ideal spatial adaptation by wavelet shrinkage summary with ideal spatial adaptation an oracle furnishes information about how best to adapt a spatially variable estimator whether piecewise constant piecewise polynomial variable knot spline or variable bandwidth kernel to the unknown function estimation with the aid of an oracle offers dramatic advantages over traditional linear estimation by nonadaptive kernels however it is a priori unclear whether such performance can be obtained by a procedure relying on the data alone we describe a new principle for spatially adaptive estimation selective wavelet reconstruction we show that variable knot spline fits and piecewise polynomial fits when equipped with an oracle to select the knots are not dramatically more powerful than selective wavelet reconstruction with an oracle we develop a practical spatially adaptive method riskshrink which works by shrinkage of empirical wavelet coefficients riskshrink mimics the performance of an oracle for selective wavelet reconstruction as well as it is possible to do so a new inequality in multivariate normal decision theory which we call the oracle inequality shows that attained performance differs from ideal performance by at most a factor of approximately 2 log n where n is the sample size moreover no estimator can give a better guarantee than this within the class of spatially adaptive procedures riskshrink is essentially optimal relying only on the data it comes within a factor log 2 n of the performance of piecewise polynomial and variableknot spline methods equipped with an oracle in contrast it is unknown how or if piecewise polynomial methods could be made to function this well when denied access to an oracle and forced to rely on data alone

coherent states associated with the wavefunctions and the spectrum of the isotonic oscillator classes of coherent states are presented by replacing the labelling parameter z of klauder perelomov type coherent states by confluent hypergeometric functions with specific parameters temporally stable coherent states for the isotonic oscillator hamiltonian are presented and these states are identified as a particular case of the so called mittag leffler coherent states

estimating normal means with a dirichlet process prior abstract in this article the dirichlet process prior is used to provide a nonparametric bayesian estimate of a vector of normal means in the past there have been computational difficulties with this model this article solves the computational difficulties by developing a gibbs sampler algorithm the estimator developed in this article is then compared to parametric empirical bayes estimators peb and nonparametric empirical bayes estimators npeb in a monte carlo study the monte carlo study demonstrates that in some conditions the peb is better than the npeb and in other conditions the npeb is better than the peb the monte carlo study also shows that the estimator developed in this article produces estimates that are about as good as the peb when the peb is better and produces estimates that are as good as the npeb estimator when that method is better

spectral analysis for discrete longitudinal data abstract we develop a fourier type of analysis for data consisting of many short strings x 1 x 2 x n with x i x i 1 x ip the paper offers an approach testing and residual analysis based on a group theoretic decomposition of the sample space this is illustrated on a physical chance type data set where it is natural to allow each string to have its own parameter i i d coin tossing with parameter varying from string to string the usual model is rejected

stepwise signal extraction via marginal likelihood this article studies the estimation of a stepwise signal to determine the number and locations of change points of the stepwise signal we formulate a maximum marginal likelihood estimator which can be computed with a quadratic cost using dynamic programming we carry out an extensive investigation on the choice of the prior distribution and study the asymptotic properties of the maximum marginal likelihood estimator we propose to treat each possible set of change points equally and adopt an empirical bayes approach to specify the prior distribution of segment parameters a detailed simulation study is performed to compare the effectiveness of this method with other existing methods we demonstrate our method on single molecule enzyme reaction data and on dna array comparative genomic hybridization cgh data our study shows that this method is applicable to a wide range of models and offers appealing results in practice supplementary materials for this article are available online

periodic and chaotic behaviour in a reduction of the perturbed korteweg de vries equation the dynamical behaviour of a reduction of the forced and damped korteweg de vries equation is studied numerically chaos arising from subharmonic instability and homoclinic crossings are observed both period doubling bifurcations and the melnikov sequence of subharmonic bifurcations are found and lead to chaotic behaviour here characterised by a positive lyapunov exponent supporting theoretical analysis includes the construction of periodic solutions and homoclinic orbits and their behaviour under perturbation using melnikov functions

bayesian detection of changepoints in finite state markov chains for multiple sequences we consider the analysis of sets of categorical sequences consisting of piecewise homogenous markov segments the sequences are assumed to be governed by a common underlying process with segments occurring in the same order for each sequence segments are defined by a set of unobserved changepoints where the positions and number of changepoints can vary from sequence to sequence we propose a bayesian framework for analyzing such data placing priors on the locations of the changepoints and on the transition matrices and using markov chain monte carlo mcmc techniques to obtain posterior samples given the data experimental results using simulated data illustrate how the methodology can be used for inference of posterior distributions for parameters and changepoints as well as the ability to handle considerable variability in the locations of the changepoints across different sequences we also investigate the application of the approach to sequential data from an application involving monsoonal rainfal

integrable multi boson systems and orthogonal polynomials the strict relation between a certain class of multi boson hamiltonian systems and the corresponding class of orthogonal polynomials is established the correspondence is effectively used to integrate the systems as an explicit example we integrate the class of multi boson systems corresponding to q hahn class polynomials

regular subspaces of a quaternionic hilbert space from quaternionic hermite polynomials and associated coherent states we define quaternionic hermite polynomials by analogy with two families of complex hermite polynomials as in the complex case these polynomials constitute orthogonal families of vectors in ambient quaternionic l2 spaces using these polynomials we then define regular and anti regular subspaces of these l2 spaces the associated reproducing kernels and the ensuing quaternionic coherent states

a class of vector coherent states defined over matrix domains a general scheme is proposed for constructing vector coherent states in analogy with the well known canonical coherent states and their deformed versions when these latter are expressed as infinite series in powers of a complex variable z in the present scheme the variable z is replaced by matrix valued functions over appropriate domains as particular examples we analyze the quaternionic extensions of the canonical coherent states and the gilmore perelomov and barut girardello coherent states arising from representations of su 1 1 possible physical applications are indicated

a sequential particle filter method for static models summary particle filter methods are complex inference procedures which combine importance sampling and monte carlo schemes in order to explore consistently a sequence of multiple distributions of interest we show that such methods can also offer an efficient estimation

on line inference for multiple changepoint problems we propose an on line algorithm for exact filtering of multiple changepoint problems this algorithm enables simulation from the true joint posterior distribution of the number and position of the changepoints for a class of changepoint models the computational cost of this exact algorithm is quadratic in the number of observations we further show how resampling ideas from particle filters can be used to reduce the computational cost to linear in the number of observations at the expense of introducing small errors and propose two new optimum resampling algorithms for this problem one a version of rejection control allows the particle filter to automatically choose the number of particles required at each time step the new resampling algorithms substantially out perform standard resampling algorithms on examples we consider and we demonstrate how the resulting particle filter is practicable for segmentation of human gc content

statistical inference in hidden markov models using k segment constraints hidden markov models hmms are one of the most widely used statistical methods for analyzing sequence data however the reporting of output from hmms has largely been restricted to the presentation of the most probable map hidden state sequence found via the viterbi algorithm or the sequence of most probable marginals using the forward backward algorithm in this article we expand the amount of information we could obtain from the posterior distribution of an hmm by introducing linear time dynamic programming recursions that conditional on a user specified constraint in the number of segments allow us to i find map sequences ii compute posterior probabilities and iii simulate sample paths we collectively call these recursions k segment algorithms and illustrate their utility using simulated and real examples we also highlight the prospective and retrospective use of k segment constraints for fitting hmms or exploring existing model fits supplementary materials for this article are available online

coherent states and hermite polynomials on quaternionic hilbert spaces coherent states similar to the canonical coherent states of the harmonic oscillator labeled by quaternions are established on the right and left quaternionic hilbert spaces on the left quaternionic hilbert space reproducing kernels are established as was claimed by adler and millard j math phys 1997 38 2117 26 it is proved that these coherent states cannot be realized as a group action on a quaternionic hilbert space as an extension of the complex hermite polynomials quaternionic hermite polynomials are defined and these polynomials are associated with an operator as eigenfunctions

deconvolution and estimation of transfer function phase and coefficients for nongaussian linear processes nongaussian linear processes are considered it is shown that the phase of the transfer function can be estimated under broad conditions this is not true of gaussian linear processes and in this sense gaussian linear processes are atypical the asymptotic behavior of a phase estimate is determined the phase estimates make use of bispectral estimates these ideas are applied to a problem of deconvolution which is effective even when the transfer function is not minimum phase a number of computational illustrations are given

product partition models for change point problems product partition models assume that observations in different components of a random partition of the data are independent if the probability distribution of random partitions is in a certain product form prior to making the observations it is also in product form given the observations the product model thus provides a convenient machinery for allowing the data to weight the partitions likely to hold and inference about particular future observations may then be made by first conditioning on the partition and then averaging over all partitions these models apply with special computational simplicity to change point problems where the partitions divide the sequence of observations into components within which different regimes hold we show with appropriate selection of prior product models that the observations can eventually determine approximately the true partition

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

multiple changepoint fitting via quasilikelihood with application to dna sequence segmentation summary we consider situations where a step function with a variable number of steps provides an adequate model for a regression relationship while the variance of the observations depends on their mean this model provides for discontinuous jumps at changepoints and for constant means and error variances in between changepoints the basic statistical problem consists of identification of the number of changepoints their locations and the levels the function assumes in between we embed this problem into a quasilikelihood formulation and utilise the minimum deviance criterion to fit the model for the choice of the number of changepoints we discuss a modified schwarz criterion a dynamic programming algorithm makes the segmentation feasible for sequences of moderate length the performance of the segmentation method is demonstrated in an application to the segmentation of the bacteriophage l sequence

vector coherent state theory as a theory of induced representations a general definition is given of vector coherent state vcs representation theory it is shown that the theory is more general than suggested by previous applications and that it incorporates the standard theories of induced representations as special cases the associated k matrix theory is also given a fuller treatment than hitherto and shown to provide a rather general algorithm both for projecting vcs representations from larger representations in which they are embedded and for determining the hermitian form with respect to which an isometric equivalent representation is in fact isometric

identification of nonminimum phase systems using higher order statistics a method is presented for identification of linear time variant nonminimum phase systems when only output data are available the input sequence need not be independent but it must be non gaussian with some special properties described in the test the authors model a finite dimensional system as an arma autoregressive moving average rational function of known orders but the special cases of ar ma and all pass models are also considered to estimate the parameters of their model the authors utilize both second and higher order statistics of the output which may be contaminated by additive zero mean gaussian white noise of unknown variance the parameter estimators obtained are proved under mild conditions to be consistent simulations verify the performance of the proposed method in the case of relatively low signal to noise ratios and when there is a model order mismatch

bayesian multiple change points and segmentation application to homogenization of climatic series 1 in this paper we describe a new multiple change point detection technique based on segmenting the time series under study into subsequences these segments correspond to the episodes that are likely to contain a unique jump they are found by applying bayesian decision theory through the minimization of simple cost functions all calculations can be performed explicitly without falling back on markov chain monte carlo methods and resulting in particularly light implementation through prior distributions derived from a stochastic renewal process description of jump occurrences expert knowledge of jump amplitude and return period is also introduced in our decision process comparison to several multiple change point methods on simulated series lead to similar or better performance achieved at lower computational cost

phase operators phase states and vector phase states for su3 and su2 1 this paper focuses on phase operators phase states and vector phase states for the sl3 lie algebra we introduce a one parameter generalized oscillator algebra a 2 which provides a unified scheme for dealing with su3 for 0 and h4 h4 for 0 symmetries finite and infinite dimensional representations of a 2 are constructed for 0 and 0 respectively phase operators associated with a 2 are defined and temporally stable phase states as well as vector phase states are constructed as eigenstates of these operators finally we discuss a relation between quantized phase states and a quadratic discrete fourier transform and show how to use these states for constructing mutually unbiased bases

exact bayesian curve fitting and signal segmentation we consider regression models where the underlying functional relationship between the response and the explanatory variable is modeled as independent linear regressions on disjoint segments we present an algorithm for perfect simulation from the posterior distribution of such a model even allowing for an unknown number of segments and an unknown model order for the linear regressions within each segment the algorithm is simple can scale well to large data sets and avoids the problem of diagnosing convergence that is present with monte carlo markov chain mcmc approaches to this problem we demonstrate our algorithm on standard denoising problems on a piecewise constant ar model and on a speech segmentation problem

temporally stable coherent states for infinite well and poschl teller potentials this article is a direct illustration of a construction of coherent states which has been recently proposed by two of us jpg and jk we have chosen the example of a particle trapped in an infinite square well and also in poschl teller potentials of the trigonometric type in the construction of the corresponding coherent states we take advantage of the simplicity of the solutions which ultimately stems from the fact they share a common su 1 1 symmetry a la barut girardello many properties of these states are then studied both from mathematical and from physical points of view

penalized clustering of large scale functional data with multiple covariates in this article we propose a penalized clustering method for large scale data with multiple covariates through a functional data approach in our proposed method responses and covariates are linked together through nonparametric multivariate functions fixed effects which have great flexibility in modeling various function features such as jump points branching and periodicity functional anova is used to further decompose multivariate functions in a reproducing kernel hilbert space and provide associated notions of main effect and interaction parsimonious random effects are used to capture various correlation structures the mixed effects models are nested under a general mixture model in which the heterogeneity of functional data is characterized we propose a penalized henderson s likelihood approach for model fitting and design a rejection controlled em algorithm for the estimation our method selects smoothing parameters through generalized cross validation furthermore bayesian confidence in

model change detection with the mdl principle we are concerned with the issue of detecting model changes in probability distributions we specifically consider the strategies based on the minimum description length mdl principle we theoretically analyze their basic performance from the two aspects data compression and hypothesis testing from the view of data compression we derive a new bound on the minimax regret for model changes here the mini max regret is defined as the minimum of the worst case code length relative to the least normalized maximum likelihood code length over all model changes from the view of hypothesis testing we reduce the model change detection into a simple hypothesis testing problem we thereby derive upper bounds on error probabilities for the mdl based model change test the error probabilities are valid for finite sample size and are related to the information theoretic complexity as well as the discrepancy measure of the hypotheses to be tested

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

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

bayesian analysis of isochores statistical identification of isochore structure the variation in large scale gc composition proportion of dna bases that are g or c as opposed to a or t of mammalian genomes is a necessary requirement for understanding both the evolution of base composition and the many genomic features such as mutation and recombination rates which covary with base composition we have developed a bayesian method for isochore analysis that we demonstrate to be more accurate than the commonly used binary segmentation approach implemented within the program isofinder the method accounts for both fine scale and large scale structure we adapt direct simulation methods to allow for iid samples from the posterior distribution of our model and provide an accurate approximation to this that can analyze data from a chromosome in a matter of seconds we apply our method to human chromosome 1 the resulting estimate of how gc content varies across this region is shown to be a better predictor of local recombination rates t

on line inference for hidden markov models via particle filters we consider the on line bayesian analysis of data by using a hidden markov model where inference is tractable conditional on the history of the state of the hidden component a new particle filter algorithm is introduced and shown to produce promising results when analysing data of this type the algorithm is similar to the mixture kalman filter but uses a different resampling algorithm we prove that this resampling algorithm is computationally efficient and optimal among unbiased resampling algorithms in terms of minimizing a squared error loss function in a practical example that of estimating break points from well log data our new particle filter outperforms two other particle filters one of which is the mixture kalman filter by between one and two orders of magnitude

blind restoration of linearly degraded discrete signals by gibbs sampling this paper addresses the problem of simultaneous parameter estimation and restoration of discrete valued signals that are blurred by an unknown fir filter and contaminated by additive gaussian white noise with unknown variance assuming that the signals are stationary markov chains with known state space but unknown initial and transition probabilities bayesian inference of all unknown quantities is made from the blurred and noisy observations a monte carlo procedure called the gibbs sampler is employed to calculate the bayesian estimates simulation results are presented to demonstrate the effectiveness of the method

coherent states and bayesian duality we demonstrate how large classes of discrete and continuous statistical distributions can be incorporated into coherent states using the concept of a reproducing kernel hilbert space each family of coherent states is shown to contain in a sort of duality which resembles an analogous duality in bayesian statistics a discrete probability distribution and a discretely parametrized family of continuous distributions it turns out that nonlinear coherent states of the type widely studied in quantum optics are a particularly useful class of coherent states from this point of view in that they contain many of the standard statistical distributions we also look at vector coherent states and multidimensional coherent states as carriers of mixtures of probability distributions and joint probability distributions

sequential monte carlo samplers summary we propose a methodology to sample sequentially from a sequence of probability distributions that are defined on a common space each distribution being known up to a normalizing constant these probability distributions are approximated by a cloud of weighted random samples which are propagated over time by using sequential monte carlo methods this methodology allows us to derive simple algorithms to make parallel markov chain monte carlo algorithms interact to perform global optimization and sequential bayesian estimation and to compute ratios of normalizing constants we illustrate these algorithms for various integration tasks arising in the context of bayesian inference

change point detection for recursive bayesian geoacoustic inversions in order to carry out geoacoustic inversion in low signal to noise ratio snr conditions extended duration observations coupled with source and or receiver motion may be necessary as a result change in the underlying model parameters due to time or space is anticipated in this paper an inversion method is proposed for cases when the model parameters change abruptly or slowly a model parameter change point detection method is developed to detect the change in the model parameters using the importance samples and corresponding weights that already are available from the recursive bayesian inversion if the model parameter change abruptly a change point will be detected and the inversion will restart with the pulse measurement after the changepoint if the model parameters change gradually the inversion based on constant model parameters may proceed until the accumulated model parameter mismatch is significant and triggers the detection of a change point these change point detections form the heu

vector coherent states from plancherel s theorem clifford algebras and matrix domains as a substantial generalization of the technique for constructing canonical and the related nonlinear and q deformed coherent states we present here a method for constructing vector coherent states vcs in the same spirit these vcs may have a finite or an infinite number of components the resulting formalism which involves an assumption on the existence of a resolution of the identity is broad enough to include all the definitions of coherent states existing in the current literature subject to this restriction as examples we first apply the technique to construct vcs using the plancherel isometry for groups and vcs associated with clifford algebras in particular quaternions as physical examples we discuss vcs for a quantum optical model and finally apply the general technique to build vcs over certain matrix domains

estimation and comparison of multiple change point models this paper provides a new bayesian approach for models with multiple change points the centerpiece of the approach is a formulation of the change point model in terms of a latent discrete state variable that indicates the regime from which a particular observation has been drawn this state variable is specified to evolve according to a discrete time discrete state markov process with the transition probabilities constrained so that the state variable can either stay at the current value or jump to the next higher value this parameterization exactly reproduces the change point model the model is estimated by markov chain monte carlo methods using an approach that is based on chib 1996 this methodology is quite valuable since it allows for the fitting of more complex change point models than was possible before methods for the computation of bayes factors are also developed all the techniques are illustrated using simulated and real data sets

coherent states on hilbert modules we generalize the concept of coherent states traditionally defined as special families of vectors on hilbert spaces to hilbert modules we show that hilbert modules over c algebras are the natural settings for a generalization of coherent states defined on hilbert spaces we consider those hilbert c modules which have a natural left action from another c algebra say a the coherent states are well defined in this case and they behave well with respect to the left action by a certain classical objects like the cuntz algebra are related to specific examples of coherent states finally we show that coherent states on modules give rise to a completely positive definite kernel between two c algebras in complete analogy to the hilbert space situation related to this there is a dilation result for positive operator valued measures in the sense of naimark a number of examples are worked out to illustrate the theory some possible physical applications are also mentioned

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

spatial chaos in weakly dispersive and viscous media a nonperturbative theory of the driven kdv burgers equation abstract the asymptotic travelling wave solution of the kdv burgers equation driven by the long scale periodic driver is constructed the solution represents a shock train in which the quasi periodic sequence of dispersive shocks or soliton chains is interspersed by smoothly varying regions it is shown that the periodic solution which has the spatial driver period undergoes period doublings as the governing parameter changes two types of chaotic behavior are considered the first type is a weak chaos where only a small chaotic deviation from the periodic solution occurs the second type corresponds to the developed chaos where the solution ignores the driver period and represents a random sequence of uncorrelated shocks in the case of weak chaos the shock coordinate being repeatedly mapped over the driver period moves on a chaotic attractor while in the case of developed chaos it moves on a repeller both solutions depend on a parameter indicating the reference shock position in the shock train the structure of a one dimensional set to which this parameter belongs is investigated this set contains measure one intervals around the fixed points in the case of periodic or weakly chaotic solutions and it becomes a fractal in the case of strong chaos the capacity dimension of this set is calculated

annealing markov chain monte carlo with applications to ancestral inference abstract markov chain monte carlo mcmc the metropolis hastings algorithm has been used for many statistical problems including bayesian inference likelihood inference and tests of significance though the method generally works well doubts about convergence often remain here we propose mcmc methods distantly related to simulated annealing our samplers mix rapidly enough to be usable for problems in which other methods would require eons of computing time they simulate realizations from a sequence of distributions allowing the distribution being simulated to vary randomly over time if the sequence of distributions is well chosen then the sampler will mix well and produce accurate answers for all the distributions even when there is only one distribution of interest these annealing like samplers may be the only known way to get a rapidly mixing sampler these methods are essential for attacking very hard problems which arise in areas such as statistical genetics we illustrate the methods wi

multiscale change point inference summary we introduce a new estimator the simultaneous multiscale change point estimator smuce for the change point problem in exponential family regression an unknown step function is estimated by minimizing the number of change points over the acceptance region of a multiscale test at a level the probability of overestimating the true number of change points k is controlled by the asymptotic null distribution of the multiscale test statistic further we derive exponential bounds for the probability of underestimating k by balancing these quantities will be chosen such that the probability of correctly estimating k is maximized all results are even non asymptotic for the normal case on the basis of these bounds we construct asymptotically honest confidence sets for the unknown step function and its change points at the same time we obtain exponential bounds for estimating the change point locations which for example yield the minimax rate up to a log term finally the simultaneous multiscale change point estimator achieves the optimal detection rate of vanishing signals as n even for an unbounded number of change points we illustrate how dynamic programming techniques can be employed for efficient computation of estimators and confidence regions the performance of the multiscale approach proposed is illustrated by simulations and in two cutting edge applications from genetic engineering and photoemission spectroscopy

vector coherent state representations induced representations and geometric quantization i scalar coherent state representations coherent state theory is shown to reproduce three categories of representations of the spectrum generating algebra for an algebraic model i classical realizations which are the starting point for geometric quantization ii induced unitary representations corresponding to prequantization and iii irreducible unitary representations obtained in geometric quantization by choice of a polarization these representations establish an intimate relation between coherent state theory and geometric quantization in the context of induced representations

multivariate density estimation by bayesian sequential partitioning consider a class of densities that are piecewise constant functions over partitions of the sample space defined by sequential coordinate partitioning we introduce a prior distribution for a density in this function class and derive in closed form the marginal posterior distribution of the corresponding partition a computationally efficient method based on sequential importance sampling is presented for the inference of the partition from this posterior distribution compared to traditional approaches such as the kernel method or the histogram the bayesian sequential partitioning bsp method proposed here is capable of providing much more accurate estimates when the sample space is of moderate to high dimension we illustrate this by simulated as well as real data examples the examples also demonstrate how bsp can be used to design new classification methods competitive with the state of the art

rejection control and sequential importance sampling abstract we discuss ways of combining rejection sampling and importance sampling methods in monte carlo computations and demonstrate their usefulness in updating dynamic systems specifically we propose the rejection controlled sequential importance sampling rc sis algorithm which is designed to simultaneously reduce monte carlo variation and retain independent samples in sequential importance sampling the proposed method is demonstrated by three examples taken from econometrics hierarchical bayes analysis and digital telecommunications they all show significant improvements over previous results

empirical bayes confidence intervals based on bootstrap samples abstract consider the model with data generated by the following two stage process first a parameter is sampled from a prior distribution g and then an observation is sampled from the conditional distribution f y if the prior distribution is known then the bayes estimate under squared error loss is the posterior expectation of conditional on the data y for example if g is gaussian with mean and variance 2 and f y is gaussian with mean and variance 2 then the posterior distribution is gaussian with mean b 1 b y and variance 2 1 b where b 2 2 2 inferences about are based on this distribution we study the application of the bootstrap to situations where the prior must be estimated from the data empirical bayes methods for this model we observe data y t y 1 y k t each independent y k following the compound model described previously as first shown by james and stein 1961 setting each k equal to its estimated posterior mean where and pr

adapting the number of particles in sequential monte carlo methods through an online scheme for convergence assessment particle filters are broadly used to approximate posterior distributions of hidden states in state space models by means of sets of weighted particles while the convergence of the filter is guaranteed when the number of particles tends to infinity the quality of the approximation is usually unknown but strongly dependent on the number of particles in this paper we propose a novel method for assessing the convergence of particle filters in an online manner as well as a simple scheme for the online adaptation of the number of particles based on the convergence assessment the method is based on a sequential comparison between the actual observations and their predictive probability distributions approximated by the filter we provide a rigorous theoretical analysis of the proposed methodology and as an example of its practical use we present simulations of a simple algorithm for the dynamic and online adaptation of the number of particles during the operation of a particle filter on a stochastic version of the lorenz 63 system

reversible jump markov chain monte carlo computation and bayesian model determination markov chain monte carlo methods for bayesian computation have until recently been restricted to problems where the joint distribution of all variables has a density with respect to some fixed standard underlying measure they have therefore not been available for application to bayesian model determination where the dimensionality of the parameter vector is typically not fixed this paper proposes a new framework for the construction of reversible markov chain samplers that jump between parameter subspaces of differing dimensionality which is flexible and entirely constructive it should therefore have wide applicability in model determination problems the methodology is illustrated with applications to multiple change point analysis in one and two dimensions and to a bayesian comparison of binomial experiments

vector coherent states with matrix moment problems canonical coherent states can be written as infinite series in powers of a single complex number z and a positive integer m the requirement that these states realize a resolution of the identity typically results in a moment problem where the moments form the positive sequence of real numbers m m 0 in this paper we obtain new classes of vector coherent states by simultaneously replacing the complex number z and the moments m of the canonical coherent states by n n matrices associated oscillator algebras are discussed with the aid of a generalized matrix factorial two physical examples are discussed in the first example coherent states are obtained for the jaynes cummings model in the weak coupling limit and some physical properties are discussed in terms of the constructed coherent states in the second example coherent states are obtained for a conditionally exactly solvable supersymmetric radial harmonic oscillator

rao blackwellisation of sampling schemes summary this paper proposes a post simulation improvement for two common monte carlo methods the accept reject and metropolis algorithms the improvement is based on a rao blackwellisation method that integrates over the uniform random variables involved in the algorithms and thus post processes the standard estimators we show how the rao blackwellised versions of these algorithms can be implemented and through examples illustrate the improvement in variance brought by these new procedures we also compare the improved version of the metropolis algorithm with ordinary and rao blackwellised importance sampling procedures for independent and general metropolis set ups

blind deconvolution via sequential imputations abstract the sequential imputation procedure is applied to adaptively and sequentially reconstruct discrete input signals that are blurred by an unknown linear moving average channel and contaminated by additive gaussian noises a problem known as blind deconvolution in digital communication a rejuvenation procedure for improving the efficiency of sequential imputation is introduced and theoretically justified the proposed method does not require the channel to be nonminimum phase and can be used in real time signal restoration two simulated systems are studied to illustrate the proposed method our result shows that the ideas of multiple imputations and flexible simulation techniques are as powerful in engineering as in survey sampling

quantum algebras and q special functions related to coherent states maps of the disc the quantum algebras generated by the coherent states maps of the disc are investigated it is shown that the analytic realization of these algebras leads to a generalized analysis which includes standard analysis as well as q analysis the applications of the analysis to star product quantizations and q special functions theory are given among others the meromorphic continuation of the generalized basic hypergeometric series is found and a reproducing measure is constructed when the series is treated as a reproducing kernel

bayesian curve fitting using mcmc with applications to signal segmentation we propose some bayesian methods to address the problem of fitting a signal modeled by a sequence of piecewise constant linear in the parameters regression models for example autoregressive or volterra models a joint prior distribution is set up over the number of the changepoints knots their positions and over the orders of the linear regression models within each segment if these are unknown hierarchical priors are developed and as the resulting posterior probability distributions and bayesian estimators do not admit closed form analytical expressions reversible jump markov chain monte carlo mcmc methods are derived to estimate these quantities results are obtained for standard denoising and segmentation of speech data problems that have already been examined in the literature these results demonstrate the performance of our methods

mixture kalman filters in treating dynamic systems sequential monte carlo methods use discrete samples to represent a complicated probability distribution and use rejection sampling importance sampling and weighted resampling to complete the on line filtering task we propose a special sequential monte carlo method the mixture kalman filter which uses a random mixture of the gaussian distributions to approximate a target distribution it is designed for on line estimation and prediction of conditional and partial conditional dynamic linear models which are themselves a class of widely used non linear systems and also serve to approximate many others compared with a few available filtering methods including monte carlo methods the gain in efficiency that is provided by the mixture kalman filter can be very substantial another contribution of the paper is the formulation of many non linear systems into conditional or partial conditional linear form to which the mixture kalman filter can be applied examples in target tracking and digital communications are given to demonstrate the procedures proposed

on chaotic wave patterns in periodically forced steady state kdvb and extended kdvb equations the periodically forced kdvb and extended kdvb equations are considered we investigate the structure of the totality of steady profiles the existence of profiles that are close to any shuffling o

periodic and chaotic behaviour in a reduced form of the perturbed generalized korteweg de vries and kadomtsev petviashvili equations abstract the dynamical behaviour of a reduced form of the perturbed generalized korteweg de vries and kadomtsev petviashvili equations extension of the korteweg de vries equation to two space variables are studied in this paper harmonic solutions of non resonance and primary resonance are obtained using the perturbation method chaotic motion under harmonic excitations is studied using the melnikov method a wide range of solutions for the reduced perturbed generalized korteweg de vries equations in which non linear phenomena appearing within transition from regular harmonic response periodic solutions to chaotic motion are obtained using the time integration runge kutta method when chaos is found it is detected by examining the phase plane the poincare map the sensitivity solution of the solution to initial conditions and by calculating the largest lyapunov exponent

a pairwise likelihood based approach for changepoint detection in multivariate time series models this paper develops a composite likelihood based approach for multiple changepoint estimation in multivariate time series we derive a criterion based on pairwise likelihood and minimum description length for estimating the number and locations of changepoints and for performing model selection in each segment the number and locations of the changepoints can be consistently estimated under mild conditions and the computation can be conducted efficiently with a pruned dynamic programming algorithm simulation studies and real data examples demonstrate the statistical and computational efficiency of the proposed method

nonparametric hierarchical bayes via sequential imputations we consider the empirical bayes estimation of a distribution using binary data via the dirichlet process let d denote a dirichlet process with being a finite measure on 0 1 instead of having direct samples from an unknown random distribution f from d we assume that only indirect binomial data are observable this paper presents a new interpretation of lo s formula and thereby relates the predictive density of the observations based on a dirichlet process model to likelihoods of much simpler models as a consequence the log likelihood surface as well as the maximum likelihood estimate of c 0 1 is found when the shape of is assumed known together with a formula for the fisher information evaluated at the estimate the sequential imputation method of kong liu and wong is recommended for overcoming computational difficulties commonly encountered in this area the related approximation formulas are provided an analysis of the tack data of beckett and diaconis which motivated this study is supplemented to illustrate our methods