variation in baseline risk as an explanation of heterogeneity in meta analysis a relationship of baseline risk to treatment effect size has been suggested as a possible explanation of between study heterogeneity in meta analyses to address this question we develop regression models to examine the relationship between the logits or other response measure in the intervention and control groups a weighted least squares wls approach is described that allows for the heterogeneous sampling variation in the two groups together with a correction of the coefficients for sampling error two approximate maximum likelihood ml solutions are also obtained with or without an assumption of equal variances between groups within studies a closed form ml solution exists with the assumption of equal variances both methods appear preferable to a previously suggested regression model of the log odds ratio on the control event rate the methods proposed here use the same scale of measurement for both study groups and eliminate an artifactual correlation in the regression error structure the ml approach may be preferable because of its symmetric treatment of study groups but wls is more easily implemented with standard software the methods are illustrated with data from meta analyses on pre term delivery and on therapies to lower serum cholesterol

bayesian random effects meta analysis of trials with binary outcomes methods for the absolute risk difference and relative risk scales when conducting a meta analysis of clinical trials with binary outcomes a normal approximation for the summary treatment effect measure in each trial is inappropriate in the common situation where some of the trials in the meta analysis are small or the observed risks are close to 0 or 1 this problem can be avoided by making direct use of the binomial distribution within trials a fully bayesian method has already been developed for random effects meta analysis on the log odds scale using the bugs implementation of gibbs sampling in this paper we demonstrate how this method can be extended to perform analyses on both the absolute and relative risk scales within each approach we exemplify how trial level covariates including underlying risk can be considered data from 46 trials of the effect of single dose ibuprofen on post operative pain are analysed and the results contrasted with those derived from classical and bayesian summary statistic methods the clinical interpretation of the odds ratio scale is not straightforward the advantages and flexibility of a fully bayesian approach to meta analysis of binary outcome data considered on an absolute risk or relative risk scale are now available

baseline risk as predictor of treatment benefit three clinical meta re analyses a relationship between baseline risk and treatment effect is increasingly investigated as a possible explanation of between study heterogeneity in clinical trial meta analysis an approach that is still often applied in the medical literature is to plot the estimated treatment effects against the estimated measures of risk in the control groups as a measure of baseline risk and to compute the ordinary weighted least squares regression line however it has been pointed out by several authors that this approach can be seriously flawed the main problem is that the observed treatment effect and baseline risk measures should be viewed as estimates rather than the true values in recent years several methods have been proposed in the statistical literature to potentially deal with the measurement errors in the estimates in this article we propose a vague priors bayesian solution to the problem which can be carried out using the bayesian inference using gibbs sampling bugs implementation of markov chain monte carlo numerical integration techniques different from other proposed methods it uses the exact rather than an approximate likelihood while it can handle many different treatment effect measures and baseline risk measures the method differs from a recently proposed bayesian method in that it explicitly models the distribution of the underlying baseline risks we apply the method to three meta analyses published in the medical literature and compare the results with the outcomes of the other recently proposed methods in particular we compare our approach to mcintosh s method for which we show how it can be carried out using standard statistical software we conclude that our proposed method offers a very general and flexible solution to the problem which can be carried out relatively easily with existing bayesian analysis software a confidence band for the underlying relationship between true effect measure and baseline risk and a confidence interval for the value of the baseline risk measure for which there is no treatment effect are easily obtained by products of our approach

reference bayesian methods for generalized linear mixed models abstract bayesian methods furnish an attractive approach to inference in generalized linear mixed models in the absence of subjective prior information for the random effect variance components these analyses are typically conducted using either the standard invariant prior for normal responses or diffuse conjugate priors previous work has pointed out serious difficulties with both strategies and we show here that as in normal mixed models the standard invariant prior leads to an improper posterior distribution for generalized linear mixed models this article proposes and investigates two alternative reference i e objective or noninformative priors an approximate uniform shrinkage prior and an approximate jeffreys s prior we give conditions for the existence of the posterior distribution under any prior for the variance components in conjunction with a uniform prior for the fixed effects the approximate uniform shrinkage prior is shown to satisfy these conditions for several families of d

a note on n estimators for the binomial distribution abstract consider k success counts from a binomial distribution with unknown n and success probability p we examine the problem of estimating n by integrating the likelihood for n and p over a beta density for p we obtain the beta binomial distribution resulting in stable and reasonably efficient estimators of n which compare favorably with and are often better than the estimates introduced by olkin et al 1981

gibbs sampling methods for stick breaking priors a rich and flexible class of random probability measures which we call stick breaking priors can be constructed using a sequence of independent beta random variables examples of random measures that have this characterization include the dirichlet process its two parameter extension the two parameter poisson dirichlet process finite dimensional dirichlet priors and beta two parameter processes the rich nature of stick breaking priors offers bayesians a useful class of priors for nonparametric problems while the similar construction used in each prior can be exploited to develop a general computational procedure for fitting them in this article we present two general types of gibbs samplers that can be used to fit posteriors of bayesian hierarchical models based on stick breaking priors the first type of gibbs sampler referred to as a polya urn gibbs sampler is a generalized version of a widely used gibbs sampling method currently employed for dirichlet process computing this method applies t

incorporating variability in estimates of heterogeneity in the random effects model in meta analysis when combining results from separate investigations in a meta analysis random effects methods enable the modelling of differences between studies by incorporating a heterogeneity parameter tau 2 that accounts explicitly for across study variation we develop a simple form for the variance of cochran s homogeneity statistic q leading to interval estimation of tau 2 utilizing an approximating distribution for q this enables us to extend the point estimation of dersimonian and laird we also develop asymptotic likelihood methods and compared them with this method we then use these approximating distributions to give a new method of calculating the weight given to the individual studies results when estimating the overall mean which takes into account variation in these point estimates of tau 2 two examples illustrate the methods presented where we show that the new weighting scheme is between the standard fixed and random effects models in down weighting the results of large studies and up weighting those of small studies

robustifying bayesian nonparametric mixtures for count data our motivating application stems from surveys of natural populations and is characterized by large spatial heterogeneity in the counts which makes parametric approaches to modeling local animal abundance too restrictive we adopt a bayesian nonparametric approach based on mixture models and innovate with respect to popular dirichlet process mixture of poisson kernels by increasing the model flexibility at the level both of the kernel and the nonparametric mixing measure this allows to derive accurate and robust estimates of the distribution of local animal abundance and of the corresponding clusters the application and a simulation study for different scenarios yield also some general methodological implications adding flexibility solely at the level of the mixing measure does not improve inferences since its impact is severely limited by the rigidity of the poisson kernel with considerable consequences in terms of bias however once a kernel more flexible than the poisson is chosen inferences can be robustified by choosing a prior more general than the dirichlet process therefore to improve the performance of bayesian nonparametric mixtures for count data one has to enrich the model simultaneously at both levels the kernel and the mixing measure

bayesian kernel mixtures for counts although bayesian nonparametric mixture models for continuous data are well developed the literature on related approaches for count data is limited a common strategy is to use a mixture of poissons which unfortunately is quite restrictive in not accounting for distributions with variance less than the mean other approaches include mixing multinomials which requires finite support and using a dirichlet process prior with a poisson base measure which does not allow for smooth deviations from the poisson we propose broad class of alternative models nonparametric mixtures of rounded continuous kernels we develop an efficient gibbs sampler for posterior computation and perform a simulation study to assess performance focusing on the rounded gaussian case we generalize the modeling framework to account for multivariate count data joint modeling with continuous and categorical variables and other complications we illustrate our methods through applications to a developmental toxicity study and m

bayesian semiparametric regression in the presence of conditionally heteroscedastic measurement and regression errors summary we consider the problem of robust estimation of the regression relationship between a response and a covariate based on sample in which precise measurements on the covariate are not available but error prone surrogates for the unobserved covariate are available for each sampled unit existing methods often make restrictive and unrealistic assumptions about the density of the covariate and the densities of the regression and the measurement errors for example normality and for the latter two also homoscedasticity and thus independence from the covariate in this article we describe bayesian semiparametric methodology based on mixtures of b splines and mixtures induced by dirichlet processes that relaxes these restrictive assumptions in particular our models for the aforementioned densities adapt to asymmetry heavy tails and multimodality the models for the densities of regression and measurement errors also accommodate conditional heteroscedasticity in simulation experiments our method vastly outperforms existing methods we apply our method to data from nutritional epidemiology

frequentist performance of bayesian confidence intervals for comparing proportions in 2 2 contingency tables this article investigates the performance in a frequentist sense of bayesian confidence intervals cis for the difference of proportions relative risk and odds ratio in 2 x 2 contingency tables we consider beta priors logit normal priors and related correlated priors for the two binomial parameters the goal was to analyze whether certain settings for prior parameters tend to provide good coverage performance regardless of the true association parameter values for the relative risk and odds ratio we recommend tail intervals over highest posterior density hpd intervals for invariance reasons to protect against potentially very poor coverage probabilities when the effect is large it is best to use a diffuse prior and we recommend the jeffreys prior otherwise with relatively small samples bayesian cis using more informative even uniform priors tend to have poorer performance than the frequentist cis based on inverting score tests which perform uniformly quite well for these parameters

estimating the number of classes in a finite population abstract we use an extension of the generalized jackknife approach of gray and schucany to obtain new nonparametric estimators for the number of classes in a finite population of known size we also show that generalized jackknife estimators are closely related to certain horvitz thompson estimators to an estimator of shlosser and to estimators based on sample coverage in particular the generalized jackknife approach leads to a modification of shlosser s estimator that does not suffer from the erratic behavior of the original estimator the performance of both new and previous estimators is investigated by means of an asymptotic variance analysis and a monte carlo simulation study

a unified parametric regression model for recapture studies with random removals in continuous time nous combinons la vraisemblance conditionnelle dans des processus de comptage avec l estimateur de horvitz thompson pour obtenir un estimateur de la taille de la population plus efficient que les estimateurs existants des suppressions aleatoires peuvent etre introduites dans le processus de recapture on presente des etudes de simulation pour determiner la performance des estimateurs proposes on donne des exemples sur une repartition d oiseaux et une petite etude de recapture de mammiferes

inference in components of variance models with low replication in components of variance models the data are viewed as arising through a sum of two random variables representing between and within group variation respectively the former is generally interpreted as a group effect and the latter as error it is assumed that these variables are stochastically independent and that the distributions of the group effect and the error do not vary from one instance to another if each group effect can be replicated a large number of times then standard methods can be used to estimate the distributions of both the group effect and the error this cannot be achieved without replication however how feasible is distribution estimation if it is not possible to replicate prolifically can the distributions of random effects and errors be estimated consistently from a small number of replications of each of a large number of noisy group effects for example in a nonparametric setting often extensive replication is practically infeasible in particular if inherently small numbers of individuals exhibit any given group effect yet it is quite unclear how to conduct inference in this case we show that inference is possible even if the number of replications is as small as 2 two methods are proposed both based on fourier inversion one which is substantially more computer intensive than the other exhibits better performance in numerical experiments

nonparametric prediction in measurement error models predicting the value of a variable y corresponding to a future value of an explanatory variable x based on a sample of previously observed independent data pairs x1 y1 xn yn distributed like x y is very important in statistics in the error free case where x is observed accurately this problem is strongly related to that of standard regression estimation since prediction of y can be achieved via estimation of the regression curve e y x when the observed xis and the future observation of x are measured with error prediction is of a quite different nature here if t denotes the future contaminated available version of x prediction of y can be achieved via estimation of e y t in practice estimating e y t can be quite challenging as data may be collected under different conditions making the measurement errors on xi and x nonidentically distributed we take up this problem in the nonparametric setting and introduce estimators which allow a highly adaptive approach to smoothing

estimation of an errors in variables regression model when the variances of the measurement errors vary between the observations it is common in the analysis of aggregate data in epidemiology that the variances of the aggregate observations are available the analysis of such data leads to a measurement error situation where the known variances of the measurement errors vary between the observations assuming multivariate normal distribution for the true observations and normal distributions for the measurement errors we derive a simple em algorithm for obtaining maximum likelihood estimates of the parameters of the multivariate normal distributions the results also facilitate the estimation of regression parameters between the variables as well as the true values of the observations the approach is applied to re estimate recent results of the who monica project on cardiovascular disease and its risk factors where the original estimation of the regression coefficients did not adjust for the regression attenuation caused by the measurement errors

nonparametric regression estimation in the heteroscedastic errors in variables problem in the classical errors in variables problem the goal is to estimate a regression curve from data in which the explanatory variable is measured with error in this context nonparametric methods have been proposed that rely on the assumption that the measurement errors are identically distributed although there are many situations in which this assumption is too restrictive nonparametric estimators in the more realistic setting of heteroscedastic errors have not been studied in the literature we propose an estimator of the regression function in such a setting and show that it is optimal we give estimators in cases in which the error distributions are unknown and replicated observations are available practical methods including an adaptive bandwidth selector for the errors in variables regression problem are suggested and their finite sample performance is illustrated through simulated and real data examples

parametric regression models for continuous time removal and recapture studies we use a class of parametric counting process regression models that are commonly employed in the analysis of failure time data to formulate the subject specific capture probabilities for removal and recapture studies conducted in continuous time we estimate the regression parameters by modifying the conventional likelihood score function for left truncated and right censored data to accommodate an unknown population size and missing covariates on uncaptured subjects and we subsequently estimate the population size by a martingale based estimating function the resultant estimators for the regression parameters and population size are consistent and asymptotically normal under appropriate regularity conditions we assess the small sample properties of the proposed estimators through monte carlo simulation and we present an application to a bird banding exercise

hypothesis testing in an errors in variables model with heteroscedastic measurement errors in many epidemiological studies it is common to resort to regression models relating incidence of a disease and its risk factors the main goal of this paper is to consider inference on such models with error prone observations and variances of the measurement errors changing across observations we suppose that the observations follow a bivariate normal distribution and the measurement errors are normally distributed aggregate data allow the estimation of the error variances maximum likelihood estimates are computed numerically via the em algorithm consistent estimation of the asymptotic variance of the maximum likelihood estimators is also discussed test statistics are proposed for testing hypotheses of interest further we implement a simple graphical device that enables an assessment of the model s goodness of fit results of simulations concerning the properties of the test statistics are reported the approach is illustrated with data from the who monica project on cardiovascular disease

bayesian bivariate meta analysis of diagnostic test studies using integrated nested laplace approximations for bivariate meta analysis of diagnostic studies likelihood approaches are very popular however they often run into numerical problems with possible non convergence in addition the construction of confidence intervals is controversial bayesian methods based on markov chain monte carlo mcmc sampling could be used but are often difficult to implement and require long running times and diagnostic convergence checks recently a new bayesian deterministic inference approach for latent gaussian models using integrated nested laplace approximations inla has been proposed with this approach mcmc sampling becomes redundant as the posterior marginal distributions are directly and accurately approximated by means of a real data set we investigate the influence of the prior information provided and compare the results obtained by inla mcmc and the maximum likelihood procedure sas proc nlmixed using a simulation study we further extend the comparison of inla and sas proc nlmixed by assessing their performance in terms of bias mean squared error coverage probability and convergence rate the results indicate that inla is more stable and gives generally better coverage probabilities for the pooled estimates and less biased estimates of variance parameters the user friendliness of inla is demonstrated by documented r code

controlling the reinforcement in bayesian non parametric mixture models summary the paper deals with the problem of determining the number of components in a mixture model we take a bayesian non parametric approach and adopt a hierarchical model with a suitable non parametric prior for the latent structure a commonly used model for such a problem is the mixture of dirichlet process model here we replace the dirichlet process with a more general non parametric prior obtained from a generalized gamma process the basic feature of this model is that it yields a partition structure for the latent variables which is of gibbs type this relates to the well known exchangeable product partition models if compared with the usual mixture of dirichlet process model the advantage of the generalization that we are examining relies on the availability of an additional parameter belonging to the interval 0 1 it is shown that such a parameter greatly influences the clustering behaviour of the model a value of that is close to 1 generates a large number of clusters most of which are of small size then a reinforcement mechanism which is driven by acts on the mass allocation by penalizing clusters of small size and favouring those few groups containing a large number of elements these features turn out to be very useful in the context of mixture modelling since it is difficult to specify a priori the reinforcement rate it is reasonable to specify a prior for hence the strength of the reinforcement mechanism is controlled by the data

inadmissibility of the maximum likelihood estimator in the sequential estimation of the size of a population summary for the sequential estimation of the size of a finite population the maximum likelihood estimator is a commonly used estimator but has no explicit expression in this paper it is shown that the maximum likelihood estimator is inadmissible an estimator which is simple in form and dominates the maximum likelihood estimator asymptotically is proposed to study the optimality property of the estimator for the stopping rule sb from a decision theoretical approach we investigate the admissibility of the estimator under a general weighted squared error loss function although the maximum likelihood estimator and its risk have no closed form expression the estimator will be shown to be inadmissible by means of a general theorem that we establish later as theorem 2 1 in this paper we only consider the simple capture capture model discussed by samuel 1968 more complex and realistic capture recapture models have been developed subsequently pollack otto 1983 pickands raghavachari 1987 bonett woodward bentler 1987 cormack 1989 huggins 1989 we conjecture that many of the

combination of direct and indirect evidence in mixed treatment comparisons mixed treatment comparison mtc meta analysis is a generalization of standard pairwise meta analysis for a vs b trials to data structures that include for example a vs b b vs c and a vs c trials there are two roles for mtc one is to strengthen inference concerning the relative efficacy of two treatments by including both direct and indirect comparisons the other is to facilitate simultaneous inference regarding all treatments in order for example to select the best treatment in this paper we present a range of bayesian hierarchical models using the markov chain monte carlo software winbugs these are multivariate random effects models that allow for variation in true treatment effects across trials we consider models where the between trials variance is homogeneous across treatment comparisons as well as heterogeneous variance models we also compare models with fixed unconstrained baseline study effects with models with random baselines drawn from a common distribution these models are applied to an illustrative data set and posterior parameter distributions are compared we discuss model critique and model selection illustrating the role of bayesian deviance analysis and node based model criticism the assumptions underlying the mtc models and their parameterization are also discussed

semi parametric estimation in the nonlinear structural errors in variables model in the nonlinear structural errors in variables model we propose a consistent estimator of the unknown parameter using a modified least squares criterion we give an upper bound of its rate of convergence which is strongly related to the regularity of the regression function and is generally slower than the parametric rate of convergence n 1 2 nevertheless the rate is of order n 1 2 for some particular analytic regression functions for instance when the regression function is either a polynomial function or an exponential function we prove that our estimator achieves the parametric rate of convergence

hierarchical mixture modeling with normalized inverse gaussian priors in recent years the dirichlet process prior has experienced a great success in the context of bayesian mixture modeling the idea of overcoming discreteness of its realizations by exploiting it in hierarchical models combined with the development of suitable sampling techniques represent one of the reasons of its popularity in this article we propose the normalized inverse gaussian n ig process as an alternative to the dirichlet process to be used in bayesian hierarchical models the n ig prior is constructed via its finite dimensional distributions this prior although sharing the discreteness property of the dirichlet prior is characterized by a more elaborate and sensible clustering which makes use of all the information contained in the data whereas in the dirichlet case the mass assigned to each observation depends solely on the number of times that it occurred for the n ig prior the weight of a single observation depends heavily on the whole number of ties in the sample moreover expressio

a poisson model for the coverage problem with a genomic application summary suppose a population has infinitely many individuals and is partitioned into unknown n disjoint classes the sample coverage of a random sample from the population is the total proportion of the classes observed in the sample this paper uses a nonparametric poisson mixture model to give new understanding and results for inference on the sample coverage the poisson mixture model provides a simplified framework for inferring any general abundance f coverage the sum of the proportions of those classes that contribute exactly k individuals in the sample for some k in with being a set of nonnegative integers a new moment based derivation of the well known turing estimators is presented as an application a gene categorisation problem in genomic research is addressed since turing s approach is a moment based method maximum likelihood estimation and minimum distance estimation are indicated as alternatives for the coverage problem finally it will be shown that any turing estimator is asymptotically fully efficient

a semiparametric bayesian model for randomised block designs summary a model is proposed for a bayesian semiparametric analysis of randomised block experiments the model is a hierarchical model in which a dirichlet process is inserted at the middle stage for the distribution of the block effects this model allows an arbitrary distribution of block effects and it results in effective estimates of treatment contrasts block effects and the distribution of block effects an effective computational strategy is presented for describing the posterior distribution

small sample estimation of species richness applied to forest communities summary many well known methods are available for estimating the number of species in a forest community however most existing methods result in considerable negative bias in applications where field surveys typically represent only a small fraction of sampled communities this article develops a new method based on sampling with replacement to estimate species richness via the generalized jackknife procedure the proposed estimator yields small bias and reasonably accurate interval estimation even with small samples the performance of the proposed estimator is compared with several typical estimators via simulation study using two complete census datasets from panama and malaysia

estimating population size by recapture sampling a design called recapture debugging is proposed to get extra information to estimate the original number of faults n in a reliability system the system is observed for a fixed amount of time r and the failures are assumed to follow an exponential law with an unknown common parameter a the maximum likelihood and moment estimators of n and a are derived and compared with the existing estimators the recapture sampling provides substantially more information and improved estimators compared to the standard experiment if r is not small significance tests for testing hypotheses about n and a are developed finally for testing the system one can consider r to be determined sequentially and we present a suitable stopping rule

on estimating linear relationships when both variables are subject to heteroscedastic measurement errors this article discusses point estimation of the parameters in a linear measurement error errors in variables model when the variances in the measurement errors on both axes vary between observations a compendium of existing and new regression methods is presented application of these methods to real data cases shows that the coefficients of the regression lines depend on the method selected guidelines for choosing a suitable regression method are provided

when should one stop testing software abstract we derive an optimal rule for stopping the testing of a module of software prior to release based on the trade off between the cost of continued testing and the expected losses due to any bugs that remain in the released code our economic assumptions are that testing costs are perfectly predictable but of arbitrary form f t and that the costs of fixing a bug both during testing and subsequent to release are known constants our stochastic assumptions are as follows a the total number of bugs in the module n is unknown b n has a poisson distribution with a mean that is distributed randomly across modules according to a known gamma distribution c given a particular bug the time it takes to find it during testing is random with a known distribution g of arbitrary form and d the lifetimes of different bugs are independent with these assumptions we find conditions on f and g that ensure that the optimal stopping rule has a simple form which can be found by a dynamic progr

a random effects regression model for meta analysis many meta analyses use a random effects model to account for heterogeneity among study results beyond the variation associated with fixed effects a random effects regression approach for the synthesis of 2 x 2 tables allows the inclusion of covariates that may explain heterogeneity a simulation study found that the random effects regression method performs well in the context of a meta analysis of the efficacy of a vaccine for the prevention of tuberculosis where certain factors are thought to modify vaccine efficacy a smoothed estimator of the within study variances produced less bias in the estimated regression coefficients the method provided very good power for detecting a non zero intercept term representing overall treatment efficacy but low power for detecting a weak covariate in a meta analysis of 10 studies we illustrate the model by exploring the relationship between vaccine efficacy and one factor thought to modify efficacy the model also applies to the meta analysis of continuous outcomes when covariates are present

a bivariate approach to meta analysis the usual meta analysis of a sequence of randomized clinical trials only considers the difference between two treatments and produces a point estimate and a confidence interval for a parameter that measures this difference the usual parameter is the log odds ratio linked to mantel haenszel methodology inference is made either under the assumption of homogeneity or in a random effects model that takes account of heterogeneity between trials this paper has two goals the first is to present a likelihood based method for the estimation of the parameters in the random effects model which avoids the use of approximating normal distributions the second goal is to extend this method to a bivariate random effects model in which the effects in both groups are supposed random in this way inference can be made about the relationship between improvement and baseline effect the method is demonstrated by a meta analysis dataset of collins and langman

robust estimation of generalized linear models with measurement errors this paper considers consistent estimation of generalized linear models with covariate measurement errors in contrast to the previous approach of assuming that measurement errors are normally distributed we make no distributional assumptions on the latent variables or the measurement errors using the results of li j econometrics 110 2002 1 on the nonparametric identification and estimation of the distribution of the latent variables when replicate measurements are available we propose to maximize the criterion based on an asymptotically corrected likelihood we show that such an estimator is consistent we also evaluate the finite sample performance of our estimator through a monte carlo study

estimating the number of classes via sample coverage abstract assume that a random sample is drawn from a population with unknown number of classes and possibly unequal class probabilities a nonparametric estimation technique is proposed to estimate the number of classes using the idea of sample coverage which is defined as the sum of the cell probabilities of the observed classes since expected sample coverage can be well estimated we were motivated to find its role in the estimation of the number of classes this work generalizes the result of esty to a nonparametric approach and extends darroch and ratcliff to incorporate the heterogeneity of the class probabilities the coefficient of variation of the class sizes is shown to play an important role in the recommended estimation procedures the performance of the proposed estimators is investigated by means of monte carlo simulations

a likelihood based stopping rule for recapture debugging summary consideration is given to determining when all the faults in a reliability system have been detected assuming the use of the recapture debugging procedure introduced by nayak 1988 a stopping rule based on the likelihood ratio is proposed compared to the stopping rule suggested by nayak this likelihood based rule makes better use of the available information and for a given error level yields a small reduction in the average time taken to reach a decision a generalization is suggested for the situation where the faults in the software can be categorized into two or more classes between which detection rates are permitted to differ nayak 1988 presents a modification of the standard jelinski moranda model for the debugging of computer software in recapture debugging a detected error is not only corrected as jelinski moranda 1972 assumed but also a counter is added to note each subsequent occasion on which this area of the software is accessed initially there are n errors present and occurrences of any particular error are assumed to follow a homogeneous poisson process the n poisson processes have a common rate a and the errors are accessed independently of each other one weakness of the standard jelinski moranda model is that the information about n can only be partially disentangled from that about a the model is slow to distinguish between slow detection of a large number of errors and the relatively faster detection of a much smaller number by noting when each detected error would have recurred recapture debugging provides additional information about the rate a and this helps to reduce the effect of this confounding recapture debugging employs in a software reliability context methodology originally derived for estimating the size of animal populations a similar reapplication in the case of capturerecapture methodology is given by duran wiorkowski 1981 who describe a hypergeometric model attributed to an unpublished ibm report by h d mills mills s procedure is to insert deliberately a known number of additional errors called seeded errors into the software estimation of the number of indigenous errors already present then proceeds by using the hypergeometric distribution for the number of seeded errors observed this approach requires the major assumption that the distribution of the detection time for a seeded error is the same as that for an indigenous error recapture debugging avoids this difficulty

explaining heterogeneity in meta analysis a comparison of methods exploring the possible reasons for heterogeneity between studies is an important aspect of conducting a meta analysis this paper compares a number of methods which can be used to investigate whether a particular covariate with a value defined for each study in the meta analysis explains any heterogeneity the main example is from a meta analysis of randomized trials of serum cholesterol reduction in which the log odds ratio for coronary events is related to the average extent of cholesterol reduction achieved in each trial different forms of weighted normal errors regression and random effects logistic regression are compared these analyses quantify the extent to which heterogeneity is explained as well as the effect of cholesterol reduction on the risk of coronary events in a second example the relationship between treatment effect estimates and their precision is examined in order to assess the evidence for publication bias we conclude that methods which allow for an additive component of residual heterogeneity should be used in weighted regression a restricted maximum likelihood estimator is appropriate although a number of other estimators are also available methods which use the original form of the data explicitly for example the binomial model for observed proportions rather than assuming normality of the log odds ratios are now computationally feasible although such methods are preferable in principle they often give similar results in practice

meta analysis for 2 2 tables a bayesian approach this paper develops and implements a fully bayesian approach to meta analysis in which uncertainty about effects in distinct but comparable studies is represented by an exchangeable prior distribution specifically hierarchical normal models are used along with a parametrization that allows a unified approach to deal easily with both clinical trial and case control study data monte carlo methods are used to obtain posterior distributions for parameters of interest integrating out the unknown parameters of the exchangeable prior or random effects distribution the approach is illustrated with two examples the first involving a data set on the effect of beta blockers after myocardial infarction and the second based on a classic data set comprising 14 case control studies on the effects of smoking on lung cancer in both examples rather different conclusions from those previously published are obtained in particular it is claimed that widely used methods for meta analysis which involve complete pooling of o e values lead to understatement of uncertainty in the estimation of overall or typical effect size

slope estimation in structural line segment heteroscedastic measurement error models this paper extends the line segment parametrization of the structural measurement error me model to situations in which the error variance on both variables is not constant over all observations under these conditions we develop a method of moments estimate of the slope and derive its asymptotic variance we further derive an accurate estimator of the variability of the slope estimate based on sample data in a rather general setting we perform simulations that validate our results and demonstrate that our estimates are more precise than estimates under a different model when the me variance is not small finally we illustrate our estimation approach using real data involving heteroscedastic me and compare its performance with that of earlier models

are gibbs type priors the most natural generalization of the dirichlet process discrete random probability measures and the exchangeable random partitions they induce are key tools for addressing a variety of estimation and prediction problems in bayesian inference here we focus on the family of gibbs type priors a recent elegant generalization of the dirichlet and the pitman yor process priors these random probability measures share properties that are appealing both from a theoretical and an applied point of view i they admit an intuitive predictive characterization justifying their use in terms of a precise assumption on the learning mechanism ii they stand out in terms of mathematical tractability iii they include several interesting special cases besides the dirichlet and the pitman yor processes the goal of our paper is to provide a systematic and unified treatment of gibbs type priors and highlight their implications for bayesian nonparametric inference we deal with their distributional properties the resulting estimators frequentist asymptotic validation and the construction of time dependent versions applications mainly concerning mixture models and species sampling serve to convey the main ideas the intuition inherent to this class of priors and the neat results they lead to make one wonder whether it actually represents the most natural generalization of the dirichlet process

estimating the number of species in a stochastic abundance model consider a stochastic abundance model in which the species arrive in the sample according to independent poisson processes where the abundance parameters of the processes follow a gamma distribution we propose a new estimator of the number of species for this model the estimator takes the form of the number of duplicated species i e species represented by two or more individuals divided by an estimated duplication fraction the duplication fraction is estimated from all frequencies including singleton information the new estimator is closely related to the sample coverage estimator presented by chao and lee 1992 journal of the american statistical association 87 210 217 we illustrate the procedure using the malayan butterfly data discussed by fisher corbet and williams 1943 journal of animal ecology 12 42 58 and a 1989 christmas bird count dataset collected in florida u s a simulation studies show that this estimator compares well with maximum likelihood estimators i e empirical bayes estimators from the bayesian viewpoint for which an iterative numerical procedure is needed and may be infeasible

a chain of evidence with mixed comparisons models for multi parameter synthesis and consistency of evidence multi parameter evidence synthesis is a generalization of meta analysis in which several parameters are estimated jointly here this approach is applied to a common form of data structure in which mixed pairwise comparisons are made between treatments in a chain of evidence structure the data set investigated here which first appeared in the confidence profile method literature features three types of data relating to thrombolytic treatment following acute myocardial infarction there is information on reperfusion coronary patency following treatment information on survival in reperfused and non reperfused patients conditional survival and independent information on the effect of treatment on survival without specifying reperfusion state overall survival the objective of this study is to explore models for combining these three types of evidence within a single model and some of the evidence consistency issues that arise bayesian markov chain monte carlo methods are used to fit two models the first proposed in the confidence profile literature assumes there are no differences between studies in baseline effects equal study effects the second model assumes fixed treatment effects but allows for study differences in baseline reperfusion and conditional survival rates by assuming random study effects the equal study effects model fits the data poorly and cross validation shows that the overall survival evidence is not consistent with the reperfusion and conditional survival evidence under this model the evidence appears to be consistent within the more loosely structured random study effects model but results are sensitive to prior assumptions about the between study variance the inconsistency between the three evidence types relates to overall survival rather than to the effect of treatment on survival multi parameter evidence synthesis with suitable checks for evidence consistency can be used to help determine whether chains of evidence add up epidemiologically within an overall model and to construct parameter distributions for an entire model simultaneously consistent with all the available data

issues in the selection of a summary statistic for meta analysis of clinical trials with binary outcomes meta analysis of binary data involves the computation of a weighted average of summary statistics calculated for each trial the selection of the appropriate summary statistic is a subject of debate due to conflicts in the relative importance of mathematical properties and the ability to intuitively interpret results this paper explores the process of identifying a summary statistic most likely to be consistent across trials when there is variation in control group event rates four summary statistics are considered odds ratios or risk differences rd and risk ratios of beneficial rr b and harmful outcomes rr h each summary statistic corresponds to a different pattern of predicted absolute benefit of treatment with variation in baseline risk the greatest difference in patterns of prediction being between rr b and rr h selection of a summary statistic solely based on identification of the best fitting model by comparing tests of heterogeneity is problematic principally due to low numbers of trials it is proposed that choice of a summary statistic should be guided by both empirical evidence and clinically informed debate as to which model is likely to be closest to the expected pattern of treatment benefit across baseline risks empirical investigations comparing the four summary statistics on a sample of 551 systematic reviews provide evidence that the rr and or models are on average more consistent than rd there being no difference on average between rr and or from a second sample of 114 meta analyses evidence indicates that for interventions aimed at preventing an undesirable event greatest absolute benefits are observed in trials with the highest baseline event rates corresponding to the model of constant rr h the appropriate selection for a particular meta analysis may depend on understanding reasons for variation in control group event rates in some situations uncertainty about the choice of summary statistic will remain

modeling unobserved sources of heterogeneity in animal abundance using a dirichlet process prior in surveys of natural populations of animals a sampling protocol is often spatially replicated to collect a representative sample of the population in these surveys differences in abundance of animals among sample locations may induce spatial heterogeneity in the counts associated with a particular sampling protocol for some species the sources of heterogeneity in abundance may be unknown or unmeasurable leading one to specify the variation in abundance among sample locations stochastically however choosing a parametric model for the distribution of unmeasured heterogeneity is potentially subject to error and can have profound effects on predictions of abundance at unsampled locations in this article we develop an alternative approach wherein a dirichlet process prior is assumed for the distribution of latent abundances this approach allows for uncertainty in model specification and for natural clustering in the distribution of abundances in a data adaptive way we apply this approach in an analysis of counts based on removal samples of an endangered fish species the okaloosa darter results of our data analysis and simulation studies suggest that our implementation of the dirichlet process prior has several attractive features not shared by conventional fully parametric alternatives

estimating the number of faults in a system abstract we consider a reliability system with an unknown number of faults which is observed for a fixed length of time failures are assumed to follow an exponential distribution with an unknown mean and we concentrate on estimation of the number of faults v the likelihood function considered as a function of v has its maximum at one of the boundary points the observed number of faults or infinity with substantial probability likelihood interval estimates and improved point estimates are discussed the harmonic mean of the endpoints of the likelihood interval turns out to be a reasonable point estimate we comment on some extensions of this problem suggested in the software reliability literature

the two parameter poisson dirichlet distribution derived from a stable subordinator the two parameter poisson dirichlet distribution denoted mathsf pd alpha theta is a probability distribution on the set of decreasing positive sequences with sum 1 the usual poisson dirichlet distribution with a single parameter theta introduced by kingman is mathsf pd 0 theta known properties of mathsf pd 0 theta including the markov chain description due to vershik shmidt and ignatov are generalized to the two parameter case the size biased random permutation of mathsf pd alpha theta is a simple residual allocation model proposed by engen in the context of species diversity and rediscovered by perman and the authors in the study of excursions of brownian motion and bessel processes for 0 alpha 1 mathsf pd alpha 0 is the asymptotic distribution of ranked lengths of excursions of a markov chain away from a state whose recurrence time distribution is in the domain of attraction of a stable law of index alpha formulae in this case trace back to work of darling lamperti and wendel in the 1950s and 1960s the distribution of ranked lengths of excursions of a one dimensional brownian motion is mathsf pd 1 2 0 and the corresponding distribution for a brownian bredge is mathsf pd 1 2 1 2 the mathsf pd alpha 0 and mathsf pd alpha alpha distributions admit a similar interpretation in terms of the ranked lengths of excursions of a semistable markov process whose zero set is the range of a stable subordinator of index alpha

bayesian density estimation and inference using mixtures abstract we describe and illustrate bayesian inference in models for density estimation using mixtures of dirichlet processes these models provide natural settings for density estimation and are exemplified by special cases where data are modeled as a sample from mixtures of normal distributions efficient simulation methods are used to approximate various prior posterior and predictive distributions this allows for direct inference on a variety of practical issues including problems of local versus global smoothing uncertainty about density estimates assessment of modality and the inference on the numbers of components also convergence results are established for a general class of normal mixture models

simulation extrapolation the measurement error jackknife abstract this article provides theoretical support for our simulation based estimation procedure simex for measurement error models we do so by establishing a strong relationship between simex estimation and jackknife estimation a result of our investigation is the identification of a variance estimation method for simex that parallels jackknife variance estimation data from the framingham heart study are used to illustrate the variance estimation procedure in logistic regression measurement error models

analysis of overdispersed count data by mixtures of poisson variables and poisson processes count data often show overdispersion compared to the poisson distribution overdispersion is typically modeled by a random effect for the mean based on the gamma distribution leading to the negative binomial distribution for the count this paper considers a larger family of mixture distributions including the inverse gaussian mixture distribution it is demonstrated that it gives a significantly better fit for a data set on the frequency of epileptic seizures the same approach can be used to generate counting processes from poisson processes where the rate or the time is random a random rate corresponds to variation between patients whereas a random time corresponds to variation within patients

bayesian nonparametric estimation of the probability of discovering new species summary we consider the problem of evaluating the probability of discovering a certain number of new species in a new sample of population units conditional on the number of species recorded in a basic sample we use a bayesian nonparametric approach the different species proportions are assumed to be random and the observations from the population exchangeable we provide a bayesian estimator under quadratic loss for the probability of discovering new species which can be compared with well known frequentist estimators the results we obtain are illustrated through a numerical example and an application to a genomic dataset concerning the discovery of new genes by sequencing additional single read sequences of cdna fragments

initial size estimation for the linear pure death process summary consider a linear pure death process in which the common death rate and the initial size n of the population are both unknown an estimate of n is required based on the observed times of the firstj deaths i e with censored sampling it is shown that the only reliable non bayesian method is to use interval estimates for all the standard point estimation techniques are liable to fail appropriate interval estimators are derived and discussed the corresponding truncated sampling model is briefly considered the linear pure death process may be characterized as representing a dying population in which the lifetimes are independently and identically distributed each with probability density ae t t 0 for some a 0 we assume that both the initial population size n and the rate parameter a are unknown and our aim is to estimate n for many years work on the estimation of population size such as by johnson 1962 hoel 1968 and marcus blumenthal 1974 assumed a lifetime distribution which was general but completely specified recently interest has been shown in lifetime distributions with unknown parameters in particular in papers by sanathanan 1977 who gives asymptotic results for maximum likelihood estimation and blumenthal marcus 1975 who consider precisely the above problem we consider mainly the censored sampling model under which an estimate of n is required immediately after the jth death where j is a preassigned integer known not to exceed n in 2 we derive an invariantly sufficient statistic and its distribution in 3 we discuss point estimation of n unbiased estimators do not exist while the methods of moments and of maximum likelihood are both liable to fail in that there is positive probability sometimes close to 2 that the equation for the estimator has no finite solution in 4 we derive an interval estimator and discuss its properties while an interval estimate is always available it is in some circumstances quite vague this brings out clearly that for the present problem it is more than usually inadvisable to rely on point

assessing evidence inconsistency in mixed treatment comparisons randomized comparisons among several treatments give rise to an incomplete blocks structure known as mixed treatment comparisons mtcs to analyze such data structures it is crucial to assess whether the disparate evidence sources provide consistent information about the treatment contrasts in this article we propose a general method for assessing evidence inconsistency in the framework of bayesian hierarchical models we begin with the distinction between basic parameters which have prior distributions and functional parameters which are defined in terms of basic parameters based on a graphical analysis of mtc structures evidence inconsistency is defined as a relation between a functional parameter and at least two basic parameters supported by at least three evidence sources the inconsistency degrees of freedom icdf is the number of such inconsistencies we represent evidence consistency as a set of linear relations between effect parameters on the log odds ratio scale then relax these rela

a new estimator of the discovery probability summary species sampling problems have a long history in ecological and biological studies and a number of issues including the evaluation of species richness the design of sampling experiments and the estimation of rare species variety are to be addressed such inferential problems have recently emerged also in genomic applications however exhibiting some peculiar features that make them more challenging specifically one has to deal with very large populations genomic libraries containing a huge number of distinct species genes and only a small portion of the library has been sampled sequenced these aspects motivate the bayesian nonparametric approach we undertake since it allows to achieve the degree of flexibility typically needed in this framework based on an observed sample of size n focus will be on prediction of a key aspect of the outcome from an additional sample of size m namely the so called discovery probability in particular conditionally on an observed basic sample of size n we derive a novel estimator of the probability of detecting at the n m 1 th observation species that have been observed with any given frequency in the enlarged sample of size n m such an estimator admits a closed form expression that can be exactly evaluated the result we obtain allows us to quantify both the rate at which rare species are detected and the achieved sample coverage of abundant species as m increases natural applications are represented by the estimation of the probability of discovering rare genes within genomic libraries and the results are illustrated by means of two expressed sequence tags datasets

nonparametric regression with errors in variables the effect of errors in variables in nonparametric regression estimation is examined to account for errors in covariates deconvolution is involved in the construction of a new class of kernel estimators it is shown that optimal local and global rates of convergence of these kernel estimators can be characterized by the tail behavior of the characteristic function of the error distribution in fact there are two types of rates of convergence according to whether the error is ordinary smooth or super smooth it is also shown that these results hold uniformly over a class of joint distributions of the response and the covariate which is rich enough for many practical applications furthermore to achieve optimality we show that the convergence rates of all possible estimators have a lower bound possessed by the kernel estimators

bayesian approaches to random effects meta analysis a comparative study current methods for meta analysis still leave a number of unresolved issues such as the choice between fixed and random effects models the choice of population distribution in a random effects analysis the treatment of small studies and extreme results and incorporation of study specific covariates we describe how a full bayesian analysis can deal with these and other issues in a natural way illustrated by a recent published example that displays a number of problems such analyses are now generally available using the bugs implementation of markov chain monte carlo numerical integration techniques appropriate proper prior distributions are derived and sensitivity analysis to a variety of prior assumptions carried out current methods are briefly summarized and compared to the full bayes analysis

stopping rules and estimation for recapture debugging with unequal failure rates summary a theoretical optimal stopping rule based on the minimization of the testing cost and expected penalty due to the unremoved bugs is derived without the equal failure rate assumption under nayak s 1988 recapture debugging procedure two adaptive stopping rules suitable for practical use are constructed and tested by simulation the estimation of the number of undetected bugs is also considered via remaining failure rate estimation

a penalized nonparametric maximum likelihood approach to species richness estimation we propose a class of penalized nonparametric maximum likelihood estimators npmles for the species richness problem we use a penalty term on the likelihood because likelihood estimators that lack it have an extreme instability problem the estimators are constructed using a conditional likelihood that is simpler than the full likelihood we show that the full likelihood npmle solution given by norris and pollock can be found with great accuracy by using an appropriate penalty term on the conditional likelihood so it is an element of our class of estimators a simple and fast algorithm for the penalized npmle is developed it can be used to greatly speed up computation of the unconditional npmle it can also be used to find profile mixture likelihoods based on our goal of attaining high stability while retaining sensitivity we propose an adaptive quadratic penalty function a systematic simulation study using a wide range of scenarios establishes the success of this method relative to its competi

why add anything to nothing the arcsine difference as a measure of treatment effect in meta analysis with zero cells for clinical trials with binary endpoints there are a variety of effect measures for example risk difference risk ratio and odds ratio or the choice of metric is not always straightforward and should reflect the clinical question additional issues arise if the event of interest is rare in systematic reviews trials with zero events in both arms are encountered and often excluded from the meta analysis the arcsine difference as is a measure which is rarely considered in the medical literature it appears to have considerable promise because it handles zeros naturally and its asymptotic variance does not depend on the event probability this paper investigates the pros and cons of using the as as a measure of intervention effect we give a pictorial representation of its meaning and explore its properties in relation to other measures based on analytical calculation of the variance of the arcsine transformation a more conservative variance estimate for the rare event setting is proposed motivated by a published meta analysis in cardiac surgery we examine the statistical properties of the various metrics in the rare event setting we find the variance estimate of the as to be more stable than that of the log or even if events are rare however parameter estimation is biased if the groups are markedly unbalanced though from a theoretical viewpoint the as is a natural choice its practical use is likely to continue to be limited by its less direct interpretation

estimating the number of component processes of a superimposed process summary we consider a superposition of an unknown number of independent homogeneous poisson processes with unknown rates and suppose that when an event occurs the component process in which it occurred can be identified the number of component processes and their rates are to be estimated by observing the system for some time in the general case it is difficult to estimate all of the parameters but we derive the best unbiased estimators of some parametric functions inferences for the special case where all the rates are equal are discussed in detail

a hierarchical semiparametric regression model for combining hiv 1 phylogenetic analyses using iterative reweighting algorithms phylogenetic modeling is computationally challenging and most phylogeny models fit a single phylogeny to a single set of molecular sequences individual phylogenetic analyses are typically performed independently using publicly available software that fits a computationally intensive bayesian model using markov chain monte carlo mcmc simulation we develop a bayesian hierarchical semiparametric regression model to combine multiple phylogenetic analyses of hiv 1 nucleotide sequences and estimate parameters of interest within and across analyses we use a mixture of dirichlet processes as a prior for the parameters to relax inappropriate parametric assumptions and to ensure the prior distribution for the parameters is continuous we use several reweighting algorithms for combining completed mcmc analyses to shrink parameter estimates while adjusting for data set specific covariates this avoids constructing a large complex model involving all the original data which would be computationally challenging and would require rewriting the existing stand alone software