accelerated iterative reconstruction for positron emission tomography based on the em algorithm for maximum likelihood estimation the em method that was originally developed for maximum likelihood estimation in the context of mathematical statistics may be applied to a stochastic model of positron emission tomography pet the result is an iterative algorithm for image reconstruction that is finding increasing use in pet due to its attractive theoretical and practical properties its major disadvantage is the large amount of computation that is often required due to the algorithm s slow rate of convergence this paper presents an accelerated form of the em algorithm for pet in which the changes to the image as calculated by the standard algorithm are multiplied at each iteration by an overrelaxation parameter the accelerated algorithm retains two of the important practical properties of the standard algorithm namely the selfnormalization and nonnegativity of the reconstructed images experimental results are presented using measured data obtained from a hexagonal detector system for pet the likelihood function and the norm of the data residual were monitored during the iterative process according to both of these measures the images reconstructed at iterations 7 and 11 of the accelerated algorithm are similar to those at iterations 15 and 30 of the standard algorithm for two different sets of data important theoretical properties remain to be investigated namely the convergence of the accelerated algorithm and its performance as a maximum likelihood estimator

integrable harmonic functions on symmetric spaces of rank one if f l1 d is harmonic in the spaceg k where is a radial measure with g k 1 we have by the mean value propertyf f conversely does this mean value property imply thatfis harmonic in this paper we give a new and natural proof of a result obtained by p ahern a flores w rudin j funct anal 11 1993 380 397 and a koranyi contemp math 191 1995 107 116 and generalize their result by providing sufficient conditions for a finite set of radial measures ion a symmetric space of rank one for whichf i fimply thatfis harmonic

estimating rate constants in hidden markov models by the em algorithm the em algorithm e g the baum welch 1970 re estimation is an important tool for parameter estimation in discrete time hidden markov models we present a direct re estimation of rate constants for applications in which the underlying markov process is continuous in time previous estimation of discrete time transition probabilities is not necessary

the complexity of finding minimum length generator sequences abstract the computational complexity of the following problem is investigated given a permutation group specified as a set of generators and a single target permutation which is a member of the group what is the shortest expression for the target permutation in terms of the generators the general problem is demonstrated to be psppace complete and indeed is shown to remain so even when the generator set is restricted to contain only two permutations the restriction on generator set cardinality is the best possible as the problem becomes soluble in polynomial time if the generator set cantains only one permutation an interesting feature of this problem is that it does not fall under the headings of two person games or formal languages which cover the great majority of known pspace complete problems some restricted versions of the problem in which the generator set is fixed rather than being part of the problem instance are also investigated and shown to be computationally tractable one result of this kind is that determining the most compact expression of a permutation in terms of cyclicly adjacent transpositions can be achieved in polynomial time thus from an initial arrangement of distinct objects on a circle one can quickly compute the smallest number of interchanges of adjacent objects required to realise any other arrangement surprisingly this problem appears substantially more difficult to solve than the related one for which a solution has been known for some time in which the objects are arranged on a line segment

critical size of neural population for reliable information transmission it is known that the probability of decoding error has a phase transition at information rate equal to the channel capacity the corresponding thermodynamic limit requires infinite coding dimension hence making the actual decoding practically impossible in this rapid communication we analyze finite size effects that occur in limited neural populations we report that the achievable rate approaches the asymptote in a remarkably nonlinear manner with the population size qualitatively our findings do not seem to depend on the details of the model

asymptotical statistics of misspecified hidden markov models this paper deals with the problem of modeling data generated by an ergodic stochastic process as the output of a hidden markov model hmm more specifically we consider the problem of fitting a parametric family of hmm with continuous output to an ergodic stochastic process with continuous values which does not necessarily belong to the family in this context we derive the main asymptotic results almost sure consistency of the maximum likelihood estimator asymptotic normality of the estimation error and the exact rates of almost sure convergence

upper bounds on the capacities of noncontrollable finite state channels with without feedback noncontrollable finite state channels fscs are fscs in which the channel inputs have no influence on the channel states i e the channel states evolve freely since single letter formulas for the channel capacities are rarely available for general noncontrollable fscs computable bounds are usually utilized to numerically bound the capacities in this paper we take the delayed channel state as part of the channel input and then define the directed information rate from the new channel input including the source and the delayed channel state sequence to the channel output sequence with this technique we derive a series of upper bounds on the capacities of noncontrollable fscs with without feedback these upper bounds can be achieved by conditional markov sources and computed by solving an average reward per stage stochastic control problem arscp with a compact state space and a compact action space by showing that the arscp has a uniformly continuous reward function we transform the original arscp into a finite state and finite action arscp that can be solved by a value iteration method under a mild assumption the value iteration algorithm is convergent and delivers a near optimal stationary policy and a numerical upper bound

an invariant volume mean value property if is harmonic and integrable over the open unit disc u then so is for every moebius transformation of u and therefore 1 u d a 0 for every conversely does this mean value property imply that is harmonic a more general question with the unit ball bn of c for arbitrary n 1 in place of the disc is investigated in the present paper the answer is found to be affirmative if n 11 negative if n 12

comparison techniques for random walk on finite groups we develop techniques for bounding the rate of convergence of a symmetric random walk on a finite group to the uniform distribution the techniques gives bounds on the second largest and other eigenvalues in terms of the eigenvalues of a comparison chain with known eigenvalues the techniques yield sharp rates for a host of previously intractable problems on the symmetric group

easily computed lower bounds on the information rate of intersymbol interference channels provable lower bounds are presented for the information rate i x x s n where x is the symbol drawn independently and uniformly from a finite size alphabet s is a discrete valued random variable rv and n is a gaussian rv it is well known that with s representing the precursor intersymbol interference isi at the decision feedback equalizer dfe output i x x s n serves as a tight lower bound for the symmetric information rate sir as well as capacity of the isi channel corrupted by gaussian noise when evaluated on a number of well known finite isi channels these new bounds provide a very similar level of tightness against the sir to the conjectured lower bound by shamai and laroia at all signal to noise ratio snr ranges while being actually tighter when viewed closed up at high snrs the new lower bounds are obtained in two steps first a mismatched mutual information function is introduced which can be proved as a lower bound to i x x s n secondly this function is further bounded from below by an expression that can be computed easily via a few single dimensional integrations with a small computational load

regression analysis of interval censored survival data with covariates using log linear models we considered the regression analysis of the event time data with left right or interval censored observations we extended life table techniques for censored survival data using log linear models to incorporate interval censored failures the em algorithm was used to calculate maximum likelihood estimates for the parameters we assumed that the hazard function was a stepwise function over disjoint intervals of time thus the nonparametric model the parametric exponential model and the semiparametric cox proportional hazard model were easily implemented as special cases we adapted the restricted em algorithm to test hypotheses and to construct confidence intervals for the parameters these methods were applied in an analysis of the recurrence time for treated melanoma patients

bounds on the information rate of intersymbol interference channels based on mismatched receivers we consider the problem of bounding the information rate of intersymbol interference channels via simulation based algorithms the adopted approach which is based on a general class of reduced complexity receivers that includes several previously studied receivers as special cases leads to provable upper and lower bounds on the information rate of interest as a by product of the information theoretic investigations novel insights on the design of efficient reduced complexity receivers are also provided since the proposed lower bounds are known to be achievable by practical receivers in many scenarios our novel approach significantly outperforms the existing ones for all practical values of the signal to noise ratio

a quick method for estimation of parameters of individual pulses in a multipath signal abstract consider a multipath signal whose individual signals are deterministic known increasing or decreasing pulses the problem is to estimate the amplitudes and delay times of individual signals several methods have been devoted to the solution of these unknown parameters the maximum likelihood ml estimation and the estimate maximize em algorithm are commonly used but they are computationally intensive and still insufficient to obtain accurate estimations the method can provide a quick and accurate estimate of the amplitudes and arrival delay times even in the closely spaced multipaths and heavy noise

integrable harmonic functions on rn a class of radial measures on rnis defined so that integrable harmonic functionsfon rnmay be characterized as solutions of convolution equationsf f in particular we show thatf e 2 x is harmonic if and only ifn 9

em and beyond the basic theme of the em algorithm to repeatedly use complete data methods to solve incomplete data problems is also a theme of several more recent statistical techniques these techniques multiple imputation data augmentation stochastic relaxation and sampling importance resampling combine simulation techniques with complete data methods to attack problems that are difficult or impossible for em

simulation based computation of information rates for channels with memory the information rate of finite state source channel models can be accurately estimated by sampling both a long channel input sequence and the corresponding channel output sequence followed by a forward sum product recursion on the joint source channel trellis this method is extended to compute upper and lower bounds on the information rate of very general channels with memory by means of finite state approximations further upper and lower bounds can be computed by reduced state methods

an incomplete data approach to the analysis of covariance structures in this paper linear structural equation models with latent variables are considered it is shown how many common models arise from incomplete observation of a relatively simple system subclasses of models with conditional independence interpretations are also discussed using an incomplete data point of view the relationships between the incomplete and complete data likelihoods assuming normality are highlighted for computing maximum likelihood estimates the em algorithm and alternatives are surveyed for the alternative algorithms simplified expressions for computing function values and derivatives are given likelihood ratio tests based on complete and incomplete data are related and an example on using their relationship to improve the fit of a model is given

signal modeling with filtered discrete fractional noise processes filtered versions of fractionally differenced gaussian noise fdgn processes are studied fractionally differenced gaussian noise is a discrete time equivalent of fractional brownian motion filtered versions of such processes are ideally suited for modeling signals with different short term and long term correlation structure two iterative algorithms for estimating the parameters of filtered fdgn processes are described the first technique is based on the expectation maximization algorithm it converges to a stationary point of the log likelihood function corresponding to the parameters of the model the second technique is a computationally efficient approximate approach it is found to converge experimentally but no proof of its convergence is given the usefulness of filtered fdgn models and the performance of the proposed iterative algorithms are illustrated by fitting filtered fdgn models to speech waveforms and other data corresponding to natural phenomena

weighted berezin transform in the polydisc abstract for c 1 let c denote a weighted radial measure on c normalized so that c d 1 if f is harmonic and integrable with respect to c over the open unit disc d then d f d c f 0 for every aut d equivalently f is invariant under the weighted berezin transform b c f f conversely does the invariance under the weighted berezin transform imply the harmonicity of a function in this paper we prove that for any 1 p and c 1 c 2 1 a function f l p d 2 c 1 c 2 which is invariant under the weighted berezin transform b c 1 c 2 f f needs not be 2 harmonic

optimization of information rate upper and lower bounds for channels with memory we consider the problem of minimizing upper bounds and maximizing lower bounds on information rates of stationary and ergodic discrete time channels with memory the channels we consider can have a finite number of states such as partial response channels or they can have an infinite state space such as time varying fading channels we optimize recently proposed information rate bounds for such channels which make use of auxiliary finite state machine channels fsmcs our main contribution in this paper is to provide iterative expectation maximization em type algorithms to optimize the parameters of the auxiliary fsmc to tighten these bounds we provide an explicit iterative algorithm that improves the upper bound at each iteration we also provide an effective method for iteratively optimizing the lower bound to demonstrate the effectiveness of our algorithms we provide several examples of partial response and fading channels where the proposed optimization techniques significantly tighten the initial upper and lower bounds finally we compare our results with results obtained by the conjugate gradient optimization algorithm and an improved variation of the simplex algorithm called soblex while the computational complexities of our algorithms are similar to the conjugate gradient method and less than the soblex algorithm our algorithms robustly find the tightest bounds interestingly from a channel coding decoding perspective optimizing the lower bound is related to increasing the achievable mismatched information rate i e the information rate of a communication system where the decoder at the receiver is matched to the auxiliary channel and not to the original channel

computing short generator sequences abstract the diameter of a group is the length of the longest product of generators required to reach a group element we show that the diameter of a permutation group of degree n generated by cycles of bounded degree is o n 2 this bound is the best possible additionally such short products can be found in polynomial time the techniques presented here may be applied to many permutation group puzzles such as alexander s star the hungarian rings rubik s cube and some of their generalizations

characterization of eigenfunctions of the laplace beltrami operator using fourier multipliers abstract let x be a rank one riemannian symmetric space of noncompact type and be the laplace beltrami operator of x the space x can be identified with the quotient space g k where g is a connected noncompact semisimple lie group of real rank one with finite center and k is a maximal compact subgroup of g thus g acts naturally on x by left translations through this identification a function or measure on x is radial i e depends only on the distance from ek when it is invariant under the left action of k we consider right convolution operators on functions f on x defined by f f where is a radial possibly complex measure on x these operators will be called multipliers in particular is a radial average when is a radial probability measure notable examples of radial averages are ball sphere and annular averages and the heat operator in this paper we address problems of the following type fix a multiplier in particular an averaging operator suppose that f k k z is a bi infinite sequence of functions on x such that for all k z f k a f k 1 and f k m for some constants a c m 0 and a suitable norm from this hypothesis we try to infer that f 0 hence every f k is an eigenfunction of

orthogonalizing em a design based least squares algorithm we introduce an efficient iterative algorithm intended for various least squares problems based on a design of experiments perspective the algorithm called orthogonalizing em oem works for ordinary least squares ols and can be easily extended to penalized least squares the main idea of the procedure is to orthogonalize a design matrix by adding new rows and then solve the original problem by embedding the augmented design in a missing data framework we establish several attractive theoretical properties concerning oem for the ols with a singular regression matrix an oem sequence converges to the moore penrose generalized inverse based least squares estimator for ordinary and penalized least squares with various penalties it converges to a point having grouping coherence for fully aliased regression matrices convergence and the convergence rate of the algorithm are examined finally we demonstrate that oem is highly efficient for large scale least squares and penalized least squares proble

feedback capacity of finite state machine channels we consider a finite state machine channel with a finite memory length e g finite length intersymbol interference channels with finite input alphabets also known as partial response channels for such a finite state machine channel we show that feedback dependent markov sources achieve the feedback capacity and that the required memory length of the markov process matches the memory length of the channel further we show that the whole history of feedback is summarized by the causal posterior channel state distribution which is computed by the sum product forward recursion of the bahl cocke jelinek raviv bcjr baum welch discrete time wonham filtering algorithm these results drastically reduce the space over which the optimal feedback dependent source distribution needs to be sought further the feedback capacity computation may then be formulated as an average reward per stage stochastic control problem which is solved by dynamic programming with the knowledge of the capacity achieving source distribution the value of the capacity is easily estimated using markov chain monte carlo methods when the feedback is delayed we show that the feedback capacity can be computed by similar procedures we also show that the delayed feedback capacity is a tight upper bound on the feedforward capacity by comparing it to tight existing lower bounds we demonstrate the applicability of the method by computing the feedback capacity of partial response channels and the feedback capacity of run length limited rll sequences over binary symmetric channels bscs

nonparametric estimation of the distribution of time to onset for specific diseases in survival sacrifice experiments this paper concerns the analysis of an animal survival sacrifice experiment designed to investigate the incidence of a particular disease of interest the disease is assumed to be irreversible and detectable only at death for example by a necropsy each observation can be of one of three types i death caused by the disease ii death from a competing cause such as sacrifice with the disease present or iii death with the disease absent a two dimensional em algorithm is proposed for the nonparametric maximum likelihood estimation of the distributions of the time to onset and of the time to death from the disease these can be compared with nonparametric estimators recently proposed by kodell shaw and johnson 1982 biometrics 38 43 58 and by dinse and lagakos 1982 biometrics 38 921 932 a slight modification of the algorithm permits the construction of likelihood based interval estimates of quantiles of the distributions some extensions and generalizations are indicated

em algorithms for ml factor analysis the details of em algorithms for maximum likelihood factor analysis are presented for both the exploratory and confirmatory models the algorithm is essentially the same for both cases and involves only simple least squares regression operations the largest matrix inversion required is for aq q symmetric matrix whereq is the matrix of factors the example that is used demonstrates that the likelihood for the factor analysis model may have multiple modes that are not simply rotations of each other such behavior should concern users of maximum likelihood factor analysis and certainly should cast doubt on the general utility of second derivatives of the log likelihood as measures of precision of estimation

on the convergence properties of the em algorithm two convergence aspects of the em algorithm are studied i does the em algorithm find a local maximum or a stationary value of the incomplete data likelihood function ii does the sequence of parameter estimates generated by em converge several convergence results are obtained under conditions that are applicable to many practical situations two useful special cases are a if the unobserved complete data specification can be described by a curved exponential family with compact parameter space all the limit points of any em sequence are stationary points of the likelihood function b if the likelihood function is unimodal and a certain differentiability condition is satisfied then any em sequence converges to the unique maximum likelihood estimate a list of key properties of the algorithm is included

an em algorithm for fitting two level structural equation models maximum likelihood is an important approach to analysis of two level structural equation models different algorithms for this purpose have been available in the literature in this paper we present a new formulation of two level structural equation models and develop an em algorithm for fitting this formulation this new formulation covers a variety of two level structural equation models as a result the proposed em algorithm is widely applicable in practice a practical example illustrates the performance of the em algorithm and the maximum likelihood statistic

mismatched decoding revisited general alphabets channels with memory and the wide band limit the mismatch capacity of a channel is the highest rate at which reliable communication is possible over the channel with a given possibly suboptimal decoding rule this quantity has been studied extensively for single letter decoding rules over discrete memoryless channels dmcs here we extend the study to memoryless channels with general alphabets and to channels with memory with possibly non single letter decoding rules we also study the wide band limit and in particular the mismatch capacity per unit cost and the achievable rates on an additive noise spread spectrum system with single letter decoding and binary signaling

dual capacity upper bounds for binary input single tap isi channels the capacity of noisy channels with memory and finite input has been difficult to characterize explicitly in many cases in this paper we consider single tap binary input gaussian channels with inter symbol interference isi the dual capacity method is used to obtain upper bounds using markov test distributions the bound expressed as a single letter optimization problem is solved numerically for higher memory the notion of cycle basis is used to provide an exponential reduction in the computational complexity of the optimization problem bounds were obtained for the important case of the dicode channel and these are better than the previously known upper bounds and are close to achievable rates over a wide range of snrs

em based joint data detection and channel estimation of ds cdma signals we present two efficient iterative receiver structures of tractable complexity for joint multiuser detection and multichannel estimation jde of direct sequence code division multiple access signals the schemes result from an application of the expectation maximization em and the space alternating generalized expectation maximization sage algorithms respectively the em jde receiver updates the data bit sequences in parallel while the sage jde receiver reestimates them successively the channel parameters are updated in parallel in both schemes the em algorithm provides a set of free parameters called weight coefficients which can be selected to optimize its performance two optimality criteria are defined and analytical expressions for the corresponding optimized weight coefficients are given monte carlo simulations of a synchronous scenario show that the proposed jde receivers have excellent multiuser efficiency and are robust against errors in the estimation of the channel parameters moreover very short training sequences are required for the jde schemes to converge simulation results further demonstrate that the sage jde receiver exhibits a better performance when the users bit sequences are updated in the order of increasing signal strength i e the bit sequence of the user with the weakest signal strength is updated first at each stage

bounds on the information rate for sparse channels with long memory and i u d inputs in this paper we propose new bounds on the achievable information rate for discrete time gaussian channels with intersymbol interference isi and independent and uniformly distributed i u d channel input symbols drawn from finite order modulation alphabets specifically we are interested in developing new bounds on the achievable rates for sparse channels with long memory we obtain a lower bound which can be achieved by practical receivers based on mmse channel shortening and suboptimal symbol detection for a reduced state channel an upper bound is given in the form of a semi analytical solution derived using basic information theoretic inequalities by a grouping of the channel taps into several clusters resulting in a newly defined single input multiple output simo channel we show that the so obtained time dispersive simo channel can be represented by an equivalent single input single output siso channel with a significantly shorter channel memory the reduced computational complexity allows the use of the bcjr algorithm for the newly defined channel the proposed bounds are illustrated through several sparse channel examples and i u d input symbols showing that the upper bound significantly outperforms existing bounds performance of our lower bound strongly depends on the channel structure showing best results for minimum phase and maximum phase systems

image classification by a two dimensional hidden markov model for block based classification an image is divided into blocks and a feature vector is formed for each block by grouping statistics extracted from the block conventional block based classification algorithms decide the class of a block by examining only the feature vector of this block and ignoring context information in order to improve classification by context an algorithm is proposed that models images by two dimensional 2 d hidden markov models hmms the hmm considers feature vectors statistically dependent through an underlying state process assumed to be a markov mesh which has transition probabilities conditioned on the states of neighboring blocks from both horizontal and vertical directions thus the dependency in two dimensions is reflected simultaneously the hmm parameters are estimated by the em algorithm to classify an image the classes with maximum a posteriori probability are searched jointly for all the blocks applications of the hmm algorithm to document and aerial image segmentation show that the algorithm outperforms cart sup tm lvq and bayes vq

lower bounds and approximations for the information rate of the isi channel we consider the discrete time intersymbol interference isi channel model with additive gaussian noise and fixed independent identically distributed inputs in this setting we investigate the expression put forth by shamai and laroia as a conjectured lower bound for the input output mutual information after application of a minimum mean square error decision feedback equalizer receiver a low signal to noise ratio snr expansion is used to prove that the conjectured bound does not hold under general conditions and to characterize inputs for which it is particularly ill suited one such input is used to construct a counterexample indicating that the shamai laroia expression does not always bound even the achievable rate of the channel thus excluding a natural relaxation of the original conjectured bound however this relaxed bound is then shown to hold for any finite entropy input and isi channel when the snr is sufficiently high we derive two conditions under which the relaxed bound holds involving compound channel capacity and quasiconvexity arguments finally new simple bounds for the achievable rate are proven and compared with other known bounds information estimation relations and estimation theoretic bounds play a key role in establishing our results

robust continuous time smoothers without two sided stochastic integrals we consider the problem of fixed interval smoothing of a continuous time partially observed nonlinear stochastic dynamical system existing results for such smoothers require the use of two sided stochastic calculus the main contribution of the paper is to present a robust formulation of the smoothing equations under this robust formulation the smoothing equations are nonstochastic parabolic partial differential equations with random coefficients and hence the technical machinery associated with two sided stochastic calculus is not required furthermore the robust smoothed state estimates are locally lipschitz in the observations which is useful for numerical simulation as examples finite dimensional robust versions of the benes and hidden markov model smoothers and smoothers for piecewise linear dynamics are derived these finite dimensional smoothers do not involve stochastic integrals

asymptotic convergence rate of the em algorithm for gaussian mixtures it is well known that the convergence rate of the expectation maximization em algorithm can be faster than those of convention first order iterative algorithms when the overlap in the given mixture is small but this argument has not been mathematically proved yet this article studies this problem asymptotically in the setting of gaussian mixtures under the theoretical framework of xu and jordan 1996 it has been proved that the asymptotic convergence rate of the em algorithm for gaussian mixtures locally around the true solution is o e0 5 e where e 0 is an arbitrarily small number o x means that it is a higher order infinitesimal as x 0 and e is a measure of the average overlap of gaussians in the mixture in other words the large sample local convergence rate for the em algorithm tends to be asymptotically superlinear when e tends to zero

combining monte carlo and mean field like methods for inference in hidden markov random fields issues involving missing data are typical settings where exact inference is not tractable as soon as nontrivial interactions occur between the missing variables approximations are required and most of them are based either on simulation methods or on deterministic variational methods while variational methods provide fast and reasonable approximate estimates in many scenarios simulation methods offer more consideration of important theoretical issues such as accuracy of the approximation and convergence of the algorithms but at a much higher computational cost in this work we propose a new class of algorithms that combine the main features and advantages of both simulation and deterministic methods and consider applications to inference in hidden markov random fields hmrfs these algorithms can be viewed as stochastic perturbations of variational expectation maximization vem algorithms which are not tractable for hmrf we focus more specifically on one of these perturbations and we prove their almost sure convergence to the same limit set as the limit set of vem in addition experiments on synthetic and real world images show that the algorithm performance is very close and sometimes better than that of other existing simulation based and variational em like algorithms

an expert system for predicting nonlinear aeroelastic behavior of an airfoil in this paper we present an expert system to perform steady state response predictions we consider an aeroelastic model simulating a two degree of freedom airfoil oscillating in pitch and plunge with a freeplay nonlinearity in the pitch degree of freedom in the proposed data driven methodology a freeplay is first confirmed and then the locations of the switching points are determined a state space formulation is constructed to model the piece wise linear system the parameters of the system are estimated using the kalman filter and the expectation maximization algorithm the attractive feature of the present approach is its ability to accurately predict the steady state behavior of the nonlinear aeroelastic system with freeplay using only a limited amount of transient input data to demonstrate the effectiveness of the proposed methodology we present applications to freeplay aeroelastic data arising from wind tunnel experiments and numerical simulations

sparse kalman filtering approaches to realized covariance estimation from high frequency financial data estimation of the covariance matrix of asset returns from high frequency data is complicated by asynchronous returns market microstructure noise and jumps one technique for addressing both asynchronous returns and market microstructure is the kalman expectation maximization kem algorithm however the kem approach assumes log normal prices and does not address jumps in the return process which can corrupt estimation of the covariance matrix in this paper we extend the kem algorithm to price models that include jumps we propose a sparse kalman filtering approach to this problem in particular we develop a kalman expectation conditional maximization algorithm to determine the unknown covariance as well as detecting the jumps in order to promote a sparse estimate of the jumps we consider both laplace and the spike and slab jump priors numerical results using simulated data show that each of these approaches provide for improved covariance estimation relative to the kem method in a variety of settings where jumps occur

diversity combining for ds ss systems with time varying correlated fading branches diversity combining of multiple time varying and correlated fading branches is investigated for direct sequence spread spectrum systems the correlated branches are modeled and estimated jointly as a vector autoregressive var process the joint estimation is shown to provide performance gain over separate estimation of the fading branches the parameter matrices of the var model are estimated via the method of expectation maximization em with two algorithms the first algorithm using results from kalman smoothing provides a closed form solution to the maximization problem in the iterative em procedure however the iterative em kalman algorithm operates repeatedly on a batch of training data and results in large storage requirements and long processing delays to overcome these disadvantages a new algorithm with only forward time recursions is proposed that approximates the iterative em solution and efficiently adapts to slowly changing doppler spreads as a result the new algorithm significantly reduces memory and training sequence requirements through computer simulations a near ideal bit error rate performance is found for both algorithms and the efficacy of the new adaptive algorithm for channels with changing doppler spreads is demonstrated