mixed h_2 h_ infty control via nonsmooth optimization we present a new approach to mixed h 2 h infty output feedback control synthesis our method uses nonsmooth mathematical programming techniques to compute locally optimal h 2 h infty controllers which may have a predefined structure we prove global convergence of our method and present tests to validate it numerically

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

an infeasible bundle method for nonsmooth convex constrained optimization without a penalty function or a filter global convergence in constrained optimization algorithms has traditionally been enforced by the use of parametrized penalty functions recently the filter strategy has been introduced as an alternative at least part of the motivation for using filter methods consists of avoiding the need for estimating a suitable penalty parameter which is often a delicate task in this paper we demonstrate that the use of a parametrized penalty function in nonsmooth convex optimization can be avoided without using the relatively complex filter methods we propose an approach which appears to be more direct and easier to implement in the sense that it is closer in spirit and structure to the well developed unconstrained bundle methods preliminary computational results are also reported

convex proximal bundle methods in depth a unified analysis for inexact oracles the last few years have seen the advent of a new generation of bundle methods capable to handle inexact oracles polluted by noise proving convergence of a bundle method is never simple and coping with inexact oracles substantially increases the technicalities besides several variants exist to deal with noise each one needing an ad hoc proof to show convergence we state a synthetic convergence theory in which we highlight the main arguments and specify which assumption is used to establish each intermediate result the framework is comprehensive and generalizes in various ways a number of algorithms proposed in the literature based on the ingredients of our synthetic theory we consider various bundle methods adapted to oracles for which high accuracy is possible yet it is preferable not to make exact calculations often because they are too time consuming

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

a monte carlo approach to nonnormal and nonlinear state space modeling abstract a solution to multivariate state space modeling forecasting and smoothing is discussed we allow for the possibilities of nonnormal errors and nonlinear functionals in the state equation the observational equation or both an adaptive monte carlo integration technique known as the gibbs sampler is proposed as a mechanism for implementing a conceptually and computationally simple solution in such a framework the methodology is a general strategy for obtaining marginal posterior densities of coefficients in the model or of any of the unknown elements of the state space missing data problems including the k step ahead prediction problem also are easily incorporated into this framework we illustrate the broad applicability of our approach with two examples a problem involving nonnormal error distributions in a linear model setting and a one step ahead prediction problem in a situation where both the state and observational equations are nonlinear and involve unknown parameters

recursive noise adaptive kalman filtering by variational bayesian approximations this article considers the application of variational bayesian methods to joint recursive estimation of the dynamic state and the time varying measurement noise parameters in linear state space models the proposed adaptive kalman filtering method is based on forming a separable variational approximation to the joint posterior distribution of states and noise parameters on each time step separately the result is a recursive algorithm where on each step the state is estimated with kalman filter and the sufficient statistics of the noise variances are estimated with a fixed point iteration the performance of the algorithm is demonstrated with simulated data

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

inference for dynamic and latent variable models via iterated perturbed bayes maps iterated filtering algorithms are stochastic optimization procedures for latent variable models that recursively combine parameter perturbations with latent variable reconstruction previously theoretical support for these algorithms has been based on the use of conditional moments of perturbed parameters to approximate derivatives of the log likelihood function here a theoretical approach is introduced based on the convergence of an iterated bayes map an algorithm supported by this theory displays substantial numerical improvement on the computational challenge of inferring parameters of a partially observed markov process

c ondensation conditional density propagation forvisual tracking the problem of tracking curves in dense visual clutter is challenging kalman filtering is inadequate because it is based on gaussian densities which being unimo dal cannot represent simultaneous alternative hypotheses the condensation algorithm uses factored sampling previously applied to the interpretation of static images in which the probability distribution of possible interpretations is represented by a randomly generated set condensation uses learned dynamical models together with visual observations to propagate the random set over time the result is highly robust tracking of agile motion notwithstanding the use of stochastic methods the algorithm runs in near real time

classification of joinings for kleinian groups we classify all locally finite joinings of a horospherical subgroup action on g when g psl2 r or psl2 c and is a geometrically finite zariski dense subgroup of g this generalizes ratner s 1983 joining theorem for the case when is a lattice in g

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

performance analysis of the kalman filter with mismatched noise covariances the kalman filter is a powerful state estimator and has been successfully applied in many fields to guarantee the optimality of the kalman filter the noise covariances need to be exactly known however this is not necessarily true in many practical applications usually they are either completely unknown or at most partially known in this technical note we study performance of the kalman filter with mismatched process and measurement noise covariances for this purpose three mean squared errors mses are used namely the ideal mse imse the filter calculated mse fmse and the true mse tmse the main contribution of this work is that the relationships between the three mses are disclosed from two points of views the first view is about their ordering and the second view is about the relative closeness from the fmse and tmse to the imse using the first view it is found that for the case with positive definite deviation from the truth the fmse is the worst and the imse is the best and for the case with negative definite deviation the tmse is the worst and the best is the fmse using the second view it is found that the tmse is relatively closer to the imse than the fmse if the deviation is larger than certain threshold and the tmse will be farther away otherwise numerical examples further verify these conclusions

particle markov chain monte carlo methods summary markov chain monte carlo and sequential monte carlo methods have emerged as the two main tools to sample from high dimensional probability distributions although asymptotic convergence of markov chain monte carlo algorithms is ensured under weak assumptions the performance of these algorithms is unreliable when the proposal distributions that are used to explore the space are poorly chosen and or if highly correlated variables are updated independently we show here how it is possible to build efficient high dimensional proposal distributions by using sequential monte carlo methods this allows us not only to improve over standard markov chain monte carlo schemes but also to make bayesian inference feasible for a large class of statistical models where this was not previously so we demonstrate these algorithms on a non linear state space model and a levy driven stochastic volatility model

on the use of change constraints in reservoir design and operation modeling this work examines 1 the set of probabilistic and deterministic constraints binding the objective function of a reservoir design and operation problem 2 the conditions under which the solution of a reservoir design and operation problem becomes infeasible and 3 the discrepancies between the exact chance constrained formulation of the reservoir design and operation problem and alternative models the crux of the paper is the difference between chance constrained feasibility sets that restrict reservoir levels to be within zero and maximum capacity with probability one and those sets that impose a less stringent chance constraint on reservoir levels we derive the probability that a reservoir solution computed with the less stringent feasibility set is physically feasible i e reservoir levels are bounded by zero and reservoir capacity such probability is found to be a function of prespecified reliability levels the length of the planning horizon the joint distribution of streamflows and initial reservoir storage reservoir capacity and two chance constrained parameters it is concluded that physically feasible solutions yielded by alternative models are valuable if they serve as guidelines that are updated as they are implemented in response to unforeseen uncontrollable events

particle filters for joint timing and carrier estimation improved resampling guidelines and weighted bayesian cramer rao bounds this paper proposes a framework for joint blind timing and carrier offset estimation and data detection using a sequential importance sampling sis particle filter in additive white gaussian noise awgn channels we assume baud rate sampling and model the intractable posterior probability distribution functions for sampling timing and carrier offset particles using beta distributions to enable the sis approach to estimate static synchronization parameters we propose new resampling guidelines for dealing with the degeneracy problem and fine tuning the estimated values we derive the weighted bayesian cramer rao bound wbcrb for joint timing and carrier offset estimation which takes into account the prior distribution of the estimation parameters and is an accurate lower bound for all considered signal to noise ratio snr values simulation results are presented to corroborate that the mean square error mse performance of the proposed algorithm is close to optimal at higher snr values above 20 db in addition the bit error rate performance approaches that of the perfectly synchronized case for small unknown carrier offsets and any unknown timing offset the advantage of our particle filter algorithm compared to existing techniques is that it can work for the full range acquisition of carrier offsets

sequential estimation of hidden arma processes by particle filtering part ii this is part ii of a series of two papers where we address sequential estimation of wide sense stationary autoregressive moving average arma state processes by particle filtering in part i we considered a state space model where the state was an arma process of known order and where the parameters of the process could be known or unknown in this paper we extend our work from part i by considering the same type of models with the added complexity that the arma processes are now of unknown order instead of working on a scheme that first tracks the state by operating with different assumed models and then selects the best model by using a predefined criterion we present a method that directly estimates the state without the need of knowing the model order we derive the transition density of the state for unknown arma model order and propose a particle filter based on that density and the empirical bayesian methodology we demonstrate the performance of the proposed method with computer simulations and compare it with the methods from part i

deformations of group actions let g be a non compact real algebraic group and g a lattice one purpose of this paper is to show that there is a smooth volume preserving mixing action of g or on a compact manifold which admits a smooth deformation in fact we prove a stronger statement by exhibiting large finite dimensional spaces of deformations we also describe some other rather special deformations when g so 1 n

markov chain monte carlo for dynamic generalised linear models summary this paper presents a new methodological approach for carrying out bayesian inference about dynamic models for exponential family observations the approach is simulationbased and involves the use of markov chain monte carlo techniques a metropolishastings algorithm is combined with the gibbs sampler in repeated use of an adjusted version of normal dynamic linear models different alternative schemes based on sampling from the system disturbances and state parameters separately and in a block are derived and compared the approach is fully bayesian in obtaining posterior samples with state parameters and unknown hyperparameters illustrations with real datasets with sparse counts and missing values are presented extensions to accommodate more general evolution forms and distributions for observations and disturbances are outlined

on raghunathan s measure conjecture this paper represents the last in our three part series on raghunathan s measure conjecture see r1 r2 for parts i and ii more specifically let g be a real lie group all groups in this paper are assumed to be second countable with the lie algebra r a discrete subgroup of g and ir g r g the projection lwg rg the group g acts by right translations on r g x x g x e r g g e g let gt be a borel probability measure on r g define

a proximal bundle method with approximate subgradient linearizations we give a proximal bundle method for minimizing a convex function f over a closed convex set it only requires evaluating f and its subgradients with an accuracy epsilon 0 which is fixed but possibly unknown it asymptotically finds points that are epsilon optimal when applied to lagrangian relaxation it allows for epsilon accurate solutions of lagrangian subproblems and finds epsilon optimal solutions of convex programs

on some properties of markov chain monte carlo simulation methods based on the particle filter abstract andrieu et al 2010 prove that markov chain monte carlo samplers still converge to the correct posterior distribution of the model parameters when the likelihood estimated by the particle filter with a finite number of particles is used instead of the likelihood a critical issue for performance is the choice of the number of particles we add the following contributions first we provide analytically derived practical guidelines on the optimal number of particles to use second we show that a fully adapted auxiliary particle filter is unbiased and can drastically decrease computing time compared to a standard particle filter third we introduce a new estimator of the likelihood based on the output of the auxiliary particle filter and use the framework of del moral 2004 to provide a direct proof of the unbiasedness of the estimator fourth we show that the results in the article apply more generally to markov chain monte carlo sampling schemes with the likelihood estimated in an unbiased manner

dynamic conditional independence models and markov chain monte carlo methods abstract in dynamic statistical modeling situations observations arise sequentially causing the model to expand by progressive incorporation of new data items and new unknown parameters for example in clinical monitoring patients and data arrive sequentially and new patient specific parameters are introduced with each new patient markov chain monte carlo mcmc might be used for continuous updating of the evolving posterior distribution but would need to be restarted from scratch at each expansion stage thus mcmc methods are often too slow for real time inference in dynamic contexts by combining mcmc with importance resampling we show how real time sequential updating of posterior distributions can be effected the proposed dynamic sampling algorithms use posterior samples from previous updating stages and exploit conditional independence between groups of parameters to allow samples of parameters no longer of interest to be discarded such as when a patient dies or is discharged we apply the

a sequential monte carlo method for motif discovery we propose a sequential monte carlo smc based motif discovery algorithm that can efficiently detect motifs in datasets containing a large number of sequences the statistical distribution of the motifs is modeled by an underlying position weight matrix pwm and both the pwm and the positions of the motifs within the sequences are estimated by the smc algorithm the proposed smc motif discovery technique can locate motifs under a number of scenarios including the single block model two block model with unknown gap length motifs of unknown lengths motifs with unknown abundance and sequences with multiple unique motifs the accuracy of the smc motif discovery algorithm is shown to be superior to that of the existing methods based on mcmc or em algorithms furthermore it is shown that the proposed method can be used to improve the results of existing motif discovery algorithms by using their results as the priors for the smc algorithm

constrained bundle methods for upper inexact oracles with application to joint chance constrained energy problems joint chance constrained problems give rise to many algorithmic challenges even in the convex case i e when an appropriate transformation of the probabilistic constraint is a convex function its cutting plane linearization is just an approximation produced by an oracle providing subgradient and function values that can only be evaluated inexactly as a result the cutting plane model may lie above the true constraint for dealing with such upper inexact oracles and still solving the problem up to certain precision a special numerical algorithm must be put in place we introduce a family of constrained bundle methods based on the so called improvement functions that is shown to be convergent and encompasses many previous approaches as well as new algorithms depending on the oracle accuracy we analyze to what extent the considered methods solve the joint chance constrained program the approach is assessed on real life energy problems arising when dealing with stochastic hydroreservoir management

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

a gradient formula for linear chance constraints under gaussian distribution we provide an explicit gradient formula for linear chance constraints under a possibly singular multivariate gaussian distribution this formula allows one to reduce the calculus of gradients to the calculus of values of the same type of chance constraints in smaller dimension and with different distribution parameters this is an important aspect for the numerical solution of stochastic optimization problems because existing efficient codes for e g calculating singular gaussian distributions or regular gaussian probabilities of polyhedra can be employed to calculate gradients at the same time moreover the precision of gradients can be controlled by that of function values which is a great advantage over using finite difference approximations finally higher order derivatives are easily derived explicitly the use of the obtained formula is illustrated for an example of a transportation network with stochastic demands

a method of centers with approximate subgradient linearizations for nonsmooth convex optimization we give a proximal bundle method for constrained convex optimization it requires only evaluating the problem functions and their subgradients with an unknown accuracy epsilon employing a combination of the classic method of centers improvement function with an exact penalty function it does not need a feasible starting point it asymptotically finds points with at least epsilon optimal objective values that are epsilon feasible when applied to the solution of linear programming problems via column generation it allows for epsilon accurate solutions of column generation subproblems

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

a polyhedral study on chance constrained program with random right hand side the essential structure of the mixed integer programming formulation for chance constrained program ccp is the intersection of multiple mixing sets with a 0 1 knapsack to improve our computational capacity on ccp an underlying substructure the single mixing set with a 0 1 knapsack has received substantial attentions recently in this study we consider a ccp problem with stochastic right hand side under a finite discrete distribution we first present a family of strong inequalities that subsumes known facet defining ones for that single mixing set due to the flexibility of our generalized inequalities we develop a new separation heuristic that has a complexity much less than existing one and guarantees generated cutting planes are facet defining for the polyhedron of ccp then we study lifting and superadditive lifting on knapsack cover inequalities and provide an implementable procedure on deriving another family of strong inequalities for the single mixing set finally different from the traditional approach that aggregates original constraints to investigate polyhedral implications due to their interactions we propose a novel blending procedure that produces strong valid inequalities for ccp by integrating those derived from individual mixing sets we show that under certain conditions they are the first type of facet defining inequalities describing intersection of multiple mixing sets and design an efficient separation heuristic for implementation in the computational experiments we perform a systematic study and illustrate the efficiency of the proposed inequalities on solving chance constrained static probabilistic lot sizing problems

an inexact bundle variant suited to column generation we give a bundle method for constrained convex optimization instead of using penalty functions it shifts iterates towards feasibility by way of a slater point assumed to be known besides the method accepts an oracle delivering function and subgradient values with unknown accuracy our approach is motivated by a number of applications in column generation in which constraints are positively homogeneous so that zero is a natural slater point and an exact oracle may be time consuming finally our convergence analysis employs arguments which have been little used so far in the bundle community the method is illustrated on a number of cutting stock problems

dynamic generalized linear models and bayesian forecasting abstract dynamic bayesian models are developed for application in nonlinear non normal time series and regression problems providing dynamic extensions of standard generalized linear models a key feature of the analysis is the use of conjugate prior and posterior distributions for the exponential family parameters this leads to the calculation of closed standard form predictive distributions for forecasting and model criticism the structure of the models depends on the time evolution of underlying state variables and the feedback of observational information to these variables is achieved using linear bayesian prediction methods data analytic aspects of the models concerning scale parameters and outliers are discussed and some applications are provided dynamic bayesian models are developed for application in nonlinear non normal time series and regression problems providing dynamic extensions of standard generalized linear models a key feature of the analysis is the use of conjugate prior and

sequential monte carlo methods for state and parameter estimation in abruptly changing environments this paper develops a novel sequential monte carlo smc approach for joint state and parameter estimation that can deal efficiently with abruptly changing parameters which is a common case when tracking maneuvering targets the approach combines bayesian methods for dealing with change points with methods for estimating static parameters within the smc framework the result is an approach that adaptively estimates the model parameters in accordance with changes to the target s trajectory the developed approach is compared against the interacting multiple model imm filter for tracking a maneuvering target over a complex maneuvering scenario with nonlinear observations in the imm filter a large combination of models is required to account for unknown parameters in contrast the proposed approach circumvents the combinatorial complexity of applying multiple models in the imm filter through bayesian parameter estimation techniques the developed approach is validated over complex maneuvering scenarios where both the system parameters and measurement noise parameters are unknown accurate estimation results are presented

eventual convexity of probability constraints with elliptical distributions probability constraints are often employed to intuitively define safety of given decisions in optimization problems they simply express that a given system of inequalities depending on a decision vector and a random vector is satisfied with high enough probability it is known that even if this system is convex in the decision vector the associated probability constraint is not convex in general in this paper we show that some degree of convexity is still preserved for the large class of elliptical random vectors encompassing for example gaussian or student random vectors more precisely our main result establishes that under mild assumptions eventual convexity holds i e the probability constraint is convex when the safety level is large enough we also provide tools to compute a concrete convexity certificate from nominal problem data our results are illustrated on several examples including the situation of polyhedral systems with random technology matrices and arbitrary covariance structure

an incremental method for solving convex finite min max problems we introduce a new approach to minimizing a function defined as the pointwise maximum over finitely many convex real functions next referred to as the component functions with the aim of working on the basis of incomplete knowledge of the objective function a descent algorithm is proposed which need not require at the current point the evaluation of the actual value of the objective function namely of all the component functions thus extending to min max problems the philosophy of the incremental approaches widely adopted in the nonlinear least squares literature given the nonsmooth nature of the problem we resort to the well established machinery of bundle methods we provide global convergence analysis of our method and in addition we study a subgradient aggregation scheme aimed at simplifying the problem of finding a tentative step this paper is completed by the numerical results obtained on a set of standard test problems

a sequential monte carlo filter for joint linear nonlinear state estimation with application to ds cdma a sequential monte carlo filter is considered which combines previously developed sequential importance sampling sis techniques for conditional linear gaussian models with measurement linearization for construction of approximate simulation densities the resulting sequential monte carlo kalman filter smc kf consists of a bank of conventional kalman filters individually tuned to sampled trajectories of the nonlinear state variables sampling is according to a gaussian distribution with mean and covariance determined by extended kalman filter type equations the smc kf is then applied to joint delay and multipath channel estimation in direct sequence code division multiple access ds cdma a combined analytical simulation technique is employed to compare performance of the smc kf and a previously derived extended kalman filter ekf based ds cdma channel estimator

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

following a moving target monte carlo inference for dynamic bayesian models markov chain monte carlo mcmc sampling is a numerically intensive simulation technique which has greatly improved the practicality of bayesian inference and prediction however mcmc sampling is too slow to be of practical use in problems involving a large number of posterior target distributions as in dynamic modelling and predictive model selection alternative simulation techniques for tracking moving target distributions known as particle filters which combine importance sampling importance resampling and mcmc sampling tend to suffer from a progressive degeneration as the target sequence evolves we propose a new technique based on these same simulation methodologies which does not suffer from this progressive degeneration

measurable quotients of unipotent translations on homogeneous spaces let u be a nilpotent unipotent subgroup of a lie group g and let f be a closed subgroup of g marina ratner showed that every ergodic u invariant probability measure on the homogeneous space f g is of a simple algebraic form we use this fundamental new result to show that every measurable quotient of the u action on j g is of a simple algebraic form roughly speaking any quotient is a double coset space a g k

divide to conquer decomposition methods for energy optimization modern electricity systems provide a plethora of challenging issues in optimization the increasing penetration of low carbon renewable sources of energy introduces uncertainty in problems traditionally modeled in a deterministic setting the liberalization of the electricity sector brought the need of designing sound markets ensuring capacity investments while properly reflecting strategic interactions in all these problems hedging risk possibly in a dynamic manner is also a concern the fact of representing uncertainty and or competition of different companies in a multi settlement power market considerably increases the number of variables and constraints for this reason usually a trade off needs to be found between modeling and numerical tractability the more details are brought into the model the harder becomes the optimization problem for structured optimization and generalized equilibrium problems we explore some variants of solution methods based on lagrangian relaxation and on benders decomposition throughout we keep as a leading thread the actual practical value of such techniques in terms of their efficiency to solve energy related problems

practical filtering with sequential parameter learning summary the paper develops a simulation based approach to sequential parameter learning and filtering in general state space models our approach is based on approximating the target posterior by a mixture of fixed lag smoothing distributions parameter inference exploits a sufficient statistic structure and the methodology can be easily implemented by modifying state space smoothing algorithms we avoid reweighting particles and hence sample degeneracy problems that plague particle filters that use sequential importance sampling the method is illustrated by using two examples a benchmark auto regressive model with observation error and a high dimensional dynamic spatiotemporal model we show that the method provides accurate inference in the presence of outliers model misspecification and high dimensionality

joinings of higher rank diagonalizable actions on locally homogeneous spaces we classify joinings between a fairly general class of higher rank diagonalizable actions on locally homogeneous spaces in particular we classify joinings of the action of a maximal r split torus on g with g a simple lie group of r rank 2 and g a lattice we deduce from this a classification of measurable factors of such actions as well as certain equidistribution properties

gradient formulae for nonlinear probabilistic constraints with gaussian and gaussian like distributions probabilistic constraints represent a major model of stochastic optimization a possible approach for solving probabilistically constrained optimization problems consists in applying nonlinear programming methods to do so one has to provide sufficiently precise approximations for values and gradients of probability functions for linear probabilistic constraints under gaussian distribution this can be done successfully by analytically reducing these values and gradients to values of gaussian distribution functions and computing the latter for instance by genz s code for nonlinear models one may fall back on the spherical radial decomposition of gaussian random vectors and apply for instance deak s sampling scheme for the uniform distribution on the sphere in order to compute values of corresponding probability functions the present paper demonstrates how the same sampling scheme can be used to simultaneously compute gradients of these probability functions more precisely we prove a formula repre

a self organizing state space model a self organizing filter and smoother for the general nonlinear non gaussian state space model is proposed an expanded state space model is defined by augmenting the state vector with the unknown parameters of the original state space model the state of the augmented state space model and hence the state and the parameters of the original state space model are estimated simultaneously by either a non gaussian filter smoother or a monte carlo filter smoother in contrast to maximum likelihood estimation of model parameters in ordinary state space modeling for which the recursive filter computation has to be done many times model parameter estimation in the proposed self organizing filter smoother is achieved with only two passes of the recursive filter and smoother operations examples such as automatic tuning of dispersion and the shape parameters adaptation to changes of the amplitude of a signal in seismic data state estimation for a nonlinear state space model with unknown parameters and seasonal adjustment with a nonlinear model with changing variance parameters are shown to exemplify the usefulness of the proposed method

the estimation of time invariant parameters of noisy nonlinear oscillatory systems the inverse problem of estimating time invariant static parameters of a nonlinear system exhibiting noisy oscillation is considered in this paper firstly a markov chain monte carlo mcmc simulation is used for the time invariant parameter estimation which exploits a non gaussian filter namely the ensemble kalman filter enkf for state estimation required to compute the likelihood function secondly a recently proposed particle filter pf that uses the enkf for its proposal density for the state estimation has been adapted for combined state and parameter estimation numerical illustrations highlight the strengths and limitations of the mcmc enkf and pf algorithms for time invariant parameter estimation for low measurement noise and dense measurement data the performances of the mcmc enkf and pf algorithms are comparable for high measurement noise and sparse observational data the enkf fails to provide accurate parameter estimates hence the adapted pf algorithm becomes necessary in order to obtain parameter estimates comparable in accuracy to the mcmc simulation with enkf it highlights the fact that the augmented state space model for the combined state and parameter estimation contains stronger nonlinearity than the original state space model hence the enkf effectively handles the state estimation of the original state space model but it fails for the combined state and parameter estimation using the augmented system the effectiveness of the enkf for the state estimation is therefore leveraged in the mcmc simulation for the time invariant parameter estimation in order to obtain accurate parameter estimates using the augmented system the adapted pf becomes necessary to match the parameter estimates obtained using the mcmc simulation complemented by enkf for likelihood function computation

rigidity of group actions on homogeneous spaces iii consider homogeneous g h and g f for an s algebraic group g a lattice acts on the left strictly conservatively the following rigidity results are obtained morphisms factors and joinings defined apriori only in the measurable category are in fact algebraically constrained arguing in an elementary fashion we manage to classify all the measurable commuting with the action assuming ergodicity we find they are algebraically defined

local scale models state space alternative to integrated garch processes state space alternative to autoregressive conditional heteroskedasticity models are proposed the initial model which is labelled the gaussian local scale model has a measurement density which is gaussian conditional on the unobservable precision the precision is assumed to be a gamma variable which evolves by being scaled by a beta variable the resulting forecast is a student s t random variable with a scale which is approximately an exponentially weighted moving average ewma of the squares of the past observations the degrees of freedom of the student s t distribution is controlled by the size of the discount parameter of the ewma procedure the gaussianity of the measurement density is potentially inadequate when the model is applied to heavy tailed finance data instead this assumption can be replaced by an exponential power density which allows the observed excess kurtosis to be modelled the choice of the exponential power means that the model still maintains conjugacy so allowing the derivation of an exact filter and likelihood function this model is called the generalised local scale model it has been used to model two exchange rate series

inexact bundle methods for two stage stochastic programming stochastic programming problems arise in many practical situations in general the deterministic equivalents of these problems can be very large and may not be solvable directly by general purpose optimization approaches for the particular case of two stage stochastic programs we consider decomposition approaches akin to a regularized l shaped method that can handle inexactness in the subproblem solution from a nonsmooth optimization perspective these variants amount to applying a proximal bundle method to an oracle that gives inaccurate values for the objective function and a subgradient rather than forcing early termination of the subproblem optimization to define inexact oracles we select a small subset of scenarios for which the subproblem solution is exact and we replace the information for the remaining scenarios by a fast procedure that does not involve solving an optimization problem the inaccurate oracle information creates inexact cuts in the master program which are well handled by th

orbit equivalence rigidity consider a countable group acting ergodically by measure p reserving transformations on a probability space x and let r be the corresponding orbit equivalence relation on x the following rigidity phenomenon is shown there exist group actions such that the equivalence relation r on x determines the group and the action x uniquely up to finite groups the natural action of sln z on the n torus r n z n for n 2 is one of such examples the interpretation of these results in the context of von neumann algebras provides some support to the conjecture of connes on rigidity of group algebras for groups with property t our rigidity results also give examples of countable equivalence relations of type ii1 which cannot be generated mod 0 by a free action of any group this gives a negative answer to a long standing problem of feldman and moore

sequential reconstruction of driving forces from nonlinear nonstationary dynamics abstract this paper describes a functional analysis based method for the estimation of driving forces from nonlinear dynamic systems the driving forces account for the perturbation inputs induced by the external environment or the secular variations in the internal variables of the system the proposed algorithm is applicable to the problems for which there is too little or no prior knowledge to build a rigorous mathematical model of the unknown dynamics we derive the estimator conditioned on the differentiability of the unknown system s mapping and smoothness of the driving force the proposed algorithm is an adaptive sequential realization of the blind prediction error method where the basic idea is to predict the observables and retrieve the driving force from the prediction error our realization of this idea is embodied by predicting the observables one step into the future using a bank of echo state networks esn in an online fashion and then extracting the raw estimates from the prediction error and smoothing these estimates in two adaptive filtering stages the adaptive nature of the algorithm enables to retrieve both slowly and rapidly varying driving forces accurately which are illustrated by simulations logistic and moran ricker maps are studied in controlled experiments exemplifying chaotic state and stochastic measurement models the algorithm is also applied to the estimation of a driving force from another nonlinear dynamic system that is stochastic in both state and measurement equations the results are judged by the posterior cramer rao lower bounds the method is finally put into test on a real world application extracting sun s magnetic flux from the sunspot time series