of the true underlying marginal model our proposed bic is shown to be selection consistent under some mild regularity conditions where the number of potential model parameters is allowed to increase to infinity at a certain rate of the sample size simulation studies demonstrate the empirical performance of this new bic especially for the scenario where the number of parameters increases with sample size technical proofs of our theoretical results are provided in the online supplemental materials

data integration with high dimensionality we consider situations where the data consist of a number of responses for each individual which may include a mix of discrete and continuous variables the data also include a class of predictors where the same predictor may have different physical measurements across different experiments depending on how the predictor is measured the goal is to select which predictors affect any of the responses where the number of such informative predictors tends to infinity as the sample size increases there are marginal likelihoods for each experiment we specify a pseudolikelihood combining the marginal likelihoods and propose a pseudolikelihood information criterion under regularity conditions we establish selection consistency for this criterion with unbounded true model size the proposed method includes a bayesian information criterion with appropriate penalty term as a special case simulations indicate that data integration can dramatically improve upon using only one data source

a composite likelihood inference in latent variable models for ordinal longitudinal responses the paper proposes a composite likelihood estimation approach that uses bivariate instead of multivariate marginal probabilities for ordinal longitudinal responses using a latent variable model the model considers time dependent latent variables and item specific random effects to be accountable for the interdependencies of the multivariate ordinal items time dependent latent variables are linked with an autoregressive model simulation results have shown composite likelihood estimators to have a small amount of bias and mean square error and as such they are feasible alternatives to full maximum likelihood model selection criteria developed for composite likelihood estimation are used in the applications furthermore lower order residuals are used as measures of fit for the selected models

fleming viot processes in population genetics fleming and viot indiana univ math j 28 1979 pp 817 843 introduced a class of probability measure valued diffusion processes that has attracted the interest of both pure and applied probabilists this paper surveys the subject of fleming viot processes as it relates to population genetics topics include 1 introduction 2 some measure valued markov chains 2 1 a diploid model 2 2 the wright fisher model 2 3 a moran model 3 the fleming viot process characterization 4 convergence 5 ergodicity 6 an infinite particle system 7 bounded mutation operators 8 reversibility 9 examples 9 1 continuous state stepwise mutation model 9 2 infinitely many neutral alleles model 9 3 infinitely many neutral alleles model with ages 9 4 two locus model with recombination 9 5 n locus model with gene conversion 9 6 infinitely many sites model without recombination 9 7 infinitely many neutral alleles model with allelic genealogies

new monte carlo method for the self avoiding walk we introduce a new monte carlo algorithm for the self avoiding walk saw and show that it is particularly efficient in the critical region long chains we also introduce new and more efficient statistical techniques we employ these methods to extract numerical estimates for the critical parameters of the saw on the square lattice we find 2 63820 0 00004 0 00030 1 352 0 006 0 025 v 0 7590 0 0062 0 0042 where the first error bar represents systematic error due to corrections to scaling subjective 95 confidence limits and the second bar represents statistical error classical 95 confidence limits these results are based on saws of average length 166 using 340 hours cpu time on a cdc cyber 170 730 we compare our results to previous work and indicate some directions for future research

safe and effective importance sampling abstract we present two improvements on the technique of importance sampling first we show that importance sampling from a mixture of densities using those densities as control variates results in a useful upper bound on the asymptotic variance that bound is a small multiple of the asymptotic variance of importance sampling from the best single component density this allows one to benefit from the great variance reductions obtainable by importance sampling while protecting against the equally great variance increases that might take the practitioner by surprise the second improvement is to show how importance sampling from two or more densities can be used to approach a zero sampling variance even for integrands that take both positive and negative values

maximum likelihood estimation of order m for stationary stochastic processes sometimes the likelihood cannot be computed even introducing approximations whose effect is asymptotically negligible to overcome this problem for inference from a stochastic process we approximate the log likelihood by a sum whose generic term is the density function of the corresponding sample element conditional on the m most recent observations for some m s 0 general results on the asymptotic properties of the associated estimates are given and numerical comparisons with other estimators are carried out in special cases

metric regularity of newton s iteration for a version of newton s method applied to a generalized equation with a parameter we extend the paradigm of the lyusternik graves theorem to the framework of a mapping acting from the pair parameter starting point to the set of corresponding convergent newton sequences under ample parameterization metric regularity of the mapping associated with convergent newton sequences becomes equivalent to the metric regularity of the mapping associated with the generalized equation we also discuss an inexact newton method and present an application to discretized optimal control

graph estimation with joint additive models in recent years there has been considerable interest in estimating conditional independence graphs in high dimensions most previous work has assumed that the variables are multivariate gaussian or that the conditional means of the variables are linear in fact these two assumptions are nearly equivalent unfortunately if these assumptions are violated the resulting conditional independence estimates can be inaccurate we propose a semi parametric method graph estimation with joint additive models which allows the conditional means of the features to take on an arbitrary additive form we present an efficient algorithm for our estimator s computation and prove that it is consistent we extend our method to estimation of directed graphs with known causal ordering using simulated data we show that our method performs better than existing methods when there are non linear relationships among the features and is comparable to methods that assume multivariate normality when the conditional means are linear we illustrate our method on a cell signaling data set

a pairwise likelihood based approach for changepoint detection in multivariate time series models this paper develops a composite likelihood based approach for multiple changepoint estimation in multivariate time series we derive a criterion based on pairwise likelihood and minimum description length for estimating the number and locations of changepoints and for performing model selection in each segment the number and locations of the changepoints can be consistently estimated under mild conditions and the computation can be conducted efficiently with a pruned dynamic programming algorithm simulation studies and real data examples demonstrate the statistical and computational efficiency of the proposed method

a countable representation of the fleming viot measure valued diffusion the fleming viot measure valued diffusion arises as the infinite population limit of various discrete genetic models with general type space the paper gives a countable construction of the process as the empirical measure carried by a certain interactive particle system this explicit representation facilitates the study of various properties of the fleming viot process the construction also carries versions of the familiar genealogical processes from population genetics in particular kingman s coalescent thus unifying the genealogical and measure valued approaches to the subject

correlated binary regression using a quadratic exponential model summary a model of quadratic exponential form is parameterized in terms of marginal means and pairwise correlations for the regression analysis of correlated binary data pseudo maximum likelihood methods using a special case termed the multiplicative model are proposed but are noted to be computationally unattractive if the blocks of correlated responses are at all large on the other hand score estimating functions for mean and correlation parameters are shown to be of a particularly simple form under the quadratic exponential family special cases of such estimating functions having attractive computational properties are identified and illustrated

particle representations for measure valued population models models of populations in which a type or location represented by a point in a metric space e is associated with each individual in the population are considered a population process is neutral if the chances of an individual replicating or dying do not depend on its type measurevalued processes are obtained as infinite population limits for a large class of neutral population models and it is shown that these measure valued processes can be represented in terms of the total mass of the population and the de finetti measures associated with an e valued particle model

the use of subseries values for estimating the variance of a general statistic from a stationary sequence let z i infty i infty be a strictly stationary infty mixing sequence without specifying the dependence model giving rise to z i and without specifying the marginal distribution of z i we address the question of variance estimation for a general statistic t n t n z 1 z n for estimating var t n from just the available data z 1 z n we propose computing subseries values t m z i 1 z i 2 z i m 0 leq i i m leq n these subseries values are used as replicates to model the sampling variability of t n in particular we use adjacent nonoverlapping subseries of length m m n with m rightarrow infty and m n n rigtharrow 0 our variance estimator is just the usual sample variance computed amongst these subseries values after appropriate standardization this estimator is shown to be consistent under mild integrability conditions we present optimal i e minimum m s e choices of m n for the special case where t n overset z n and z i is a normal ar 1 sequence a simulation study is conducted showing that those same choices of m n are effective when t n is a robust estimator of location and z i is subject to contamination

model selection for multivariate regression in small samples we develop a small sample criterion aicc for selecting multivariate regression models this criterion adjusts the akaike information criterion to be an exact unbiased estimator for the expected kullback leibler information a small sample comparison shows that aicc provides better model order choices than other available model selection methods data from an agricultural experiment are analyzed

bayesian information criteria and smoothing parameter selection in radial basis function networks summary by extending schwarz s 1978 basic idea we derive a bayesian information criterion which enables us to evaluate models estimated by the maximum penalised likelihood method or the method of regularisation the proposed criterion is applied to the choice of smoothing parameters and the number of basis functions in radial basis function net work models monte carlo experiments were conducted to examine the performance of the nonlinear modelling strategy of estimating the weight parameters by regularisation and then determining the adjusted parameters by the bayesian information criterion the simulation results show that our modelling procedure performs well in various situations

akaike s information criterion in generalized estimating equations correlated response data are common in biomedical studies regression analysis based on the generalized estimating equations gee is an increasingly important method for such data however there seem to be few model selection criteria available in gee the well known akaike information criterion aic cannot be directly applied since aic is based on maximum likelihood estimation while gee is nonlikelihood based we propose a modification to aic where the likelihood is replaced by the quasi likelihood and a proper adjustment is made for the penalty term its performance is investigated through simulation studies for illustration the method is applied to a real data set

sampling based approaches to calculating marginal densities abstract stochastic substitution the gibbs sampler and the sampling importance resampling algorithm can be viewed as three alternative sampling or monte carlo based approaches to the calculation of numerical estimates of marginal probability distributions the three approaches will be reviewed compared and contrasted in relation to various joint probability structures frequently encountered in applications in particular the relevance of the approaches to calculating bayesian posterior densities for a variety of structured models will be discussed and illustrated

a note on composite likelihood inference and model selection a composite likelihood consists of a combination of valid likelihood objects usually related to small subsets of data the merit of composite likelihood is to reduce the computational complexity so that it is possible to deal with large datasets and very complex models even when the use of standard likelihood or bayesian methods is not feasible in this paper we aim to suggest an integrated general approach to inference and model selection using composite likelihood methods in particular we introduce an information criterion for model selection based on composite likelihood we also describe applications to the modelling of time series of counts through dynamic generalised linear models and to the analysis of the well known old faithful geyser dataset

composite conditional likelihood for sparse clustered data summary sparse clustered data arise in finely stratified genetic and epidemiologic studies and pose at least two challenges to inference first it is difficult to model and interpret the full joint probability of dependent discrete data which limits the utility of full likelihood methods second standard methods for clustered data such as pairwise likelihood and the generalized estimating function approach are unsuitable when the data are sparse owing to the presence of many nuisance parameters we present a composite conditional likelihood for use with sparse clustered data that provides valid inferences about covariate effects on both the marginal response probabilities and the intracluster pairwise association our primary focus is on sparse clustered binary data in which case the method proposed utilizes doubly discordant quadruplets drawn from each stratum to conduct inference about the intracluster pairwise odds ratios

fixed point theorems for multi valued contractive mappings and multi valued caristi type mappings abstract in this paper the famous banach contraction principle and caristi s fixed point theorem are generalized to the case of multi valued mappings our results are extensions of the well known nadler s fixed point theorem s b nadler jr multi valued contraction mappings pacific j math 30 1969 475 487 as well as of some caristi type theorems for multi valued operators see n mizoguchi w takahashi fixed point theorems for multivalued mappings on complete metric spaces j math anal appl 141 1989 177 188 j p aubin optima and equilibria an introduction to nonlinear analysis grad texts in math springer verlag berlin 1998 p 17 s s zhang q luo set valued caristi fixed point theorem and ekeland s variational principle appl math mech 10 2 1989 111 113 in chinese english translation appl math mech english ed 10 2 1989 119 121 etc

bayesian analysis of isochores statistical identification of isochore structure the variation in large scale gc composition proportion of dna bases that are g or c as opposed to a or t of mammalian genomes is a necessary requirement for understanding both the evolution of base composition and the many genomic features such as mutation and recombination rates which covary with base composition we have developed a bayesian method for isochore analysis that we demonstrate to be more accurate than the commonly used binary segmentation approach implemented within the program isofinder the method accounts for both fine scale and large scale structure we adapt direct simulation methods to allow for iid samples from the posterior distribution of our model and provide an accurate approximation to this that can analyze data from a chromosome in a matter of seconds we apply our method to human chromosome 1 the resulting estimate of how gc content varies across this region is shown to be a better predictor of local recombination rates t

a model based approach to simultaneous clustering and dimensional reduction of ordinal data the literature on clustering for continuous data is rich and wide differently that one developed for categorical data is still limited in some cases the clustering problem is made more difficult by the presence of noise variables dimensions that do not contain information about the clustering structure and could mask it the aim of this paper is to propose a model for simultaneous clustering and dimensionality reduction of ordered categorical data able to detect the discriminative dimensions discarding the noise ones following the underlying response variable approach the observed variables are considered as a discretization of underlying first order latent continuous variables distributed as a gaussian mixture to recognize discriminative and noise dimensions these variables are considered to be linear combinations of two independent sets of second order latent variables where only one contains the information about the cluster structure while the other one contains noise dimensions the model specification involves multidimensional integrals that make the maximum likelihood estimation cumbersome and in some cases infeasible to overcome this issue the parameter estimation is carried out through an em like algorithm maximizing a composite log likelihood based on low dimensional margins examples of application of the proposal on real and simulated data are performed to show the effectiveness of the proposal

estimating space and space time covariance functions for large data sets a weighted composite likelihood approach in this article we propose two methods for estimating space and space time covariance functions from a gaussian random field based on the composite likelihood idea the first method relies on the maximization of a weighted version of the composite likelihood function while the second one is based on the solution of a weighted composite score equation this last scheme is quite general and could be applied to any kind of composite likelihood an information criterion for model selection based on the first estimation method is also introduced the methods are useful for practitioners looking for a good balance between computational complexity and statistical efficiency the effectiveness of the methods is illustrated through examples simulation experiments and by analyzing a dataset on ozone measurements

maximum likelihood symbol synchronization for the direct detection optical on off keying channel the maximum likelihood symbol synchronization statistic is derived from noisy observations of randomly modulated on off keying data for the direct detection optical channel a similar statistic for the case when the transmitter sends a special pattern of alternating o s and 1 s for synchronization purposes only is also derived various approximations to the optimal statistic are introduced and their performance compared to the optimal one under a new criterion believed to be more appropriate for the poisson channel than the mean square error criterion routinely used with other channels it is shown that although the variable associated with symbol transitions is continuous the possible values of it that maximize the maximum likelihood ml statistic belong to a discrete set with relatively few elements

on the choice of a model to fit data from an exponential family let x 1 cdots x n be iid observations coming from an exponential family the problem of interest is this given a finite number of models m j smoothly curved manifolds in mathbb r k choose the best model to fit the observations with some penalty for choosing models with dimensions which are too large a result of schwarz is made more specific and is extended to the case where the models are curved manifolds if s y n j is up to a constant c n independent of the model the log of the posterior probability of the j th model where the sample mean y n 1 n sum n i 1 x i has been replaced by y schwarz suggested an asymptotic expansion of s y n j whose leading terms are gamma y n j n sup psi in m j cap theta y psi b psi frac 1 2 k j log n in the case where the models are affine subspaces of mathbb r k we establish a similar asymptotic expansion including the next term with uniform bounds for y in a compact neighborhood of nabla b theta where theta is the true value of the parameter we suggest a criterion for the choice of the best model that consists of maximizing the three leading terms in the expansion s y n j we show that the criterion gives the correct model with probabilities p n theta rightarrow 1 as n rightarrow infty

fitting full information item factor models and an empirical investigation of bridge sampling abstract based on item response theory bock and aitken introduced a method of item factor analysis termed full information item factor fiif analysis by bartholomew because it uses all distinct item response vectors as data but a limitation of their fitting algorithm is its reliance on fixed point gauss hermite quadrature which can produce appreciable numerical errors especially in high dimension problems the first purpose of this article is to offer more reliable methods by using recent advances in statistical computation specifically we illustrate two ways of implementing monte carlo expectation maximization em algorithm to fit a fiif model using the gibbs sampler to carry out the computation for the e steps we also show how to use bridge sampling to simulate the likelihood ratios for monitoring the convergence of a monte carlo em a strategy that is useful in general simulations demonstrate substantial improvement over bock and aitken s algorithm in recovering known factor loadings in hig

discussion on the meeting on statistical modelling and analysis of genetic data david j balding imperial college school of medicine london i extendmy apologies to the authors that an unavoidable commitment arising unexpectedly in the 18 hours before the meeting robbed me of my final preparation so that my comments at the meeting were poorly presented i shall try to do a better job in this written version and to leave enough space i shall omit my introductory comments about the role of statisticians in bioinformatics

the analysis of binary longitudinal data with time independent covariates summary this paper considers extensions of logistic regression to the case where the binary outcome variable is observed repeatedly for each subject we propose two working models that lead to consistent estimates of the regression parameters and of their variances under mild assumptions about the time dependence within each subject s data the efficiency of the proposed estimators is examined an analysis of stress in mothers with infants is presented to illustrate the proposed method

jointly optimal receivers for the optical pulse position modulation channel jointly optimal receivers that make decisions in the absence of symbol synchronization are derived and analyzed for a pulse position modulation optical direct detection channel both receivers that observe the complete sample path count record data and receivers that observe histogram data are studied and approximations to them are derived it is seen that jointly optimal receivers are superior to conventional receivers that have separately designed synchronization and decision subsystems however their performance advantage is significant only at very low signal levels perhaps more significant is that an approximation to the jointly optimal receivers that is much easier to implement than an optimal separately synchronized receiver achieves nearly the same performance as the latter simulation results indicate that the much less complicated receivers that observe histogram data perform as well as receivers that observe the complete sample path at a rather small number of bins per slot

window subsampling of estimating functions with application to regression models abstract we propose a subsampling method for estimating the asymptotic standard error of a statistic n that is the solution to an estimating equation 1 n n j 1 uj y j xj 0 where the data yj may be temporally or spatially correlated and the estimating function may depend on covariates xj a key statistic that we consider in detail is a generalized linear model regression coefficient computed under the assumption of independence the availability of a consistent variance estimator allows semiparametric regression approaches for clustered and longitudinal data to be used with time series and spatial data the methods that we develop extend the subsampling ideas of carlstein sherman and garcia soidan and hall to estimating functions our approach provides an attractive alternative to the jackknife method of lele particularly for large datasets because we do not require parameter reestimation

statistical inference for max stable processes in space and time max stable processes have proved to be useful for the statistical modelling of spatial extremes several families of max stable random fields have been proposed in the literature one such representation is based on a limit of normalized and rescaled pointwise maxima of stationary gaussian processes that was first introduced by kabluchko and co workers this paper deals with statistical inference for max stable space time processes that are defined in an analogous fashion we describe pairwise likelihood estimation where the pairwise density of the process is used to estimate the model parameters for regular grid observations we prove strong consistency and asymptotic normality of the parameter estimates as the joint number of spatial locations and time points tends to furthermore we discuss extensions to irregularly spaced locations a simulation study shows that the method proposed works well for these models

weighted pseudolikelihood for snp set analysis with multiple secondary outcomes in case control genetic association studies we propose a weighted pseudolikelihood method for analyzing the association of a snp set example snps in a gene or a genetic pathway or network with multiple secondary phenotypes in case control genetic association studies to boost analysis power we assume that the snp specific effects are shared across all secondary phenotypes using a scaled mean model we estimate regression parameters using inverse probability weighted ipw estimating equations obtained from the weighted pseudolikelihood which accounts for case control sampling to prevent potential ascertainment bias to test the effect of a snp set we propose a weighted variance component pseudo score test we also propose a penalized ipw pseudolikelihood method for selecting a subset of snps that are associated with the multiple secondary phenotypes we show that the proposed variable selection procedure has the oracle properties and is robust to misspecification of the correlation structure among secondary phenotypes we select the tuning parameter using a weighted bayesian information like criterion wbic we evaluate the finite sample performance of the proposed methods via simulations and illustrate the methods by the analysis of the multiple secondary smoking behavior outcomes in a lung cancer case control genetic association study

weighted average importance sampling and defensive mixture distributions importance sampling uses observations from one distribution to estimate for another distribution by weighting the observations including the target distribution as one component of a mixture distribution bounds the weights and makes importance sampling more reliable the usual importance sampling estimate is a weighted average with weights that do not sum to 1 we discuss simple normalization and other more efficient normalization methods these innovations make importance sampling useful in a wider variety of problems we demonstrate with a case study of oil inventory reliability at a large utility

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

stopping time resampling for sequential monte carlo methods summary motivated by the statistical inference problem in population genetics we present a new sequential importance sampling with resampling strategy the idea of resampling is key to the recent surge of popularity of sequential monte carlo methods in the statistics and engineering communities but existing resampling techniques do not work well for coalescent based inference problems in population genetics we develop a new method called stopping time resampling which allows us to compare partially simulated samples at different stages to terminate unpromising partial samples and to multiply promising samples early on to illustrate the idea we first apply the new method to approximate the solution of a dirichlet problem and the likelihood function of a non markovian process then we focus on its application in population genetics all our examples show that the new resampling method can significantly improve the computational efficiency of existing sequential importance sampling methods

a bivariate pseudolikelihood for incomplete longitudinal binary data with nonignorable nonmonotone missingness for analyzing longitudinal binary data with nonignorable and non monotone missing responses a full likelihood method is complicated algebraically and often requires intensive computation especially when there are many follow up times as an alternative a pseudo likelihood approach has been proposed in the literature under minimal parametric assumptions this formulation only requires specification of the marginal distributions of the responses and missing data mechanism and uses an independence working assumption however this estimator can be inefficient for estimating both time varying and time stationary effects under moderate to strong within subject associations among repeated responses in this article we propose an alternative estimator based on a bivariate pseudo likelihood and demonstrate in simulations that the proposed method can be much more efficient than the previous pseudo likelihood obtained under the assumption of independence we illustrate the method using longitudinal data on cd4 counts from two clinical trials of hiv infected patients

infinitesimal robustness for diffusions we develop infinitesimally robust statistical procedures for the general diffusion processes we first prove the existence and uniqueness of the times series influence function of conditionally unbiased m estimators for ergodic and stationary diffusions under weak conditions on the martingale estimating function used we then characterize the robustness of m estimators for diffusions and derive a class of conditionally unbiased optimal robust estimators to compute these estimators we propose a general algorithm which exploits approximation methods for diffusions in the computation of the robust estimating function monte carlo simulation shows a good performance of our robust estimators and an application to the robust estimation of the exchange rate dynamics within a target zone illustrates the methodology in a real data application

a reliable data based bandwidth selection method for kernel density estimation we present a new method for data based selection of the bandwidth in kernel density estimation which has excellent properties it improves on a recent procedure of park and marron which itself is a good method in various ways first the new method has superior theoretical performance second it also has a computational advantage third the new method has reliably good performance for smooth densities in simulations performance that is second to none in the existing literature these methods are based on choosing the bandwidth to approximately minimize good quality estimates of the mean integrated squared error the key to the success of the current procedure is the reintroduction of a non stochastic term which was previously omitted together with use of the bandwidth to reduce bias in estimation without inflating variance

semiparametric dynamic max copula model for multivariate time series summary the paper presents a novel non linear framework for the construction of flexible multivariate dependence structure i e copulas from existing copulas based on a straightforward pairwise max rule the newly constructed max copula has a closed form and has strong interpretability compared with the classical linear symmetric mixture copula the max copula can be viewed as a non linear asymmetric framework it is capable of modelling asymmetric dependence and joint tail behaviour while also offering good performance in non extremal behaviour modelling max copulas that are based on single factor and block factor models are developed to offer parsimonious modelling for structured dependence especially in high dimensional applications combined with semiparametric time series models the max copula can be used to develop flexible and accurate models for multivariate time series a new semiparametric composite maximum likelihood method is proposed for parameter estimation where the consistency and asymptotic normality of estimators are established the flexibility of the max copula and the accuracy of the proposed estimation procedure are illustrated through extensive numerical experiments real data applications in value at risk estimation and portfolio optimization for financial risk management demonstrate the max copula s promising ability to capture accurately joint movements of high dimensional multivariate stock returns under both normal and crisis regimes of the financial market

the weak ekeland variational principle and fixed points abstract we use the weak ekeland variational principle to obtain a new proof of an improved version of the nadler fixed point theorem for set valued mappings given by dontchev and hager 1994 separately we apply the fixed point theorem to obtain an unconventional existence result for differential inclusions

pairwise likelihood ratio tests and model selection criteria for structural equation models with ordinal variables correlated multivariate ordinal data can be analysed with structural equation models parameter estimation has been tackled in the literature using limited information methods including three stage least squares and pseudo likelihood estimation methods such as pairwise maximum likelihood estimation in this paper two likelihood ratio test statistics and their asymptotic distributions are derived for testing overall goodness of fit and nested models respectively under the estimation framework of pairwise maximum likelihood estimation simulation results show a satisfactory performance of type i error and power for the proposed test statistics and also suggest that the performance of the proposed test statistics is similar to that of the test statistics derived under the three stage diagonally weighted and unweighted least squares furthermore the corresponding under the pairwise framework model selection criteria aic and bic show satisfactory results in selecting the right model in our simulation examples the derivation of the likelihood ratio test statistics and model selection criteria under the pairwise framework together with pairwise estimation provide a flexible framework for fitting and testing structural equation models for ordinal as well as for other types of data the test statistics derived and the model selection criteria are used on data on trust in the police selected from the 2010 european social survey the proposed test statistics and the model selection criteria have been implemented in the r package lavaan

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

a note on pseudolikelihood constructed from marginal densities for likelihood based inference involving distributions in which high dimensional dependencies are present it may be useful to use approximate likelihoods based for example on the univariate or bivariate marginal distributions the asymptotic properties of formal maximum likelihood estimators in such cases are outlined in particular applications in which only a single q x i vector of observations is observed are examined conditions under which consistent estimators of parameters result from the approximate likelihood using only pairwise joint distributions are studied some examples are analysed in detail

bayesian variable selection for high dimensional generalized linear models convergence rates of the fitted densities bayesian variable selection has gained much empirical success recently in a variety of applications when the number k of explanatory variables x 1 ldots x k is possibly much larger than the sample size n for generalized linear models if most of the x j s have very small effects on the response y we show that it is possible to use bayesian variable selection to reduce overfitting caused by the curse of dimensionality k gg n in this approach a suitable prior can be used to choose a few out of the many x j s to model y so that the posterior will propose probability densities p that are often close to the true density p in some sense the closeness can be described by a hellinger distance between p and p that scales at a power very close to n 1 2 which is the finite dimensional rate corresponding to a low dimensional situation these findings extend some recent work of jiang technical report 05 02 2005 dept statistics northwestern univ on consistency of bayesian variable selection for binary classification

fully exponential laplace approximations to expectations and variances of nonpositive functions abstract tierney and kadane 1986 presented a simple second order approximation for posterior expectations of positive functions they used laplace s method for asymptotic evaluation of integrals in which the integrand is written as f exp nh and the function h is approximated by a quadratic the form in which they applied laplace s method however was fully exponential the integrand was written instead as exp nh log f this allowed first order approximations to be used in the numerator and denominator of a ratio of integrals to produce a second order expansion for the ratio other second order expansions hartigan 1965 johnson 1970 lindley 1961 1980 mosteller and wallace 1964 require computation of more derivatives of the log likelihood function in this article we extend the fully exponential method to apply to expectations and variances of nonpositive functions to obtain a second order approximation to an expectation e g we use the fully exponential method to approximate

annealing markov chain monte carlo with applications to ancestral inference abstract markov chain monte carlo mcmc the metropolis hastings algorithm has been used for many statistical problems including bayesian inference likelihood inference and tests of significance though the method generally works well doubts about convergence often remain here we propose mcmc methods distantly related to simulated annealing our samplers mix rapidly enough to be usable for problems in which other methods would require eons of computing time they simulate realizations from a sequence of distributions allowing the distribution being simulated to vary randomly over time if the sequence of distributions is well chosen then the sampler will mix well and produce accurate answers for all the distributions even when there is only one distribution of interest these annealing like samplers may be the only known way to get a rapidly mixing sampler these methods are essential for attacking very hard problems which arise in areas such as statistical genetics we illustrate the methods wi

rejection control and sequential importance sampling abstract we discuss ways of combining rejection sampling and importance sampling methods in monte carlo computations and demonstrate their usefulness in updating dynamic systems specifically we propose the rejection controlled sequential importance sampling rc sis algorithm which is designed to simultaneously reduce monte carlo variation and retain independent samples in sequential importance sampling the proposed method is demonstrated by three examples taken from econometrics hierarchical bayes analysis and digital telecommunications they all show significant improvements over previous results

conditional logistic regression models for correlated binary data summary a class of conditional logistic regression models for clustered binary data is considered this includes the polychotomous logistic model of rosner 1984 as a special case properties such as the joint distribution and pairwise odds ratio are investigated a class of easily computed estimating functions is introduced which is shown to have high efficiency compared to the computationally intensive maximum likelihood approach an example on chronic obstructive pulmonary disease among sibs is presented for illustration

consistent model selection and data driven smooth tests for longitudinal data in the estimating equations approach summary model selection for marginal regression analysis of longitudinal data is challenging owing to the presence of correlation and the difficulty of specifying the full likelihood particularly for correlated categorical data the paper introduces a novel bayesian information criterion type model selection procedure based on the quadratic inference function which does not require the full likelihood or quasi likelihood with probability approaching 1 the criterion selects the most parsimonious correct model although a working correlation matrix is assumed there is no need to estimate the nuisance parameters in the working correlation matrix moreover the model selection procedure is robust against the misspecification of the working correlation matrix the criterion proposed can also be used to construct a data driven neyman smooth test for checking the goodness of fit of a postulated model this test is especially useful and often yields much higher power in situations where the classical directional test behaves poorly the finite sample performance of the model selection and model checking procedures is demonstrated through monte carlo studies and analysis of a clinical trial data set

pairwise likelihood inference for nested hidden markov chain models for multilevel longitudinal data in the context of multilevel longitudinal data where sample units are collected in clusters an important aspect that should be accounted for is the unobserved heterogeneity between sample units and between clusters for this aim we propose an approach based on nested hidden latent markov chains which are associated with every sample unit and with every cluster the approach allows us to account for the previously mentioned forms of unobserved heterogeneity in a dynamic fashion it also allows us to account for the correlation that may arise between the responses provided by the units belonging to the same cluster under the assumed model computing the manifest distribution of these response variables is infeasible even with a few units per cluster therefore we make inference on this model through a composite likelihood function based on all the possible pairs of subjects within each cluster properties of the composite likelihood estimator are assessed by simulation the proposed approach is illu

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

asymptotic normality of the maximum pseudolikelihood estimator for fully visible boltzmann machines boltzmann machines bms are a class of binary neural networks for which there have been numerous proposed methods of estimation recently it has been shown that in the fully visible case of the bm the method of maximum pseudolikelihood estimation mple results in parameter estimates which are consistent in the probabilistic sense in this brief we investigate the properties of mple for the fully visible bms further and prove that mple also yields an asymptotically normal parameter estimator these results can be used to construct confidence intervals and to test statistical hypotheses these constructions provide a closed form alternative to the current methods that require monte carlo simulation or resampling we support our theoretical results by showing that the estimator behaves as expected in simulation studies