nils-herrmann/clean_scirepeval huggingface dataset:
On a Class of Genealogical and Interacting Metropolis Models

A genealogical tree based particle model for drawing approximate samples from the conditional path-distributions of a Markov chain with respect to its terminal values is presented. This path-particle evolution model can be interpreted as the historical process associated to a sequence of interacting Metropolis Markov chains. This novel class of interacting models can also be used to obtain approximate samples from a given target distribution which is only known up to a normalizing constant. We design an original Feynman–Kac modeling technique for studying the asymptotic analysis of these path-particle and Metropolis type simulation models. We provide precise convergence results as the time or the size of the systems tends to infinity. In contrast to the traditional Metropolis model we show that the decays to equilibrium do not depend on the nature of the desired limiting distribution.
Sequential monte carlo implementation of the phd filter for multi-target tracking

Random finite sets are natural represen- tations of multi-target states and observations that al- low multi-sensor multi-target tmcking to fit in the uni- fying random set framework for Data fision. Although a rigorous foundation has been developed in the form of Finite Set Statistics, optimal Bayesian multi-target filtering is not yet practical. Sequential Monte Carlo (SMC) approzimations of the optimal filter are compu- tationally ezpensive. A practical altemative to the opti- mal filter is the Probability Hypothesis Density (PHD) filter, which propagates the PHD or first moment in- stead of the full multi-target posterior. The propagation of the PHD involves multiple integrals which do not ad- mit closed form. We propose to approzimate the PHD by a set of weighted random samples which are propa- gated over time using a generalised SMC method. The resulting algorithm is very attractive as it is general enough to handle non-linear non-Gaussian dynamics and the computational complezity is independent of the (time-varying) number of targets.
A survey of convergence results on particle filtering methods for practitioners

Optimal filtering problems are ubiquitous in signal processing and related fields. Except for a restricted class of models, the optimal filter does not admit a closed-form expression. Particle filtering methods are a set of flexible and powerful sequential Monte Carlo methods designed to. solve the optimal filtering problem numerically. The posterior distribution of the state is approximated by a large set of Dirac-delta masses (samples/particles) that evolve randomly in time according to the dynamics of the model and the observations. The particles are interacting; thus, classical limit theorems relying on statistically independent samples do not apply. In this paper, our aim is to present a survey of convergence results on this class of methods to make them accessible to practitioners.
Marginal maximum a posteriori estimation using Markov chain Monte Carlo

Markov chain Monte Carlo (MCMC) methods, while facilitating the solution of many complex problems in Bayesian inference, are not currently well adapted to the problem of marginal maximum a posteriori (MMAP) estimation, especially when the number of parameters is large. We present here a simple and novel MCMC strategy, called State-Augmentation for Marginal Estimation (SAME), which leads to MMAP estimates for Bayesian models. We illustrate the simplicity and utility of the approach for missing data interpolation in autoregressive time series and blind deconvolution of impulsive processes.
Sequential Monte Carlo tracking schemes for maneuvering targets with passive ranging

In this article we consider tracking a single maneuvering target in scenarios where range information is not available, or is denied. This tracking problem is usually referred to as passive ranging, or bearings-only tracking. Tracking any single maneuvering target naturally admits a jump Markov system, in which a collection of candidate dynamical systems is proposed to model various classes of motion, each of which is assumed to be executed by the target according to a Markov law. Standard techniques to solve this problem use the so called interacting multiple model (IMM), or its variants. Recently sequential Monte Carlo (SMC) techniques have been applied to passive ranging problems, however, most of the scenarios reported in the literature consider nonmaneuvering targets. In this article we apply a new SMC technique to the passive ranging problem in a maneuvering target scenario. The algorithm we propose is compared to the so called auxiliary particle filter (APF). A simulation study is included.
Sequential Monte Carlo samplers

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.
A policy gradient method for SMDPs with application to call admission control

Classical methods for solving a semi-Markov decision process such as value iteration and policy iteration require precise knowledge of the underlying probabilistic model and are know to suffer from the curse of dimensionality. To overcome both these limitations, this paper presents a reinforcement learning approach where one optimizes directly the performance criterion with respect to a family of parameterised policies. We propose an online algorithm that simultaneously estimates the gradient of the performance criterion and optimises it through stochastic approximation. The gradient estimator is based on the discounted score method as introduced. We demonstrate the utility of our algorithm in a Call Admission Control problem.
Recursive state estimation for multiple switching models with unknown transition probabilities

This work considers hybrid systems with continuous-valued target states and discrete-valued regime variable. The changes (switches) of the regime variable are modeled by a finite state Markov chain with unknown and random transition probabilities following Dirichlet distributions. Our work analytically derives the marginal posterior distribution of the states and regime variables, the transition probabilities being integrated out. This leads to a variety of recursive hybrid state estimation schemes which are an appealing intuitive and straightforward extension of standard algorithms. Their performance is illustrated by a maneuvering target tracking example.
Monte Carlo smoothing with application to audio signal enhancement

We describe methods for applying Monte Carlo filtering and smoothing for estimation of unobserved states in a nonlinear state-space model. By exploiting the statistical structure of the model, we develop a Rao-Blackwellized particle smoother. Due to the lengthy nature of real signals, we suggest processing the data in blocks, and a block-based smoother algorithm is developed for this purpose. All the algorithms suggested are tested with real speech and audio data, and the results are shown and compared with those generated using the generic particle smoother and the extended Kalman filter (EKF). It is found that the proposed Rao-Blackwellized particle smoother improves on the standard particle smoother and the extended Kalman smoother. In addition, the proposed block-based smoother algorithm enhances the efficiency of the proposed Rao-Blackwellized smoother by significantly reducing the storage capacity required for the particle information.
Exponential forgetting and geometric ergodicity in state-space models

In this paper, the problem of exponential forgetting and geometric ergodicity for optimal filtering in general state space models is considered. We consider here state-space models where the latent process is modeled by a Markov chain taking its values in a continuous space and the observation at each point admits a distribution dependent on both the current state of the Markov chain and the past observation. Under given regularity assumptions, we establish that: (1) the filter, and its derivatives with respect to some parameters in the model, have exponential forgetting properties; and (2) the extended Markov chain, whose components are the latent process, observation sequence, filter and its derivatives is geometrically ergodic.
On-line optimization of sequential Monte Carlo methods using stochastic approximation

Sequential Monte Carlo (SMC) methods (particle filtering techniques) are a set of powerful and versatile simulation-based methods to perform optimal state estimation in nonlinear non-Gaussian state space models. In this approach, the posterior probability distributions of interest are estimated using a cloud of random samples which are carried over time using importance sampling and resampling techniques. Current algorithms are typically designed so as to optimize some "local" criteria such as the conditional variance of the importance weights in the importance sampling step. However, the effect of these local optimizations is not clear on the global performance of the algorithm; e.g. sampling with a nonlocally optimal importance distribution might be beneficial at further time steps. We present here an alternative principled approach where the SMC is parametrized and its parameters optimized with respect to a "global" performance measure such as the (time) average entropy of the importance weights. This is achieved using stochastic approximation techniques. We demonstrate the efficiency of this approach through simulation.
Maximum a Posteriori Sequence Estimation Using Monte Carlo Particle Filters

We develop methods for performing maximum a posteriori (MAP) sequence estimation in non-linear non-Gaussian dynamic models. The methods rely on a particle cloud representation of the filtering distribution which evolves through time using importance sampling and resampling ideas. MAP sequence estimation is then performed using a classical dynamic programming technique applied to the discretised version of the state space. In contrast with standard approaches to the problem which essentially compare only the trajectories generated directly during the filtering stage, our method efficiently computes the optimal trajectory over all combinations of the filtered states. A particular strength of the method is that MAP sequence estimation is performed sequentially in one single forwards pass through the data without the requirement of an additional backward sweep. An application to estimation of a non-linear time series model and to spectral estimation for time-varying autoregressions is described.
Particle filters for state estimation of jump Markov linear systems

Jump Markov linear systems (JMLS) are linear systems whose parameters evolve with time according to a finite state Markov chain. In this paper, our aim is to recursively compute optimal state estimates for this class of systems. We present efficient simulation-based algorithms called particle filters to solve the optimal filtering problem as well as the optimal fixed-lag smoothing problem. Our algorithms combine sequential importance sampling, a selection scheme, and Markov chain Monte Carlo methods. They use several variance reduction methods to make the most of the statistical structure of JMLS. Computer simulations are carried out to evaluate the performance of the proposed algorithms. The problems of on-line deconvolution of impulsive processes and of tracking a maneuvering target are considered. It is shown that our algorithms outperform the current methods.
Optimal Estimation and Cramér-Rao Bounds for Partial Non-Gaussian State Space Models

Partial non-Gaussian state-space models include many models of interest while keeping a convenient analytical structure. In this paper, two problems related to partial non-Gaussian models are addressed. First, we present an efficient sequential Monte Carlo method to perform Bayesian inference. Second, we derive simple recursions to compute posterior Cramér-Rao bounds (PCRB). An application to jump Markov linear systems (JMLS) is given.
Convergence properties of Bayesian evolutionary algorithms with population size greater than 1

A Bayesian evolutionary algorithm is a probabilistic model of evolutionary computation for learning and optimization. It explicitly estimates the posterior distribution of the individuals and then samples offspring from the distribution. In the previous paper, using the asymptotic results from Markov chain Monte Carlo and annealing techniques, the asymptotic convergence of Bayesian evolutionary algorithms was shown for the case of population size 1. This paper presents convergence properties of Bayesian evolutionary algorithms with population size greater than 1. The basic idea is that BEAs can be reduced to Bayesian particle filters. The Bayesian particle filter approximates the posterior distribution of individuals at each generation. As the individuals evolve, the approximated posterior distribution also evolves. Then using the convergence properties of particle filters under some mild conditions, it is shown that as the number of individuals increases, a BEA converges to the posterior distribution.
Markov chain Monte Carlo data association for target tracking

We consider the estimation of the state of a discrete-time Markov process using observations which are sets of measurements from a finite number of known linear models. The measurement to model association is unknown and false measurements that do not yield any information about the Markov process are contained in the measurement set. The objective is to perform data association between the detected measurements and the models and determine optimal estimates of the state of the Markov process. The application of this problem is found in over the horizon target tracking. We derive iterative deterministic and stochastic algorithms based on Gibbs sampling. Rao-Blackwellisation allows us to solve the problem efficiently, yielding methods with computational complexity linear in the number of received data sets. Contrary to recent approaches based on the EM algorithm, the novel procedures we propose do not require an introduction of a missing data set and consequently their range of applicability is wider. A simulation study shows that the new algorithms are superior to previously proposed methods.
Maximum a Posteriori Parameter Estimation for Hidden Markov Models

An iterative stochastic algorithm to perform maximum a posteriori parameter estimation of hidden Markov models is proposed. It makes the most of the statistical model by introducing an artiicial probability model based on an increasing number of the unobserved Markov chain at each iteration. Under minor regularity assumptions, we provide suucient conditions to ensure global convergence of this algorithm. It is applied to parameter estimation for nite Gaussian mixtures, Markov-modulated Poisson processes and switching autoregressions with a Markov regime.
Stochastic sampling algorithms for state estimation of jump Markov linear systems

Jump Markov linear systems are linear systems whose parameters evolve with time according to a finite-state Markov chain. Given a set of observations, our aim is to estimate the states of the finite-state Markov chain and the continuous (in space) states of the linear system. The computational cost in computing conditional mean or maximum a posteriori (MAP) state estimates of the Markov chain or the state of the jump Markov linear system grows exponentially in the number of observations. We present three globally convergent algorithms based on stochastic sampling methods for state estimation of jump Markov linear systems. The cost per iteration is linear in the data length. The first proposed algorithm is a data augmentation (DA) scheme that yields conditional mean state estimates. The second proposed scheme is a stochastic annealing (SA) version of DA that computes the joint MAP sequence estimate of the finite and continuous states. Finally, a Metropolis-Hastings DA scheme based on SA is designed to yield the MAP estimate of the finite-state Markov chain. Convergence results of the three above-mentioned stochastic algorithms are obtained. Computer simulations are carried out to evaluate the performances of the proposed algorithms. The problem of estimating a sparse signal developing from a neutron sensor based on a set of noisy data from a neutron sensor and the problem of narrow-band interference suppression in spread spectrum code-division multiple-access (CDMA) systems are considered.
Sequential simulation-based estimation of jump Markov linear systems

Jump Markov linear systems (JMLS) are linear systems whose parameters evolve with time according to a finite state Markov chain. Our aim is to recursively compute optimal conditional mean state estimates for JMLS. We present efficient simulation-based algorithms called particle filters to solve the optimal filtering problem. Our algorithms combine sequential importance sampling, a selection scheme and Markov chain Monte Carlo methods. They use several variance reduction methods to make the most of the statistical structure of JMLS.
Monte Carlo filtering and smoothing with application to time-varying spectral estimation

We develop methods for performing filtering and smoothing in nonlinear non-Gaussian dynamical models. The methods rely on a particle cloud representation of the filtering distribution which evolves through time using importance sampling and resampling ideas. In particular, novel techniques are presented for generation of random realisations from the joint smoothing distribution and for MAP estimation of the state sequence. Realisations of the smoothing distribution are generated in a forward-backward procedure, while the MAP estimation procedure can be performed in a single forward pass of the Viterbi algorithm applied to a discretised version of the state space. An application to spectral estimation for time-varying autoregressions is described.
Bayesian Approaches to Multi-Sensor Data Fusion

Declaration I hereby declare that my thesis is not substantially the same as any that I have submitted for a degree or diploma or other qualification at any other University. I further state that no part of my thesis has already been or is being concurrently submitted for any such degree, diploma or other qualification. I hereby declare that my thesis does not exceed the limit of the length prescribed in the Special Regulations of the M.Phil. examination for which I am a candidate. The length of my thesis is less than 14000 words. Acknowledgments I am most grateful to my supervisor Dr. Bill Fitzgerald for his advice, support and constant willingness to help during the past year. I am also indebted to Dr. Christophe Andrieu and Dr. Arnaud Doucet for their endless support, encouragement and kindness in answering the questions; from them, through the numerous fruitful discussions and helpful comments, I benefited immensely. My gratitude goes to Mike Hazas and, again, Dr. Christophe Andrieu and Dr. Arnaud Doucet for their companionship, useful comments and proofreading the sections of this dissertation, and to Roger Wareham and Paul Walmsley for software and hardware support. I am thankful to my parents for their ever present love and all kinds of support. Without the tremendous sacrifices they have made for me, I would not have had a chance to come to Cambridge. At last, but not at least, I would like to thank my husband for his tolerance and for always being near ready to help, and my daughter Anastasia for making life such great fun, for her patience and understanding.
Simulation-based optimal filter for maneuvering target tracking

While single model filters are sufficient for tracking targets having fixed kinematic behavior, maneuvering targets require the use of multiple models. Jump Markov linear systems whose parameters evolve with time according to a finite state-space Markov chain, have been used in these situations with great success. However, it is well-known that performing optimal estimation for JMLS involves a prohibitive computational cost exponential in the number of observations. Many approximate methods have been proposed in the literature to circumvent this including the well-known GPB and IMM algorithms. These methods are computationally cheap but at the cost of being suboptimal. Efficient off- line methods have recently been proposed based on Markov chain Monte Carlo algorithms that out-perform recent methods based on the Expectation-Maximization algorithms. However, realistic tracking systems need on-line techniques. In this paper, we propose an original on-line Monte Carlo filtering algorithm to perform optimal state estimation of JMLS. The approach taken is loosely based on the bootstrap filter which, wile begin a powerful general algorithm in its original form, does not make the most of the structure of JMLS. The proposed algorithm exploits this structure and leads to a significant performance improvement.
Marginal MAP estimation using Markov chain Monte Carlo

Markov chain Monte Carlo (MCMC) methods are powerful simulation-based techniques for sampling from high-dimensional and/or non-standard probability distributions. These methods have recently become very popular in the statistical and signal processing communities as they allow highly complex inference problems in defection and estimation to be addressed. However, MCMC is not currently well adapted to the problem of marginal maximum a posteriori (MMAP) estimation. In this paper, we present a simple and novel MCMC strategy called state-augmentation for marginal estimation (SAME), that allows MMAP estimates to be obtained for Bayesian models. The methodology is very general and we illustrate the simplicity and utility of the approach by examples in MAP parameter estimation for hidden Markov models (HMMs) and for missing data interpolation in autoregressive time series.
Sequential Bayesian wavelet denoising

We propose a wavelet model that incorporates coefficient correlation and is expressed in state-space form, allowing the development and application of sequential estimation algorithms for wavelet denoising. We detail a sequential simulation-based estimation algorithm based on particle filters. This algorithm allows Bayesian wavelet denoising to be performed on-line, enabling it to process a vast dataset, and it is intrinsically parallelizable. The experiments indicate that the algorithm performance is comparable to the majority of Bayesian framework batch-based algorithms.
Efficient particle filters for tracking manoeuvring targets in clutter

In this paper, we propose an on-line Monte Carlo (MC) filtering algorithm to perform optimal state estimation for Jump Markov Linear Systems (JMLS). The approach taken is loosely based on the bootstrap filter which, whilst being a powerful general algorithm in its original form, does not make the most of the structure of JMLS. The proposed algorithm exploits this structure and is demonstrated to provide a performance improvement over the IMM-PDA for tracking manoeuvring targets in clutter.