the painleve property for partial differential equations in this paper we define the painleve property for partial differential equations and show how it determines in a remarkably simple manner the integrability the backlund transforms the linearizing transforms and the lax pairs of three well known partial differential equations burgers equation kdv equation and the modified kdv equation this indicates that the painleve property may provide a unified description of integrable behavior in dynamical systems ordinary and partial differential equations while at the same time providing an efficient method for determining the integrability of particular systems

on the influence of sampling and observation times on estimation of the bandwidth parameter of a gauss markov process the statistical problem of estimating the bandwidth parameter of a gauss markov gm process from a realization of fixed and finite duration t at selectable sampling interval spl delta is addressed in this paper as the observation time t is fixed and finite the variance of estimated autocorrelation and continuous time parameter does not vanish as spl delta approaches 0 this necessitates a second order taylor expansion in deriving the parameter estimator bias and variance the second order taylor expansion produces better bias and variance results than a first order one does the distribution of the estimator is also discussed according to the gradient change of the variance a key result is that three sample size regions which are termed finite large and very large corresponding to substantial gradual and very slight decrease in the variance of the parameter estimator respectively are quantified in terms of analysis bw the three regions are 23 35 35 55 and 55 spl infin db the characterization of the tradeoff between the variance decrease and sampling rate results in a practical guideline for choosing sampling rate these results are applied to the prediction problems of a time invariant gm process to show their value

feedback quadratic filtering abstract this paper concerns the state estimation problem for linear discrete time non gaussian systems it is known that filters based on quadratic functions of the measurements processes quadratic filter improve the estimation accuracy of the optimal linear filter in order to enlarge the class of systems which can be processed by a quadratic filter we rewrite the system model by introducing an output injection term the resulting filter named the feedback quadratic filter can be applied also to non asymptotically stable systems we prove that the performance of the feedback quadratic filter depends on the gain parameter of the output term which can be chosen so that the estimation error is always less than or equal to the quadratic filter

on the net reproduction rate of continuous structured populations with distributed states at birth we consider a nonlinear structured population model with a distributed recruitment term the question of the existence of non trivial steady states can be treated at least in three different ways one approach is to study spectral properties of a parametrised family of unbounded operators the alternative approach which we develop here is based on the reformulation of the partial differential equation as an integral equation in this context we introduce a density dependent net reproduction rate and discuss its relationship to a biologically meaningful quantity finally we discuss a third approach which is based on a finite rank approximation of the recruitment operator

bidirectional solitons on water a theory of bidirectional solitons on water is developed by using an integrable boussinesq surface variable equation we present an explicit transformation between the system and a member of the ablowitz kaup newell segur system and derive an exact multisoliton solution by using a darboux transformation the phase shifts and the maximum wave heights during the interaction are studied for two soliton overtaking and head on collisions they agree with the korteweg de vries solution for overtaking collision and the perturbation solution for head on collision

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

darboux transformation for the modified veselov novikov equation a darboux transformation is constructed for the modified veselov novikov equation by means of the darboux transformation two families of explicit solutions of this equation are given

a unified framework for deterministic and probabilistic mathscr d stability analysis of uncertain polynomial matrices in control theory we are often interested in robust mathscr d stability analysis which aims at verifying if all the eigenvalues of an uncertain matrix lie in a given region mathscr d although many algorithms have been developed to provide conditions for an uncertain matrix to be robustly mathscr d stable the problem of computing the probability of an uncertain matrix to be mathscr d stable is still unexplored the goal of this paper is to fill this gap in two directions first the only constraint on the stability region mathscr d that we impose is that its complement is a semialgebraic set this comprises many important cases in robust control theory second the mathscr d stability analysis problem is formulated in a probabilistic framework by assuming that only few probabilistic information is available on the uncertain parameters such as support and some moments we will show how to compute the minimum probability that the matrix is mathscr d stable by using convex relaxations based on the theory of moments

the interacting multiple model algorithm for systems with markovian switching coefficients an important problem in filtering for linear systems with markovian switching coefficients dynamic multiple model systems is the management of hypotheses which is necessary to limit the computational requirements a novel approach to hypotheses merging is presented for this problem the novelty lies in the timing of hypotheses merging when applied to the problem of filtering for a linear system with markovian coefficients the method is an elegant way to derive the interacting multiple model imm algorithm evaluation of the imm algorithm shows that it performs well at a relatively low computational load these results imply a significant change in the state of the art of approximate bayesian filtering for systems with markovian coefficients

use of the kalman filter for inference in state space models with unknown noise distributions the kalman filter is frequently used for state estimation in state space models when the standard gaussian noise assumption does not apply a problem arises however in that inference based on the incorrect gaussian assumption can lead to misleading or erroneous conclusions about the relationship of the kalman filter estimate to the true unknown state this note shows how inequalities from probability theory associated with the probabilities of convex sets have potential for characterizing the estimation error of a kalman filter in such a non gaussian distribution free setting

steady states of a selection mutation model for an age structured population abstract we introduce a selection mutation model for an age and age at maturity structured population the age at maturity is considered an evolutionary trait on which the vital rates depend subject to selection by competition and to mutation modelled by a birth term which takes the form of a convolution like operator we prove well posedness of the initial value problem and the existence of non trivial steady states under suitable hypotheses which yield uniqueness when the interaction variable is one dimensional

unimodality convexity and applications properties of univariate unimodal distributions concepts of multivariate unimodality some more notions of unimodality unimodality for discrete distributions unimodality of infinitely divisible distributions unimodality and notions of dependence ordering of distributions by peakedness applications of unimodality in statistical inference convexity in reliability theory appendix

darboux transformation and hamiltonian structure for the jaulent miodek hierarchy abstract starting from the jaulent miodek spectral problem we derive the associated hierarchy of nonlinear evolution equations in this paper it is shown that this hierarchy is completely integrable in the liouville sense and possesses the hamiltonian structure moreover by virtue of symbolic computation two types of darboux transformations for the whole hierarchy are explicitly constructed which enables us to find the new soliton like shock and anti shock solutions for the jaulent miodek hierarchy figures are presented to discuss the properties of the new soliton like solutions

on gibbs sampling for state space models summary we show how to use the gibbs sampler to carry out bayesian inference on a linear state space model with errors that are a mixture of normals and coefficients that can switch over time our approach simultaneously generates the whole of the state vector given the mixture and coefficient indicator variables and simultaneously generates all the indicator variables conditional on the state vectors the states are generated efficiently using the kalman filter we illustrate our approach by several examples and empirically compare its performance to another gibbs sampler where the states are generated one at a time the empirical results suggest that our approach is both practical to implement and dominates the gibbs sampler that generates the states one at a time

robust bayesian sample size determination in clinical trials this article deals with determination of a sample size that guarantees the success of a trial we follow a bayesian approach and we say an experiment is successful if it yields a large posterior probability that an unknown parameter of interest an unknown treatment effect or an effects difference is greater than a chosen threshold in this context a straightforward sample size criterion is to select the minimal number of observations so that the predictive probability of a successful trial is sufficiently large in the paper we address the most typical criticism to bayesian methods their sensitivity to prior assumptions by proposing a robust version of this sample size criterion specifically instead of a single distribution we consider a class of plausible priors for the parameter of interest robust sample sizes are then selected by looking at the predictive distribution of the lower bound of the posterior probability that the unknown parameter is greater than a chosen threshold for their flexibility and mathematical tractability we consider classes of epsilon contamination priors as specific applications we consider sample size determination for a phase iii trial

bayesian inference for linear dynamic models with dirichlet process mixtures using kalman techniques it is possible to perform optimal estimation in linear gaussian state space models here we address the case where the noise probability density functions are of unknown functional form a flexible bayesian nonparametric noise model based on dirichlet process mixtures is introduced efficient markov chain monte carlo and sequential monte carlo methods are then developed to perform optimal batch and sequential estimation in such contexts the algorithms are applied to blind deconvolution and change point detection experimental results on synthetic and real data demonstrate the efficiency of this approach in various contexts

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

symmetry group and exact solutions for the 2 1 dimensional ablowitz kaup newell segur equation a 2 1 dimensional ablowitz kaup newell segur akns system is obtained from the potential boiti leon manna pempinelli equation by means of an asymptotically exact reduction method based on fourier expansion and spatiotemporal rescaling furthermore applying the modified direct method to the 2 1 dimensional akns system we get its symmetry and the relationship between the new solution and the old one based on the relationship a new solution can be obtained by using a given solution of the equation

validation of state space models from a single realization of non gaussian measurements a methodology is presented for testing whether a dynamic model in linear state space form accurately describes the system under consideration unlike existing procedures it is not necessary to assume that all of the random terms in the model are normally distributed the methodology is based on a single realization of observations and is relatively easy to implement since it relies on a normalized kalman filter state estimate the testing procedure rests on an asymptotic distribution theory for the filter estimate

uncertainties for recursive estimators in nonlinear state space models with applications to epidemiology consider a nonlinear dynamic system where one wishes to estimate a state vector using noisy measurements many algorithms have been proposed to address this problem among them the extended kalman filter and its variants and constant gain stochastic approximation to quantify the efficacy of these algorithms it is necessary to describe the distribution of the state estimation error typically performance has been measured by the estimation error covariance alone which does not provide enough information to probabilistically quantify the estimation accuracy by casting the estimation error in an autoregressive type form this paper addresses the broader question of the distribution of the error for a general class of recursive algorithms we illustrate the distributional results in an epidemiological problem of disease monitoring

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

the kantorovich inequality for error analysis of the kalman filter with unknown noise distributions the state space model with random noises is widely used to model dynamic systems in many practical problems the noise terms will have unknown probability distributions which is contrary to the usual assumption of gaussian noises made in state vector estimation this assumption is usually made for reasons of mathematical tractability a problem arises however in that inference based on the incorrect gaussian assumption can lead to misleading or erroneous conclusions this note shows how the kantorovich inequality from probability theory has potential for characterizing the estimation error of a kalman filter in such a non gaussian distribution free setting

bayes theorem for choquet capacities we give an upper bound for the posterior probability of a measurable set a when the prior lies in a class of probability measures p the bound is a rational function of two choquet integrals if p is weakly compact and is closed with respect to majorization then the bound is sharp if and only if the upper prior probability is 2 alternating the result is used to compute bounds for several sets of priors used in robust bayesian inference the result may be regarded as a characterization of 2 alternating choquet capacities

the generalized moment based filter can we solve the filtering problem from the only knowledge of few moments of the noise terms in this technical note by exploiting set of distributions based filtering we solve this problem without introducing additional assumptions on the distributions of the noises e g gaussianity or on the final form of the estimator e g linear estimator given the moments e g mean and variance of random variable x it is possible to define the set of all distributions that are compatible with the moments information this set can be equivalently characterized by its extreme distributions a family of mixtures of dirac s deltas the lower and upper expectation of any function g of x are obtained in correspondence of these extremes and can be computed by solving a linear programming problem the filtering problem can then be solved by running iteratively this linear programming problem in this technical note we discuss theoretical properties of this filter we show the connection with set membership estimation and its practical applications

backlund transformations for the schrodinger equation with a spectral dependence in the potential the schrodinger equation on the line with a potential depending linearly on the spectral parameter is considered it is shown that this spectral problem admits one parameter called elementary backlund transformations and two parameter called full backlund transformations the transformations of the spectral data under all these backlund transformations bts are explicitly computed different nonlinear superposition formulae for the different bts considered are given and used to obtain soliton solutions of the evolution equations associated with the spectral problem

loop soliton interaction in an integrable nonlinear telegraphy model reciprocal and backlund transformations an integrable telegraphy equation linked in turn to the geometry of pseudospherical surfaces and a class of model nonlinear elastic stress strain laws descriptive of ideally hard material response is investigated a constant coefficient ideal formalism is introduced which leads to a reciprocal transformation between this nonlinear telegraphy equation and a system compatible with the classical sine gordon equation a backlund transformation is then constructed which is used to analyse two loop soliton interaction the latter exhibits a novel exchange particle phenomenon

robust steady state filtering for systems with deterministic and stochastic uncertainties for uncertain systems containing both deterministic and stochastic uncertainties we consider two problems of optimal filtering the first is the design of a linear time invariant filter that minimizes an upper bound on the mean energy gain between the noise affecting the system and the estimation error the second is the design of a linear time invariant filter that minimizes an upper bound on the asymptotic mean square estimation error when the plant is driven by a white noise we present filtering algorithms that solve each of these problems with the filter parameters determined via convex optimization based on linear matrix inequalities we demonstrate the performance of these robust algorithms on a numerical example consisting of the design of equalizers for a communication channel

on a class of physically important integrable equations abstract a methodology introduced by fuchssteiner and the author is used to derive a class of physically important integrable evolution equations among these equations are integrable generalizations of the korteweg devries kdv of the modified kdv of the nonlinear schrodinger nls and of the sine gordon equations the modeling of water waves as well as general asymptotic considerations are used to illustrate the occurrence of the generalized modified kdv and nls equations respectively

evaluation of convergence rate in the central limit theorem for the kalman filter state space models are used for modeling of many physical and economic processes an asymptotic distribution theory for the state estimate from a kalman filter in the absence of the usual gaussian assumption was presented by spall and wall 1984 they proved the central limit theorem for state estimators when the random terms in the model have arbitrary distribution in this study some convergence rates in the central limit theorem are given these convergence rates are used for the development of a nonparametric test of the validity of the model

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

fourier hermite kalman filter in this note we shall present a new class of gaussian filters called fourier hermite kalman filters fourier hermite kalman filters are based on expansion of nonlinear functions with the fourier hermite series in same way as the traditional extended kalman filter is based on the taylor series the first order truncation of the fourier hermite series gives the previously known statistically linearized filter

ranges of posterior probabilities for quasiunimodal priors with specified quantiles abstract suppose several quantiles of the prior distribution for are specified or equivalently the prior probabilities of a partitioning collection of intervals ii are given in addition suppose that the prior distribution is assumed to be unimodal rather than selecting a single prior distribution to perform a bayesian analysis it is of interest to consider the class of all prior distributions compatible with these inputs for this class and unimodal likelihood functions the ranges of the posterior probabilities of the ii and the ranges of the posterior cdf at the specified prior quantiles were determined in berger and o hagan in press unfortunately calculations with this class can be difficult here a similar much more easily analyzed class of quasiunimodal prior distributions is considered and compared with other classes

darboux transformation and solutions for an equation in 2 1 dimensions painleve analysis and the singular manifold method are the tools used in this paper to perform a complete study of an equation in 2 1 dimensions this procedure has allowed us to obtain the lax pair darboux transformation and functions in such a way that a plethora of different solutions with solitonic behavior can be constructed iteratively

sensitivity in bayesian statistics the prior and the likelihood abstract one paradigm for sensitivity analyses in bayesian statistics is to specify a reasonable class of priors and to compute the corresponding class of posterior inferences the class is chosen to represent uncertainty about the prior there is often additional uncertainty however about the family of sampling distributions this article introduces a method for computing ranges of posterior expectations over reasonable classes of sampling distributions that lie close to a given parametric family by treating the prior as a probability measure on the space of sampling distributions this article also gives a unified treatment to what are usually considered two separate problems sensitivity to the prior and sensitivity to the sampling model first the notion of close to is made explicit then an algorithm is given for turning ratio linear problems into sequences of linear problems in addition to solving the problem at hand the algorithm simplifies many other robust bayesian computational pro

robust bayesian analysis of a multivariate dynamic model abstract recently a bayesian approach has been widely used to infer parameters of complex models from finite sample data in business finance social and physical sciences bayesian applications in finance literature are growing due to their exposure to prior beliefs that macroeconomic variables influence the financial behavior of customers investors and firm s performance this paper employs a robust bayesian analysis model to capture a complex multi dimensional process and estimate the required parameters of interest it considers a class of prior distributions for the parameters that is a mixture of natural conjugate base priors and a contamination class of prior distributions the conditional type ii maximum likelihood posterior densities and posterior means for the coefficients vector and autoregressive parameter are derived for the coefficients vector and autoregressive parameter of interest the markov chain monte carlo mcmc method has been used for obtaining the marginal posterior densities and bayes estimators for various combinations of the parameters the usefulness of the model is demonstrated on indian financial firms balance sheets data between 1992 to 2015 to observe the sensitivity of the proposed model the result shows most of the corporate performance variables are significantly affecting the firm s profitability with the exception of interest coverage ratio

n soliton solutions of the kdv6 and mkdv6 equations the kdv6 and mkdv6 equations are solved through darboux matrix method by constructing darboux transformations for the deformed kdv and mkdv equations n soliton solutions of the kdv6 and mkdv6 equations are presented by using the darboux transformations and selecting nonconstant seed solutions of the kdv6 and mkdv6 equations

the kalman levy filter abstract the kalman filter combines forecasts and new observations to obtain an estimation which is optimal in the sense of a minimum average quadratic error the kalman filter has two main restrictions i the dynamical system is assumed linear and ii forecasting errors and observational noises are projected onto gaussian distributions here we offer an important generalization to the case where errors and noises have heavy tail distributions such as power laws and levy laws the main tool needed to solve this kalman levy filter is the tail covariance matrix which generalizes the covariance matrix in the case where it is mathematically ill defined i e for power law tail exponents 2 we present the general solution and discuss its properties on pedagogical examples the standard kalman gaussian filter is recovered for the case 2 the optimal kalman levy filter is found to deviate substantially from the standard kalman gaussian filter as deviates from 2 as decreases the filter favors more strongly the better one of the forecast and the observation based on the tail covariance matrix because a small exponent implies large errors with significant probabilities in terms of implementation the price to pay associated with the presence of heavy tail noise distributions is that the standard linear formalism valid for the gaussian case is transformed into a nonlinear matrix equation for the kalman levy filter direct numerical experiments in the univariate case confirms our theoretical predictions

testing a point null hypothesis the irreconcilability of p values and evidence abstract the problem of testing a point null hypothesis or a small interval null hypothesis is considered of interest is the relationship between the p value or observed significance level and conditional and bayesian measures of evidence against the null hypothesis although one might presume that a small p value indicates the presence of strong evidence against the null such is not necessarily the case expanding on earlier work especially edwards lindman and savage 1963 and dickey 1977 it is shown that actual evidence against a null as measured say by posterior probability or comparative likelihood can differ by an order of magnitude from the p value for instance data that yield a p value of 05 when testing a normal mean result in a posterior probability of the null of at least 30 for any objective prior distribution objective here means that equal prior weight is given the two hypotheses and that the prior is symmetric and nonincreasing away from the null other definiti

reconciling bayesian and frequentist evidence in the one sided testing problem abstract for the one sided hypothesis testing problem it is shown that it is possible to reconcile bayesian evidence against h 0 expressed in terms of the posterior probability that h 0 is true with frequentist evidence against h 0 expressed in terms of the p value in fact for many classes of prior distributions it is shown that the infimum of the bayesian posterior probability of h 0 is equal to the p value in other cases the infimum is less than the p value the results are in contrast to recent work of berger and sellke 1987 in the two sided point null case where it was found that the p value is much smaller than the bayesian infimum some comments on the point null problem are also given

bayes like decision making with upper and lower probabilities abstract we consider the use of interval valued probabilities to represent the support lent to the hypothesis that the parameter value lies in a subset a of the parameter set when we observe x know the likelihoods f e and have some prior information concerning the parameter our model for prior information is that of a salient prior distribution in which we have little confidence although we have much less confidence in any alternative prior we consider notions of acceptable and coherent decision making as well as notions of being able to achieve a bayes rule and least commitment throughout we are motivated to preserve some of the elements of bayesian decision making without thereby committing ourselves to unwarranted claims of knowledge

an event triggered approach to state estimation with multiple point and set valued measurements abstract in this work we consider state estimation based on the information from multiple sensors that provide their measurement updates according to separate event triggering conditions an optimal sensor fusion problem based on the hybrid measurement information namely point and set valued measurements is formulated and explored we show that under a commonly accepted gaussian assumption the optimal estimator depends on the conditional mean and covariance of the measurement innovations which applies to general event triggering schemes for the case that each channel of the sensors has its own event triggering condition closed form representations are derived for the optimal estimate and the corresponding error covariance matrix and it is proved that the exploration of the set valued information provided by the event triggering sets guarantees the improvement of estimation performance the effectiveness of the proposed event based estimator is demonstrated by extensive monte carlo simulation experiments for different categories of systems and comparative simulation with the classical kalman filter

ranges of posterior measures for priors with unimodal contaminations we consider the problem of robustness or sensitivity of given bayesian posterior criteria to specification of the prior distribution criteria considered include the posterior mean variance and probability of a set for credible regions and hypothesis testing uncertainty in an elicited prior go is modelled by an e contamination class f x 1 c 1t0 eq q e q where reflects the amount of probabilistic uncertainty in g and q is a class

slide window bounded error time varying systems identification this technical note presents a new identification method for discrete linear systems with time varying parameters based on bounded error approach it is assumed a bounded additive error on measurements and a bound on parameter variation each time instant the identification method uses a slide window along historical data and an explicit expression to provide an outer bound of the set of model parameters that is consistent with measurements model structure and bounds on error and variations considered furthermore the center estimation of the obtained outer solution set is a suitable nominal estimation of the parameters this center is the optimal solution of a least squares problem that penalizes the prediction error of the model and the parameter variations the explicit expression that provides the outer bound of the parameters and the optimal property of the center estimation are the main contributions of the technical note in order to clarify the proposed method an application example and a comparison with a previous recursive bounded error method are included

event based state estimation with time synchronous updates to reduce the amount of data transfer in networked systems measurements are usually taken only when an event occurs rather than at each synchronous sample instant however this complicates estimation problems considerably especially in the situation when no measurement is received anymore the goal of this paper is therefore to develop a state estimator that can successfully cope with event based measurements and attains an asymptotically bounded error covariance matrix to that extent a general mathematical description of event sampling is proposed this description is used to set up a state estimator with a hybrid update i e when an event occurs the estimated state is updated using the measurement while at synchronous instants the update is based on knowledge that the sensor value lies within a bounded subset of the measurement space furthermore to minimize computational complexity of the estimator the algorithm is implemented using a sum of gaussians approach the benefits of this implementation are demonstrated by an illustrative example of state estimation with event sampling

bayesian robustness and the stein effect abstract in simultaneous estimation of normal means it is shown that through use of the stein effect surprisingly large gains of a bayesian nature can be achieved at little or no cost if the prior information is misspecified this provides a justification in terms of robustness with respect to mis specification of the prior for employing the stein effect even when combining a priori independent problems i e problems in which no empirical bayes effects are obtainable to study this issue a class of minimax estimators that closely mimic the conjugate prior bayes estimators is introduced

a general model of size dependent population dynamics with nonlinear growth rate we study a general model of size dependent population dynamics with nonlinear growth rate the existence of a local solution is shown by using schauder s fixed point theorem uniqueness and continuous dependence on initial data are also established under additional conditions

a tutorial on particle filters for online nonlinear non gaussian bayesian tracking increasingly for many application areas it is becoming important to include elements of nonlinearity and non gaussianity in order to model accurately the underlying dynamics of a physical system moreover it is typically crucial to process data on line as it arrives both from the point of view of storage costs as well as for rapid adaptation to changing signal characteristics in this paper we review both optimal and suboptimal bayesian algorithms for nonlinear non gaussian tracking problems with a focus on particle filters particle filters are sequential monte carlo methods based on point mass or particle representations of probability densities which can be applied to any state space model and which generalize the traditional kalman filtering methods several variants of the particle filter such as sir asir and rpf are introduced within a generic framework of the sequential importance sampling sis algorithm these are discussed and compared with the standard ekf through an illustrative example

the polynomial approach to the lq non gaussian regulator problem through output injection in this paper an improved approach for the solution of the regulator problem for linear discrete time dynamical systems with non gaussian disturbances and quadratic cost functional is proposed it is known that a suboptimal recursive control can be derived from the classical linear quadratic gaussian lqg solution by substituting the linear filtering part with a quadratic or in general polynomial filter however we show that when the system is not asymptotically stable the polynomial control does not improve over the classical lqg solution due to the lack of the internal stability of the polynomial filter in order to enlarge the class of systems that can be controlled we propose a new method based on a suitable rewriting of the system by means of an output injection term we show that this allows us to overcome the problem and to design a polynomial optimal controller also for non asymptotically stable systems numerical results show the effectiveness of the method

soliton solutions for two nonlinear partial differential equations using a darboux transformation of the lax pairs two darboux transformations of the 1 1 dimensional wu zhang wz equation and the two component camassa holm 2ch system with the reciprocal transformation are obtained one loop and two loop soliton solutions and multisoliton like solutions of the 2ch system are obtained by using the darboux transformations and selecting different seed solutions of the corresponding equations the bidirectional soliton solutions of the 1 1 dimensional wz equation are also obtained the interactions of two soliton head on and overtaking collisions for the wz equation and the evolution of the two soliton like solutions for the 2ch system are studied

independent products in infinite spaces abstract probabilistic independence intended as the mutual irrelevance of given variables can be solidly founded on a notion of self consistency of an uncertainty model in particular when probabilities go imprecise there is nothing in this approach that prevents it from being adopted in very general setups and yet it has mostly been detailed for variables taking finitely many values in this mathematical study we complement previous research by exploring the extent to which such an approach can be generalised we focus in particular on the independent products of two variables we characterise the main notions including some of factorisation and productivity in the general case where both spaces can be infinite and show that however there are situations even in the case of precise probability where no independent product exists this is not the case as soon as at least one space is finite we study in depth this case at the frontiers of good behaviour detailing the relations among the most important notions we show for instance that being an independent product is equivalent to a certain productivity condition then we step back to the general case we give conditions for the existence of independent products and study ways to get around its inherent limitations

robust bayes and empirical bayes analysis with _ epsilon contaminated priors on considere deux directions dans l analyse bayesienne robuste la premiere consiste a determiner l etendue des probabilites a posteriori d un ensemble la seconde consiste a selectionner une bonne distribution a priori

on solutions of the two component camassa holm system following the approach of chen et al lett math phys 75 1 15 2006 we continue the study of the two component camassa holm system by using its relation with the first negative flow of the akns hierarchy we obtain a more general class of particular solutions including the multisoliton ones

an approach to robust bayesian analysis for multidimensional parameter spaces abstract in some multiparameter bayesian problems the prior is more naturally described as a joint density for all of the parameters and in others it is more naturally described as a product of marginal and conditional densities although ordinary quantile e contamination and density ratio classes of priors may be sensible choices for robust bayesian analyses in the former case they may be less satisfactory in the latter this article shows how to construct product classes of priors for use in the second case using one class of priors for the marginal and another for each conditional then the article introduces density bounded classes as an alternative to the more familiar classes for representing uncertainty about the prior it is often of interest to find tight bounds on posterior expectations as the prior ranges over the class of priors an apparently difficult nonlinear optimization problem regardless of which class of priors is used this article describes a technique for turning the problem into

robust filtering through coherent lower previsions the classical filtering problem is re examined to take into account imprecision in the knowledge about the probabilistic relationships involved imprecision is modeled in this paper by closed convex sets of probabilities we derive a solution of the state estimation problem under such a framework that is very general it can deal with any closed convex set of probability distributions used to characterize uncertainty in the prior likelihood and state transition models this is made possible by formulating the theory directly in terms of coherent lower previsions that is of the lower envelopes of the expectations obtained from the set of distributions the general solution is specialized to two particular classes of coherent lower previsions the first consists of a family of gaussian distributions whose means are only known to belong to an interval the second is the so called linear vacuous mixture model which is a family made of convex combinations of a known nominal distribution e g a gaussian with arbitrary distributions for the latter case we empirically compare the proposed estimator with the kalman filter this shows that our solution is more robust to the presence of modelling errors in the system and that hence appears to be a more realistic approach than the kalman filter in such a case

the simulation smoother for time series models summary recently suggested procedures for simulating from the posterior density of states given a gaussian state space time series are refined and extended we introduce and study the simulation smoother which draws from the multivariate posterior distribution of the disturbances of the model so avoiding the degeneracies inherent in state samplers the technique is important in gibbs sampling with non gaussian time series models and for performing bayesian analysis of gaussian time series

factorisation of energy dependent schrodinger operators miura maps and modified systems we consider the energy dependent schrodinger operator mathbb l sum limits i 0 n lambda i varepsilon i partial 2 u i which we have previously shown to be associated with multi hamiltonian structures 2 in this paper we use an unusual form of the lax approach to derive by asingle construction the time evolutions of the eigenfunctions of mathbb l the associated hamiltonian operators and the hamiltonian functionals we then generalise the well known factorisation of standard lax operators to the case of energy dependent operators the simple product of linear factors is replaced by a dependent quadratic form we thus generalise the resulting construction of miura maps and modified equations we show that for some of our systems there exists a sequence ofn such modifications therth modification possessing n r 1 hamiltonian structures

painleve property soliton like solutions and complexitons for a coupled variable coefficient modified korteweg de vries system in a two layer fluid model abstract as a model derived from a two layer fluid system which describes the atmospheric and oceanic phenomena a coupled variable coefficient modified korteweg de vries system is concerned in this paper with the help of symbolic computation its integrability in the painleve sense is investigated furthermore hirota s bilinear method is employed to construct the bilinear forms through the dependent variable transformations and soliton like solutions and complexitons are derived finally effects of variable coefficients are discussed graphically and it is concluded that the variable coefficients control the propagation trajectories of solitons and complexitons