Dans le contexte général de la résolution de problèmes inverses en acoustique et traitement du signal audio les défis sont nombreux. Pour la résolution de ces problèmes, leur caractère souvent mal posé nécessite de considérer des modèles de signaux appropriés. Les travaux de cette thèse montrent sur la base d'un cadre algorithmique générique polyvalent comment les différentes formes de parcimonie (à l'analyse ou à la synthèse, simple, structurée ou sociale) sont particulièrement adaptées à la reconstruction de signaux sonores dans un cadre mono ou multicanal. Le cœur des travaux de thèse permet de mettre en évidence les limites des conditions d'évaluation de l'état de l'art pour le problème de désaturation et de mettre en place un protocole rigoureux d'évaluation à grande échelle pour identifier les méthodes les plus appropriées en fonction du contexte (musique ou parole, signaux fortement ou faiblement dégradés). On démontre des améliorations de qualité substantielles par rapport à l'état de l'art dans certains régimes avec des configurations qui n'avaient pas été précédemment considérées, nous obtenons également des accélérations conséquentes. Enfin, un volet des travaux aborde la localisation de sources sonores sous l'angle de l'apprentissage statistique « virtuellement supervisé ». On montre avec cette méthode des résultats encourageants sur l'estimation de directions d'arrivée et de distance. / Today's challenges in the context of audio and acoustic signal processing inverse problems are multiform. Addressing these problems often requires additional appropriate signal models due to their inherent ill-posedness. This work focuses on designing and evaluating audio reconstruction algorithms. Thus, it shows how various sparse models (analysis, synthesis, plain, structured or “social”) are particularly suited for single or multichannel audio signal reconstruction. The core of this work notably identifies the limits of state-of-the-art methods evaluation for audio declipping and proposes a rigourous large-scale evaluation protocol to determine the more appropriate methods depending on the context (music or speech, moderately or highly degraded signals). Experimental results demonstrate substantial quality improvements for some newly considered testing configurations. We also show computational efficiency of the different methods and considerable speed improvements. Additionally, a part of this work is dedicated to the sound source localization problem. We address it with a “virtually supervised” machine learning technique. Experiments show with this method promising results on distance and direction of arrival estimation.

As equações diferenciais impulsivas (EDIs) modelam fenômenos que são contínuos por partes, isto é, que evoluem continuamente mas em certos momentos sofrem mudanças abruptas (impulsos) consideradas instantâneas quando comparadas à duração total do processo. Surgem nas mais diversas áreas das ciências, como na modelagem de concentração de medicamentos no corpo humano e no impacto de propaganda nas vendas de uma empresa. O problema direto associado a uma EDI com instantes de impulsos pré-fixados consiste em, fornecidos a equação diferencial, a condição inicial, os momentos de impulso e os saltos, determinar a solução do problema. Por outro lado, as incógnitas dos problemas inversos associados são os saltos e/ou os momentos de impulso. Em geral, os problemas inversos não podem ser resolvidos diretamente por meio de técnicas convencionais. A abordagem funcional é uma alternativa baseada na minimização de um funcional de erro que confronta dados do fenômeno real e do modelo matemático. O mínimo global deste funcional corresponde à solução do problema inverso. O objetivo principal desta dissertação é investigar os problemas inversos de identificação dos parâmetros saltos e momentos de impulso. Buscamos descrever uma técnica que permita tratar de problemas inversos associados às EDIs de forma bem geral, que não utilize informações específicas da aplicação além das medidas no tempo inicial e final do processo. Para isso, desenvolvemos um programa computacional composto por uma função para solução numérica do problema direto usando o método de Runge-Kutta de quarta ordem, função esta que é chamada diversas vezes para cada resolução do problema direto com diferentes valores para as incógnitas; e pelo método de otimização Simulated Annealing que altera sistematicamente os valores das incógnitas. Os resultados mostram que resolver os problemas inversos que surgem das EDIs não é uma tarefa simples, que a técnica estudada é promissora e que pode ser aperfeiçoada / Impulsive differential equations (IDEs) model piecewise continuous phenomena, that is, that evolve continuously but at certain moments suffer abrupt changes (impulses) considered instantaneous when compared to the total duration of the process. They arise in several areas of science, such as the modeling of drug concentration in the human body and the impact of advertising on a companys sales. The direct problem associated with an IDE with impulses at fixed times consists of determining the solution to the problem, provided the differential equation, the initial condition, the moments of impulse and the jumps. On the other hand, the unknowns of the associated inverse problems are the jumps and/or the moments of impulse. In general, the inverse problems cannot be solved directly by conventional techniques. The functional approach is an alternative based on the minimization of an error functional that confronts data of the real phenomenon and the mathematical model. The global minimum of this functional corresponds to the solution of the inverse problem. The main objective of this dissertation is to investigate the inverse problems of jumps and moments of impulse parameters identification. We have attempted to describe a technique that allows treating of the inverse problems associated with IDEs in a general way, which does not use particular information of the application besides the measurements in the initial and final time of the process. For this, we developed a computer program composed by a function to solve the direct problem numerically using the fourth-order Runge-Kutta method, which is called several times for each resolution of the direct problem with different values for the unknowns; and by the Simulated Annealing optimization method which changes the values of the unknowns systematically. The results show that solving the inverse problems that arise from IDEs is not a simple task and that the technique studied is promising and can be improved

Técnicas de reconstrução térmica inversa são muito usadas em diferentes aplicações tais como a determinação de propriedades térmicas de novos materiais, controle da produção de calor, temperatura em processos de manufatura, etc. Apesar da ampla aplicabilidade, o problema inverso é intrinsecamente mal condicionado e tem sido tema de trabalhos de vários pesquisadores. A solução de um problema térmico inverso tridimensional é significantemente complexa, e, assim requer uma formulação que não contenha condições experimentais não realistas tais como confinamento bidimensional e estabilidade do campo térmico com relação a mudanças em parâmetros internos. Uma das abordagens adotada é baseada na formulação variacional sobre a forma do erro quadrático para reconstrução da distribuição de condução de calor interna e coeficiente de condução de calor parietal para um problema tridimensional. Dentro desta estrutura, a natureza mal condicionada do problema se manifesta na superfície de otimização por produzir topologias problemáticas tais como, vários mínimos locais, pontos de sela, vales e platôs ao redor da solução etc. Para viabilizar a abordagem escolhida, um modelo numérico foi escrito baseado na discretização por diferenças finitas da equação diferencial governante e condições de contorno. O erro funcional foi definido pela comparação entre medidas experimentais e numéricas de temperatura. O objetivo foi realizar simulações numéricas a fim de mapear a superfície de otimização correspondente e identificar a estrutura problemática associada ou patologia, chegando assim à reconstrução do coeficiente de convecção h. / Inverse thermal reconstruction techniques are widely used in different applications such as the determination of thermal properties of new materials, control of heat generation, temperature in manufacturing processes, etc. Despite the broad range of applicability, an inverse problem is intrinsically ill conditioned and has been the subject of the work of several researchers. The solution of an inverse 3-dimesional thermal problem is significantly complex, and, thus, requires a formulation that do not contain unrealistic experimental conditions such as 2-dimensional confinement and steadiness of the thermal field with respect to changes in internal parameters. One of the most adopted is the variational formulation based on quadratic error forms for the reconstruction of the internal heat conduction distribution and convection coefficient for a 3-dimensional problem. Within this framework, the ill conditioned nature of the problem manifests itself on the optimization surface by producing problematic topologies such as contour and multiple local minima, saddle points, plateaux around the solution pit and so on. To be able to apply th method a numerical model was written based on a finite difference discretization of the governing differential equation and boundary conditions. An error functional was defined by comparing experimental and numerical measurement temperatures. Numerical simulations aiming at mapping the corresponding optimization surfaces andatidentifing the associated problematic structures or pathologies, resulting in the reconstruction of convection coefficient.

A identificação de esforços dinâmicos vem despertando um contínuo interesse da comunidade modal e de teste de vibrações principalmente nas duas últimas décadas. De forma semelhante como na maioria das técnicas de identificação modal, a identificação de forças, representa um problema inverso. Problemas inversos são conhecidos pelo fato de serem naturalmente mau condicionados numericamente, uma vez que os mesmos representam uma operação de deconvolução no tempo. Dentre os métodos utilizados na identificação de forças a partir de medidas de movimento, pode-se destacar a técnica da pseudo inversa no domínio da frequência. A técnica da pseudo inversa requer o conhecimento das medidas das respostas da estrutura usualmente acelerações assim como das funções repostas em frequência da estrutura (FRF). Este método requer a inversão das matrizes de FRF dos sistemas para todas as linhas espectrais na faixa de frequência de interesse. Este procedimento de inversão usualmente apresenta dificuldades numéricas em algumas frequências. Será levantado suas principais vantagens e desvantagens quando comparado com um método no domínio do tempo no caso da técnica da SWAT, para alguns tipos de formas de excitação comumente empregada sem testes modais de vibração. São apresentados resultados de simulações numéricas e resultados experimentais para uma estrutura simples. / The main goal of this dissertation is to takle a difficult problem in experimental modal analysis that is the indirect identification of input forces based on the knowledge of the structure\'s output response and dynamic characteristics, such as impulse responses and/or FRF. This represents an inverse problem in mechanics and usually offers great numerical difficulties in the process of identification of the input forces. There are methods for input force identification in the lime and in the frequency domains. In lhe time domain the SWAT method (Sum of lhe Weighet Accelerations Technique) is a method that is based on the principle of motion of the mass center. This technique alows the estimation of the resulting force acting on the structure and is primarily used with impact force signals. In the frequency domain the pseudo-inverse technique is known to give estimates of the resulting forces acting on the structure under investigation. In this work numerically simulated as well as experimental results are presented for both methods and their major advantages and disadvantages are discussed. The pseudo-inverse method is further employed in the identification of experimental transient and random multiple inputs.

Lau Kin Wing. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2000. / Includes bibliographical references (leaves 80-83). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.3 / Chapter 1.1 --- Heat conduction problem --- p.3 / Chapter 1.2 --- Direct problem --- p.4 / Chapter 1.3 --- Inverse problem --- p.4 / Chapter 1.4 --- Difficulty of the inverse problems --- p.5 / Chapter 1.5 --- A simple but important example for instability --- p.5 / Chapter 1.6 --- The purpose of this thesis --- p.7 / Chapter 2 --- Stability of the inverse problem --- p.9 / Chapter 2.1 --- Conditional stability results --- p.9 / Chapter 2.2 --- Stability of the inverse problems --- p.11 / Chapter 3 --- The continuous formulation --- p.30 / Chapter 3.1 --- Constrained minimization problem --- p.30 / Chapter 3.2 --- Existence of minimizers to the minimization problem --- p.31 / Chapter 4 --- Discretization and its convergence --- p.36 / Chapter 4.1 --- Finite element space --- p.36 / Chapter 4.2 --- Two important discrete projection operators --- p.37 / Chapter 4.3 --- Finite element problem --- p.39 / Chapter 4.4 --- Existence of minimizers to the finite element problem --- p.39 / Chapter 4.5 --- Discrete minimizers and global minimizers --- p.42 / Chapter 5 --- Numerical algorithms --- p.51 / Chapter 5.1 --- Gateaux derivative --- p.51 / Chapter 5.2 --- Nonlinear single-grid gradient method --- p.53 / Chapter 5.3 --- Nonlinear multigrid gradient method --- p.55 / Chapter 6 --- Numerical experiments --- p.60 / Chapter 6.1 --- One dimensional examples --- p.60 / Chapter 6.2 --- Two dimensional examples --- p.66

Yip Chi Ming = 守恆及開放系統的能譜反問題 / 葉志明. / Thesis submitted in 2000. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2001. / Includes bibliographical references (leaves [244]-247). / Text in English; abstracts in English and Chinese. / Yip Chi Ming = Shou heng ji kai fang xi tong de neng pu fan wen ti / Ye Zhiming. / Abstract --- p.i / Acknowledgements --- p.ii / Contents --- p.iii / List of Figures --- p.viii / List of Tables --- p.xxi / Chapter Chapter 1. --- Introduction --- p.1 / Chapter 1.1 --- The Sturm-Liouville Problem --- p.3 / Chapter 1.2 --- Historical review of inverse problems --- p.7 / Chapter 1.3 --- Conservative systems --- p.10 / Chapter 1.4 --- Open systems --- p.10 / Chapter 1.5 --- Organization of the following chapters --- p.11 / Chapter Chapter 2. --- Conservative Spectral Problem --- p.12 / Chapter 2.1 --- The system --- p.12 / Chapter 2.2 --- Properties of conservative systems --- p.13 / Chapter 2.2.1 --- Asymptotic expansion of eigenvalues --- p.14 / Chapter 2.3 --- Forward spectral problem --- p.16 / Chapter 2.3.1 --- FDM and FEM --- p.17 / Chapter 2.3.2 --- Solving transcendental equation --- p.20 / Chapter 2.4 --- Phase shift problem --- p.20 / Chapter 2.4.1 --- Square well potential --- p.22 / Chapter Chapter 3. --- Forward Spectral Problem for Open Systems --- p.25 / Chapter 3.1 --- The system --- p.26 / Chapter 3.2 --- Properties of open systems --- p.28 / Chapter 3.2.1 --- Asymptotic behaviour of QNM eigenvalues --- p.28 / Chapter 3.2.2 --- Doubling of modes --- p.33 / Chapter 3.2.3 --- Generalized norm of QNMs --- p.34 / Chapter 3.2.4 --- Completeness --- p.37 / Chapter 3.2.5 --- Eigenfunction expansion for QNMs - two component formalism --- p.39 / Chapter 3.3 --- Forward spectral problem --- p.45 / Chapter Chapter 4. --- Conservative Inverse Problem --- p.50 / Chapter 4.1 --- Sun-Young-Zou (SYZ) method --- p.51 / Chapter 4.1.1 --- Perturbative inversion --- p.53 / Chapter 4.1.2 --- The regulators (δn) --- p.54 / Chapter 4.1.3 --- Total inversion (TI) --- p.59 / Chapter 4.1.4 --- Numerical results --- p.60 / Chapter 4.2 --- Rundell and Sacks method (RS method) --- p.74 / Chapter 4.2.1 --- Completeness --- p.75 / Chapter 4.2.2 --- The integral equation --- p.78 / Chapter 4.2.3 --- Uniqueness --- p.82 / Chapter 4.2.4 --- RS formalism --- p.84 / Chapter 4.2.5 --- Numerical results and difficulties --- p.89 / Chapter 4.2.6 --- Summary --- p.110 / Chapter 4.3 --- Phase shift problem --- p.112 / Chapter 4.3.1 --- Reduction to spectral problem --- p.113 / Chapter 4.3.2 --- Modified RS algorithm for finite-range phase shift problem --- p.116 / Chapter 4.3.3 --- Discussion --- p.130 / Chapter 4.4 --- Bound states --- p.131 / Chapter Chapter 5. --- Open Inverse Problem --- p.136 / Chapter 5.1 --- SYZ method --- p.136 / Chapter 5.1.1 --- Perturbative Inversion (PI) and Total Inversion (TI) --- p.137 / Chapter 5.1.2 --- Numerical results --- p.138 / Chapter 5.1.3 --- Other choices of (δn) --- p.156 / Chapter 5.2 --- RS method --- p.158 / Chapter 5.2.1 --- The integral equation --- p.159 / Chapter 5.2.2 --- Cauchy data --- p.160 / Chapter 5.2.3 --- Completeness conjecture --- p.162 / Chapter 5.2.4 --- Numerical verification of completeness condition --- p.163 / Chapter 5.2.5 --- Inversion for Cauchy data --- p.166 / Chapter 5.2.6 --- Cauchy data on 0 < x≤ α --- p.167 / Chapter 5.2.7 --- Comparison system --- p.169 / Chapter Chapter 6. --- Conclusions and Further Studies --- p.188 / Chapter 6.1 --- Conclusions of this thesis --- p.188 / Chapter 6.2 --- Further studies --- p.189 / Chapter Appendix A. --- Singular Value Decomposition --- p.199 / Chapter Appendix B. --- Asymptotic Behaviour of Phase Shifts --- p.203 / Chapter B.1 --- Asymptotic behaviour of phase shift data --- p.203 / Chapter B.2 --- Levinson's theorem --- p.204 / Chapter Appendix C. --- Forward Problem for Conservative Systems --- p.207 / Chapter C.1 --- Finite difference method --- p.207 / Chapter C.2 --- Finite element method --- p.209 / Chapter C.2.1 --- Solving transcendental equation --- p.215 / Chapter Appendix D. --- FDM and FEM for Open Systems --- p.220 / Chapter D.1 --- Finite difference method --- p.220 / Chapter D.2 --- Finite element method --- p.222 / Chapter Appendix E. --- Asymptotic Behaviour of NM Eigenvalues --- p.226 / Chapter Appendix F. --- Asymptotic Behaviour of QNM Eigenvalues --- p.232 / Chapter Appendix G. --- QNM Forward Problem 一 Transcendental Equation --- p.239 / Chapter Appendix H. --- Forward Problem - Calculation of Phase Shifts --- p.243 / Bibliography --- p.245

by Hau-Leung Chung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2002. / Includes bibliographical references (leaves 41-42). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.5 / Chapter 1.1 --- Paper I --- p.5 / Chapter 1.2 --- Paper II --- p.6 / Chapter 2 --- The Inexact Newton-Like Method for Inverse Eigen- value Problem --- p.8 / Chapter 2.1 --- Introduction --- p.8 / Chapter 2.2 --- The Newton-Like Method --- p.9 / Chapter 2.3 --- The Inexact Newton-Like Method --- p.11 / Chapter 2.4 --- Convergence Analysis --- p.14 / Chapter 2.5 --- Numerical Experiments --- p.22 / Chapter 3 --- A DCT Based Watermarking Scheme for Copyright Protection of Images --- p.26 / Chapter 3.1 --- Introduction --- p.26 / Chapter 3.2 --- Preliminary --- p.28 / Chapter 3.2.1 --- Gray-level image --- p.28 / Chapter 3.2.2 --- Color image --- p.29 / Chapter 3.2.3 --- The Discrete Cosine transform --- p.30 / Chapter 3.3 --- Watermarking Approaches --- p.31 / Chapter 3.3.1 --- Insertion procedures --- p.31 / Chapter 3.3.2 --- Retrieval procedures --- p.33 / Chapter 3.4 --- Experimental results --- p.34 / Chapter 3.5 --- Other Applications --- p.38 / Chapter 3.5.1 --- Data Hiding --- p.38 / Chapter 3.5.2 --- Authentication --- p.39 / Chapter 3.5.3 --- Fingerprinting --- p.39 / Chapter 3.5.4 --- Copy Control --- p.39 / Chapter 3.6 --- Conclusion --- p.40 / Bibliography --- p.41

Dans une première partie théorique, nous nous penchons sur une analyse rigoureuse des performances de l'algorithme Sequential Monte Carlo (SMC) conduisant à des résultats de type bornes L^p et inégalités de concentration. Nous abordons notamment le cas particulier des SMC associés à des schémas de température, et analysons sur ce sujet un processus à schéma adaptatif.Dans une seconde partie appliquée, nous illustrons son utilisation par la résolution de problèmes inverses concrets en électromagnétisme. Le plus important d'entre eux consiste à estimer les propriétés radioélectriques de matériaux recouvrant un objet de géométrie connue, et cela à partir de mesures de champs rétrodiffusés. Nous montrons comment l'algorithme SMC, couplé à des calculs analytiques, permet une inversion bayésienne, et fournit des estimées robustes enrichies d'estimations des incertitudes. / Sequential and Quantum Monte Carlo methods, as well as genetic type search algorithms, can be interpreted as a mean field and interacting particle approximation of Feynman-Kac models in distribution spaces. The performance of these population Monte Carlo algorithms is strongly related to the stability properties of nonlinear Feynman-Kac semigroups. In a first theoretical part, we analyze these models in terms of Dobrushin ergodic coefficients of the reference Markov transitions and the oscillations of the potential functions. Sufficient conditions for uniform concentration inequalities w.r.t. time are expressed explicitly in terms of these two quantities. We provide an original perturbation analysis that applies to annealed and adaptive FK models, yielding what seems to be the first results of this kind for these type of models. Special attention is devoted to the particular case of Boltzmann-Gibbs measures' sampling. In this context, we design an explicit way of tuning the number of Markov Chain Monte Carlo iterations with temperature schedule. We also propose and analyze an alternative interacting particle method based on an adaptive strategy to define the temperature increments. In a second, applied part, we illustrate the use of these SMC algorithms in the field of inverse problems. Mainly, the following electromagnetism (EM) inverse problem is addressed. It consists in estimating local radioelectric properties of materials recovering an object from global EM scattering measurements, at various incidences and wave frequencies. This large scale ill-posed inverse problem is explored by an intensive exploitation of an efficient 2D Maxwell solver, distributed on high performance computing machines. Applied to a large training data set, a statistical analysis reduces the problem to a simpler probabilistic metamodel, on which Bayesian inference can be performed. Considering the radioelectric properties as a hidden dynamic stochastic process, that evolves in function of the frequency, it is shown how the Sequential Monte Carlo methods can take benefit of the structure and provide local EM property estimates.

This thesis introduces novel ideas in subsurface reservoir model calibration known as History Matching in the reservoir engineering community. The target of history matching is to mimic historical pressure and production data from the producing wells with the output from the reservoir simulator for the sole purpose of reducing uncertainty from such models and improving confidence in production forecast. Ensemble based methods such as the Ensemble Kalman Filter (EnKF) and Ensemble Smoother with Multiple Data Assimilation (ES-MDA) as been proposed for history matching in literature. EnKF/ES-MDA is a Monte Carlo ensemble nature filter where the representation of the covariance is located at the mean of the ensemble of the distribution instead of the uncertain true model. In EnKF/ES-MDA calculation of the gradients is not required, and the mean of the ensemble of the realisations provides the best estimates with the ensemble on its own estimating the probability density. However, because of the inherent assumptions of linearity and Gaussianity of petrophysical properties distribution, EnKF/ES-MDA does not provide an acceptable history-match and characterisation of uncertainty when tasked with calibrating reservoir models with channel like structures. One of the novel methods introduced in this thesis combines a successive parameter and shape reconstruction using level set functions (EnKF/ES-MDA-level set) where the spatial permeability fields' indicator functions are transformed into signed distances. These signed distances functions (better suited to the Gaussian requirement of EnKF/ES-MDA) are then updated during the EnKF/ES-MDA inversion. The method outperforms standard EnKF/ES-MDA in retaining geological realism of channels during and after history matching and also yielded lower Root-Mean-Square function (RMS) as compared to the standard EnKF/ES-MDA. To improve on the petrophysical reconstruction attained with the EnKF/ES-MDA-level set technique, a novel parametrisation incorporating an unsupervised machine learning method for the recovery of the permeability and porosity field is developed. The permeability and porosity fields are posed as a sparse field recovery problem and a novel SELE (Sparsity-Ensemble optimization-Level-set Ensemble optimisation) approach is proposed for the history matching. In SELE some realisations are learned using the K-means clustering Singular Value Decomposition (K-SVD) to generate an overcomplete codebook or dictionary. This dictionary is combined with Orthogonal Matching Pursuit (OMP) to ease the ill-posed nature of the production data inversion, converting our permeability/porosity field into a sparse domain. SELE enforces prior structural information on the model during the history matching and reduces the computational complexity of the Kalman gain matrix, leading to faster attainment of the minimum of the cost function value. From the results shown in the thesis; SELE outperforms conventional EnKF/ES-MDA in matching the historical production data, evident in the lower RMS value and a high geological realism/similarity to the true reservoir model.

In this thesis we introduce a framework for parallel MCMC methods which we call parallel adaptive importance sampling (PAIS). At each iteration we have an ensemble of particles, from which PAIS builds a kernel density estimate (KDE). We propose a new ensemble, using this KDE, that is weighted according to standard importance sampling rules. A state-of-the art resampling method from the optimal transportation literature, or alternatively our own novel resampling algorithm, can be used to produce an equally weighted ensemble from this weighted ensemble. This equally weighted ensemble is approximately distributed according to the target distribution and is used to progress the algorithm. The PAIS algorithm outputs a weighted sample. We introduce an adaptive scheme for PAIS which automatically tunes the scaling parameters required for efficient sampling. This adaptive tuning converges rapidly for the target distributions we have experimented with and significantly reduces the burn-in period of the algorithm. PAIS has been designed to work well on computers with parallel processing units available, and we have demonstrated that a doubling of the number of processing units available more than halves the number of iterations required to reach the same accuracy. The numerical examples have been implemented on a shared memory system. PAIS is incredibly flexible in terms of the proposal distributions and resampling methods we can use. Throughout the thesis we introduce a number of these proposal schemes, and highlight when they may be of use. Of particular interest is the transport map based proposal scheme introduced in Chapter 7 which, while more expensive than the other schemes, allows us to sample efficiently from a wide range of complex target distributions.