partial non gaussian state space summary in this paper we suggest the use of simulation techniques to extend the applicability of the usual gaussian state space filtering and smoothing techniques to a class of nongaussian time series models this allows a fully bayesian or maximum likelihood analysis of some interesting models including outlier models discrete markov chain components multiplicative models and stochastic variance models finally we discuss at some length the use of a non gaussian model to seasonally adjust the published money supply figures

identification of multi object dynamical systems consistency and fisher information learning the model parameters of a multiobject dynamical system from partial and perturbed observations is a challenging task despite recent numerical advancements in learning these parameters th

performance of convolutional codes in a direct detection optical ppm channel several strategies for combining convolutional codes ccs and pulse position modulation ppm in a direct detection optical channel are considered including binary and 2 sup n ary ppm with rate 1 n ccs 2 sup m ary ppm with a dual m cc and interleaved 2 sup l ary ppm with a rate 1 n cc in the latter case j l massey s 1981 concept of coding of l separate component channels constituting a 2 sup l ary ppm erasure channel is carried out for both the ideal photon counting and the avalanche photodetection apd cases providing a comparative evaluation of the various strategies in terms of bit error probability and achievable coding gain for different code structures and decoding schemes

central limit theorem for sequential monte carlo methods and its application to bayesian inference the term sequential monte carlo methods or equivalently particle filters refers to a general class of iterative algorithms that performs monte carlo approximations of a given sequence of distributions of interest t we establish in this paper a central limit theorem for the monte carlo estimates produced by these computational methods this result holds under minimal assumptions on the distributions t and applies in a general framework which encompasses most of the sequential monte carlo methods that have been considered in the literature including the resample move algorithm of gilks and berzuini j r stat soc ser b stat methodol 63 2001 127 146 and the residual resampling scheme the corresponding asymptotic variances provide a convenient measurement of the precision of a given particle filter we study in particular in some typical examples of bayesian applications whether and at which rate these asymptotic variances diverge in time in order to assess the long term reliability of the considered algorithm

block encoding and decoding for the optical ppm channel corresp pulse position modulation ppm is a popular signaling format in pulsed optical communication links ppm encoding is extended to include block pulse encoding over multiple ppm frames maximum likelihood decoding operations associated with this encoding are developed for both shot noise limited and thermal noise limited optical receiver models both ideal poisson and avalanche photodetectors are considered and it is shown that optimal block decoders involve combinations of linear and quadratic operations error probability bounds are presented showing the relative improvement in detectability that appears possible by resorting to block encoding over multiple frames

reml estimation for survival models with frailty a method of estimation for generalised mixed models is applied to the estimation of regression parameters in proportional hazards models for failure times when there are repeated observations of failure on each subject the subject effect is incorporated into the model as a random frailty term best linear unbiased predictors are used as an initial step in the computation of maximum likelihood and residual maximum likelihood estimates

bivariate survival models induced by frailties abstract when two observed survival times depend via a proportional hazards model on the same unobserved variable called a frailty this common dependence induces an association between the observed times this article considers the class of bivariate survival distributions that can arise in this way extends it to allow negative association and shows that the observable bivariate distribution determines the unobserved frailty distribution up to a scale parameter a cross ratio function easily estimated even from censored data is the key to both the characterization results and inferential procedures and diagnostic plots that are introduced and illustrated by real examples the models considered are the natural counterpart for survival data of the latent variable models that have long been used in factor analysis for continuous data or in latent structure analysis for binary data the main distinguishing feature of survival data is the possibility of censoring which makes the standard methods difficu

recursive parameter estimation using incomplete data abstract stochastic approximation procedures are considered for the estimation of parameters using incomplete data one procedure is stated and illustrated which often leads to asymptotically efficient estimators others are developed which although possibly not optimal in the above sense will be very much easier to apply this will be particularly advantageous when quick recursive estimates are required examples are given and a link is made between one of the sub optimal methods and the em algorithm author

particle filters for partially observed diffusions in this paper we introduce novel particle filters for a class of partially observed continuous time dynamic models where the signal is given by a multivariate diffusion process we consider a variety of observation schemes including diffusion observed with error observation of a subset of the components of the multivariate diffusion and arrival times of a poisson process whose intensity is a known function of the diffusion cox process unlike currently available methods our particle filters do not require approximations of the transition and or the observation density using time discretisations instead they build on recent methodology for the exact simulation of the diffusion process and the unbiased estimation of the transition density as described in beskos et al 2006 in particular we introduce the generalised poisson estimator which generalises the poisson estimator of beskos et al 2006 thus our filters avoid the systematic biases caused by time discretisations and they have significant computational advantages over alternative continuous time filters these advantages are supported theoretically by a central limit theorem

particle filters for state space models with the presence of unknown static parameters particle filters for dynamic state space models handling unknown static parameters are discussed the approach is based on marginalizing the static parameters out of the posterior distribution such that only the state vector needs to be considered such a marginalization can always be applied however real time applications are only possible when the distribution of the unknown parameters given both observations and the hidden state vector depends on some low dimensional sufficient statistics such sufficient statistics are present in many of the commonly used state space models marginalizing the static parameters avoids the problem of impoverishment which typically occurs when static parameters are included as part of the state vector the filters are tested on several different models with promising results

posterior likelihood methods for multivariate survival data this article deals with the semiparametric analysis of multivariate survival data with random block group effects survival times within the same group are correlated as a consequence of a frailty random block effect the standard approaches assume either a parametric or a completely unknown baseline hazard function this paper considers an intermediate solution that is a nonparametric function that is reasonably smooth this is accomplished by a bayesian model in which the conditional proportional hazards model is used with a correlated prior process for the baseline hazard the posterior likelihood based on data as well as the prior process is similar to the discretized penalized likelihood for the frailty model the methodology is exemplified with the recurrent kidney infections data of mcgilchrist and aisbett 1991 biometrics 47 461 466 in which the times to infections within the same patients are expected to be correlated the reanalysis of the data has shown that the estimates of the parameters of interest and the associated standard errors depend on the prior knowledge about the smoothness of the baseline hazard

uniform stability of a particle approximation of the optimal filter derivative particle methods also known as sequential monte carlo methods are a principled set of algorithms used to approximate numerically the optimal filter in nonlinear non gaussian state space models however when performing maximum likelihood parameter inference in state space models it is also necessary to approximate the derivative of the optimal filter with respect to the parameter of the model references g poyiadjis a doucet and s s singh particle methods for optimal filter derivative application to parameter estimation in proceedings of ieee international conference on acoustics speech and signal processing icassp 5 philadelphia 2005 pp 925 928 and g poyiadjis a doucet and s s singh biometrika 98 2011 pp 65 80 present an original particle method to approximate this derivative and it was shown in numerical examples to be numerically stable in the sense that it did not deteriorate over time in this paper we theoretically substantiate this claim mathbb l p bounds

sequential quasi monte carlo this is a written discussion of the paper sequential quasi monte carlo sampling by m gerber and n chopin following the presentation given before the royal statistical society in london on december 10th 2014

time series analysis of non gaussian observations based on state space models from both classical and bayesian perspectives the analysis of non gaussian time series by using state space models is considered from both classical and bayesian perspectives the treatment in both cases is based on simulation using importance sampling and antithetic variables markov chain monte carlo methods are not employed non gaussian disturbances for the state equation as well as for the observation equation are considered methods for estimating conditional and posterior means of functions of the state vector given the observations and the mean square errors of their estimates are developed these methods are extended to cover the estimation of conditional and posterior densities and distribution functions the choice of importance sampling densities and antithetic variables is discussed the techniques work well in practice and are computationally efficient their use is illustrated by applying them to a univariate discrete time series a series with outliers and a volatility series

bayesian models for multivariate current status data with informative censoring des donnees multivariees d etat consistent en un ensemble d indicatrices associees a la realisation de plusieurs evenements au moment d un examen nous nous interessons aux inferences sur les distributions jointes des temps d evenements les methodes conventionnelles d analyse des donnees de durees multiples ne peuvent etre utilisees parce que tous les temps d evenements sont censures et la censure peut etre informative nous prenons en compte la correlation des temps d evenements chez un sujet au moyen d une variable latente propre au sujet conditionnellement a laquelle les divers temps d evenements sont supposes independants nous supposons egalement que chaque evenement contribue independamment au risque de censure des fonctions en escalier non parametriques sont utilisees pour caracteriser les distributions de base des differents temps d evenements et des temps d examen les covariables et les effets specifiques du sujet sont incorpores grace au modele lineaire generalise un algorithme de monte carlo par chaines de markov est decrit pour l estimation des distributions a posteriori des inconnues les methodes sont illustrees par une application sur des donnees de sites multiples de tumeurs dans une etude de carcinogenicite animale

smc 2 an efficient algorithm for sequential analysis of state space models we consider the generic problem of performing sequential bayesian inference in a state space model with observation process y state process x and fixed parameter theta an idealized approach would be to apply the iterated batch importance sampling ibis algorithm of chopin 2002 this is a sequential monte carlo algorithm in the theta dimension that samples values of theta reweights iteratively these values using the likelihood increments p y t y 1 t 1 theta and rejuvenates the theta particles through a resampling step and a mcmc update step in state space models these likelihood increments are intractable in most cases but they may be unbiasedly estimated by a particle filter in the x dimension for any fixed theta this motivates the smc 2 algorithm proposed in this article a sequential monte carlo algorithm defined in the theta dimension which propagates and resamples many particle filters in the x dimension the filters in the x dimension are an example of the random weight particle filter as in fearnhead et al 2010 on the other hand the particle markov chain monte carlo pmcmc framework developed in andrieu et al 2010 allows us to design appropriate mcmc rejuvenation steps thus the theta particles target the correct posterior distribution at each iteration t despite the intractability of the likelihood increments we explore the applicability of our algorithm in both sequential and non sequential applications and consider various degrees of freedom as for example increasing dynamically the number of x particles we contrast our approach to various competing methods both conceptually and empirically through a detailed simulation study included here and in a supplement and based on particularly challenging examples

a class of multivanate failure time distributions summary a class of continuous multivariate lifetime distributions is proposed the dependence between individuals in a group is modelled by a group specific quantity which can be interpreted as an unobserved covariate common to the individuals in the group and assumed to follow a positive stable distribution it is possible to include covariates in the model and discuss whether the dependence is still present after specific covariates are taken into account if the conditional hazards are proportional then the hazards in the marginal distributions are also proportional but with different constants of proportionality also the hazard for the minimum in a group is proportional to the marginal hazards if the conditional distributions given the group quantity are weibull then the marginal distributions are also weibull this class can be used to test the hypothesis of independence of litter mates in the proportional hazards model

deviance information criterion for latent variable models and misspecified models abstract deviance information criterion dic has been widely used for bayesian model comparison especially after markov chain monte carlo mcmc is used to estimate candidate models this paper first studies the problem of using dic to compare latent variable models when dic is calculated from the conditional likelihood in particular it is shown that the conditional likelihood approach undermines theoretical underpinnings of dic a new version of dic namely dic l is proposed to compare latent variable models the large sample properties of dic l are studied a frequentist justification of dic l is provided like aic dic l provides an asymptotically unbiased estimator to the expected kullback leibler kl divergence between the dgp and a predictive distribution some popular algorithms such as the em kalman and particle filtering algorithms are introduced to compute dic l for latent variable models moreover this paper studies the problem of using dic to compare misspecified models a new version of dic namely dic m is proposed and it can be regarded as a bayesian version of tic a frequentist justification of dic m is provided under misspecification dic l and dic m are illustrated using asset pricing models and stochastic volatility models

non gaussian state space modeling of nonstationary time series abstract a non gaussian state space approach to the modeling of nonstationary time series is shown the model is expressed in state space form where the system noise and the observational noise are not necessarily gaussian recursive formulas of prediction filtering and smoothing for the state estimation and identification of the non gaussian state space model are given also given is a numerical method based on piecewise linear approximation to the density functions for realizing these formulas significant merits of non gaussian modeling and the wide range of applicability of the method are illustrated by some numerical examples a typical application of this non gaussian modeling is the smoothing of a time series that has mean value function with both abrupt and gradual changes simple gaussian state space modeling is not adequate for this situation here the model with small system noise variance cannot detect jump whereas the one with large system noise variance yields unfavorable wiggle to work

generalized poya urn for time varying pitman yor processes this article introduces a class of first order stationary time varying pitman yor processes subsuming our construction of time varying dirichlet processes presented in caron et al 2007 these models can be used for time dynamic density estimation and clustering our intuitive and simple construction relies on a generalized polya urn scheme significantly this construction yields marginal distributions at each time point that can be explicitly characterized and easily controlled inference is performed using markov chain monte carlo and sequential monte carlo methods we demonstrate our models and algorithms on epidemiological and video tracking data

specification tests based on mcmc output abstract two test statistics are proposed to determine model specification after a model is estimated by an mcmc method the first test is the mcmc version of ios a test and its asymptotic null distribution is normal the second test is motivated from the power enhancement technique of fan et al 2015 it combines a component j 1 that tests a null point hypothesis in an expanded model and a power enhancement component j 0 obtained from the first test it is shown that j 0 converges to zero when the null model is correctly specified and diverges when the null model is misspecified also shown is that j 1 is asymptotically 2 distributed suggesting that the second test is asymptotically pivotal when the null model is correctly specified the main feature of the first test is that no alternative model is needed the second test has several properties first its size distortion is small and hence bootstrap methods can be avoided second it is easy to compute from mcmc output and hence is applicable to a wide range of models including latent variable models for which frequentist methods are difficult to use third when the test statistic rejects the null model and j 1 takes a large value the test suggests the source of misspecification the finite sample performance is investigated using simulated data the method is illustrated in a linear regression model a linear state space model and a stochastic volatility model using real data

variable selection for cox s proportional hazards model and frailty model a class of variable selection procedures for parametric models via nonconcave penalized likelihood was proposed in fan and li 2001a it has been shown there that the resulting procedures perform as well as if the subset of significant variables were known in advance such a property is called an oracle property the proposed procedures were illustrated in the context of linear regression robust linear regression and generalized linear models in this paper the nonconcave penalized likelihood approach is extended further to the cox proportional hazards model and the cox proportional hazards frailty model two commonly used semi parametric models in survival analysis as a result new variable selection procedures for these two commonly used models are proposed it is demonstrated how the rates of convergence depend on the regularization parameter in the penalty function further with a proper choice of the regularization parameter and the penalty function the proposed estimators possess an oracle property standard error formulae are derived and their accuracies are empirically tested simulation studies show that the proposed procedures are more stable in prediction and more effective in computation than the best subset variable selection and they reduce model complexity as effectively as the best subset variable selection compared with the lasso which is the penalized likelihood method with the l 1 penalty proposed by tibshirani the newly proposed approaches have better theoretic properties and finite sample performance

approximate smoothing and parameter estimation in high dimensional state space models we present approximate algorithms for performing smoothing in a class of high dimensional state space models via sequential monte carlo methods particle filters in high dimensions a prohibitively large number of monte carlo samples particles growing exponentially in the dimension of the state space are usually required to obtain a useful smoother employing blocking approximations we exploit the spatial ergodicity properties of the model to circumvent this curse of dimensionality we thus obtain approximate smoothers that can be computed recursively in time and parallel in space first we show that the bias of our blocked smoother is bounded uniformly in the time horizon and in the model dimension we then approximate the blocked smoother with particles and derive the asymptotic variance of idealized versions of our blocked particle smoother to show that variance is no longer adversely effected by the dimension of the model finally we employ our method to successfully perform maximum likelihood estimation via stochastic gradient ascent and stochastic expectation maximization algorithms in a 100 dimensional state space model

independent particle filters sequential monte carlo methods especially the particle filter pf and its various modifications have been used effectively in dealing with stochastic dynamic systems the standard pf samples the current state through the underlying state dynamics then uses the current observation to evaluate the sample s importance weight however there is a set of problems in which the current observation provides significant information about the current state but the state dynamics are weak and thus sampling using the current observation often produces more efficient samples than sampling using the state dynamics in this article we propose a new variant of the pf the independent particle filter ipf to deal with these problems the ipf generates exchangeable samples of the current state from a sampling distribution that is conditionally independent of the previous states a special case of which uses only the current observation each sample can then be matched with multiple samples of the previous states in

hybrid deterministic stochastic methods for data fitting many structured data fitting applications require the solution of an optimization problem involving a sum over a potentially large number of measurements incremental gradient algorithms offer inexpensive iterations by sampling a subset of the terms in the sum these methods can make great progress initially but often slow as they approach a solution in contrast full gradient methods achieve steady convergence at the expense of evaluating the full objective and gradient on each iteration we explore hybrid methods that exhibit the benefits of both approaches rate of convergence analysis shows that by controlling the sample size in an incremental gradient algorithm it is possible to maintain the steady convergence rates of full gradient methods we detail a practical quasi newton implementation based on this approach numerical experiments illustrate its potential benefits

analyticity of entropy rates of continuous state hidden markov models the analyticity of the entropy and relative entropy rates of continuous state hidden markov models is studied here using the analytic continuation principle and the stability properties of the optimal filter the analyticity of these rates is established for analytically parameterized models the obtained results hold under relatively mild conditions and cover several useful classes of hidden markov models these results are relevant for several theoretically and practically important problems arising in statistical inference system identification and information theory

semiparametric bayesian analysis of multiple event time data abstract multiple event time data e g carcinogenic growths in different times and locations multiple attacks of cardiac arrest arise in various medical studies a bayesian analysis of such data based on proportional intensity model of multiple event time data is presented in this paper the bayesian structure is somewhat analogous to that used by kalbfleisch in a proportional hazard model an unobserved random frailty component is used in the proportional intensity model to take care of heterogeneity among the intensity processes in different subjects the monte carlo method of sampling from multivariate distributions the so called gibbs sampler is used to sample from the joint posterior distribution of the unknown parameters the methodology developed here is exemplified with the well known data set on rat tumors of gail santner and brown

selecting factors predictive of heterogeneity in multivariate event time data in multivariate survival analysis investigators are often interested in testing for heterogeneity among clusters both overall and within specific classes we represent different hypotheses about the heterogeneity structure using a sequence of gamma frailty models ranging from a null model with no random effects to a full model having random effects for each class following a bayesian approach we define prior distributions for the frailty variances consisting of mixtures of point masses at zero and inverse gamma densities since frailties with zero variance effectively drop out of the model this prior allocates probability to each model in the sequence including the overall null hypothesis of homogeneity using a counting process formulation the conditional posterior distributions of the frailties and proportional hazards regression coefficients have simple forms posterior computation proceeds via a data augmentation gibbs sampling algorithm a single run of which can be used to obtain model averaged estimates of the population parameters and posterior model probabilities for testing hypotheses about the heterogeneity structure the methods are illustrated using data from a lung cancer trial

bayesian confidence intervals for the cross validated smoothing spline summary we consider the model y t g ti ei i 17 2 n where g t t 0 1 is a smooth function and the ei are independent n 0 a2 errors with g2 unknown the cross validated smoothing spline can be used to estimate g non parametrically from

particle metropolis adjusted langevin algorithms this paper proposes a new sampling scheme based on langevin dynamics that is applicable within pseudo marginal and particle markov chain monte carlo algorithms we investigate this algorithm s theoretical properties under standard asymptotics which correspond to an increasing dimension of the parameters n our results show that the behaviour of the algorithm depends crucially on how accurately one can estimate the gradient of the log target density if the error in the estimate of the gradient is not sufficiently controlled as dimension increases then asymptotically there will be no advantage over the simpler random walk algorithm however if the error is sufficiently well behaved then the optimal scaling of this algorithm will be o n 1 6 compared to o n 1 2 for the random walk our theory also gives guidelines on how to tune the number of monte carlo samples in the likelihood estimate and the proposal step size

a bayesian chi squared test for hypothesis testing abstract a new bayesian test statistic is proposed to test a point null hypothesis based on a quadratic loss the proposed test statistic may be regarded as the bayesian version of the lagrange multiplier test its asymptotic distribution is obtained based on a set of regular conditions and follows a chi squared distribution when the null hypothesis is correct the new statistic has several important advantages that make it appealing in practical applications first it is well defined under improper prior distributions second it avoids jeffrey lindley s paradox third it always takes a non negative value and is relatively easy to compute even for models with latent variables fourth its numerical standard error is relatively easy to obtain finally it is asymptotically pivotal and its threshold values can be obtained from the chi squared distribution the method is illustrated using some real examples in economics and finance

particle approximations of the score and observed information matrix in state space models with application to parameter estimation particle methods are popular computational tools for bayesian inference in nonlinear non gaussian state space models for this class of models we present two particle algorithms to compute the score vector and observed information matrix recursively the first algorithm is implemented with computational complexity o n and the second with complexity o n 2 where n is the number of particles although cheaper the performance of the o n method degrades quickly as it relies on the approximation of a sequence of probability distributions whose dimension increases linearly with time in particular even under strong mixing assumptions the variance of the estimates computed with the o n method increases at least quadratically in time the more expensive o n 2 method relies on a nonstandard particle implementation and does not suffer from this rapid degradation it is shown how both methods can be used to perform batch and recursive parameter estimation

hierarchical generalized linear models and frailty models with bayesian nonparametric mixing summary this paper proposes bayesian nonparametric mixing for some well known and popular models the distribution of the observations is assumed to contain an unknown mixed effects term which includes a fixed effects term a function of the observed covariates and an additive or multiplicative random effects term typically these random effects are assumed to be independent of the observed covariates and independent and identically distributed from a distribution from some known parametric family this assumption may be suspect if either there is interaction between observed covariates and unobserved covariates or the fixed effects predictor of observed covariates is misspecified another cause for concern might be simply that the covariates affect more than just the location of the mixed effects distribution as a consequence the distribution of the random effects could be highly irregular in modality and skewness leaving parametric families unable to model the distribution adequately this paper therefore proposes a bayesian nonparametric prior for the random effects to capture possible deviances in modality and skewness and to explore the observed covariates effect on the distribution of the mixed effects

exact score for time series models in state space form the full text of this article is not currently available in ora citation koopman s j shephard n 1992 exact score for time series models in state space form biometrika 79 40 823 826 available at http biomet oxfordjournals org

recursive maximum likelihood algorithm for dependent observations a recursive maximum likelihood algorithm rml is proposed that can be used when both the observations and the hidden data have continuous values and are statistically dependent between different time samples the algorithm recursively approximates the probability density functions of the observed and hidden data by analytically computing the integrals with respect to the state variables where the parameters are updated using gradient steps a full convergence proof is given based on the ordinary differential equation approach which shows that the algorithm converges to a local minimum of the kullback leibler divergence between the true and the estimated parametric probability density functions a result that is useful even for a miss specified parametric model compared to other rml algorithms proposed in the literature this contribution extends the state space model and provides a theoretical analysis in a nontrivial statistical model that was not analyzed so far we further extend the rml analysis to constrained parameter estimation problems two examples including nonlinear state space models are given to highlight this contribution

filtering via simulation auxiliary particle filters this article analyses the recently suggested particle approach to filtering time series we suggest that the algorithm is not robust to outliers for two reasons the design of the simulators and the use of the discrete support to represent the sequentially updating prior distribution here we tackle the first of these problems

differential ppm has a higher throughput than ppm for the band limited and average power limited optical channel because of the optimality of the pulse position modulation ppm technique for the infinite bandwidth channel it has been suggested as a technique for the bandwidth limited channel the use of differential pulse position modulation dppm as an alternative coding scheme to ppm is proposed in dppm each new word begins at the end of the previous word to avoid synchronization problems a simple scheme that decreases the throughput of the dppm channel but is easy to analyze is chosen for some parameter values this restricted dppm scheme has greater throughput in terms of capacity and cutoff rate than ppm

riemann manifold langevin and hamiltonian monte carlo methods the paper proposes metropolis adjusted langevin and hamiltonian monte carlo sampling methods defined on the riemann manifold to resolve the shortcomings of existing monte carlo algorithms when sampling from target densities that may be high dimensional and exhibit strong correlations the methods provide fully automated adaptation mechanisms that circumvent the costly pilot runs that are required to tune proposal densities for metropolis hastings or indeed hamiltonian monte carlo and metropolis adjusted langevin algorithms this allows for highly efficient sampling even in very high dimensions where different scalings may be required for the transient and stationary phases of the markov chain the methodology proposed exploits the riemann geometry of the parameter space of statistical models and thus automatically adapts to the local structure when simulating paths across this manifold providing highly efficient convergence and exploration of the target density the performance of these riemann manifold monte carlo methods is rigorously assessed by performing inference on logistic regression models log gaussian cox point processes stochastic volatility models and bayesian estimation of dynamic systems described by non linear differential equations substantial improvements in the time normalized effective sample size are reported when compared with alternative sampling approaches matlab code that is available from http www ucl ac uk statistics research rmhmc allows replication of all the results reported

penalized maximum likelihood estimation in logistic regression and discrimination summary maximum likelihood estimation of the parameters of the binary logistic regression model for pr h i x is discussed with separate discussion of sampling from i the conditional distribution of h given x ii the joint distribution of h and x and iii the conditional distribution of x given h difficulties associated with continuous x in the latter sampling scheme are discussed to avoid these penalized maximum likelihood estimates are introduced which give estimates of the logistic parameters and a nonparametric spline estimate of the marginal distribution of x extensions to multinomial logistic regression are outlined

probability of error and capacity of ppm photon counting channel calculation of the capacity for a poisson channel with a source noise as modeled by pierce is done by bounding the error probability based on chernoff s bound properties a more general method yielding a formula for the channel capacity is outlined

trellis coded pulse position modulation for indoor wireless infrared communications we analyze the performance of trellis coded pulse position modulation ppm on indoor wireless infrared channels we show that maximum likelihood sequence detection mlsd of trellis coded ppm is very effective in mitigating the multipath dispersion on such channels we present code search results for high constraint length rate 2 3 8 ppm and rate 3 4 16 ppm codes we provide bit error rate curves and intersymbol interference power penalties for mlsd of ppm with these codes evaluated on ceiling bounce channel models with delay spread per bit duration ratios of 0 01 0 3 finally we present monte carlo simulation results to verify our analysis

bayesian semiparametric dynamic frailty models for multiple event time data many biomedical studies collect data on times of occurrence for a health event that can occur repeatedly such as infection hospitalization recurrence of disease or tumor onset to analyze such data it is necessary to account for within subject dependency in the multiple event times motivated by data from studies of palpable tumors this article proposes a dynamic frailty model and bayesian semiparametric approach to inference the widely used shared frailty proportional hazards model is generalized to allow subject specific frailties to change dynamically with age while also accommodating nonproportional hazards parametric assumptions on the frailty distribution are avoided by using dirichlet process priors for a shared frailty and for multiplicative innovations on this frailty by centering the semiparametric model on a conditionally conjugate dynamic gamma model we facilitate posterior computation and lack of fit assessments of the parametric model our proposed method is demonstrated using data from a cancer chemoprevention study

a dynamic frailty model for multivariate survival data summary we consider the statistical modeling of data consisting of many study subjects with serially correlated multivariate survival responses the ordinary frailty model handles the serial correlation in such data by introducing an unobserved multiplicative random effect term called the frailty in the hazard function the frailties are often assumed to be identical for the survival times from the same unit we have generalized the frailty model by allowing the frailties to vary stochastically with the indices we have proposed a simple scheme to update the dynamic frailties this approach assumes that the random effects are gamma distributed at each occurrence the two gamma parameters are updated according to the past information in terms of their marginal distributions the dynamic frailties form a multiplicative random walk this approach results in a tractable likelihood the small sample behavior of the mle is studied via a simulation experiment the model is then illustrated with a data set from an animal carcinogenesis experiment

dynamic modelling and penalized likelihood estimation for discrete time survival data summmary this paper describes a dynamic or state space approach for analyzing discrete time or grouped survival data simultaneous estimation of baseline hazard functions and of timevarying covariate effects is based on maximization of posterior densities or equivalently a penalized likelihood leading to kalman type smoothing algorithms data driven choice of unknown smoothing parameters is possible via an em type procedure the methods are illustrated by applications to real data