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Sequential Monte Carlo Parameter Estimation For Differential Equations
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Book Synopsis Bayesian Filtering and Smoothing by : Simo Särkkä
Download or read book Bayesian Filtering and Smoothing written by Simo Särkkä and published by Cambridge University Press. This book was released on 2013-09-05 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: A unified Bayesian treatment of the state-of-the-art filtering, smoothing, and parameter estimation algorithms for non-linear state space models.
Book Synopsis Parameter Estimation in Stochastic Volatility Models by : Jaya P. N. Bishwal
Download or read book Parameter Estimation in Stochastic Volatility Models written by Jaya P. N. Bishwal and published by Springer Nature. This book was released on 2022-08-06 with total page 634 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book develops alternative methods to estimate the unknown parameters in stochastic volatility models, offering a new approach to test model accuracy. While there is ample research to document stochastic differential equation models driven by Brownian motion based on discrete observations of the underlying diffusion process, these traditional methods often fail to estimate the unknown parameters in the unobserved volatility processes. This text studies the second order rate of weak convergence to normality to obtain refined inference results like confidence interval, as well as nontraditional continuous time stochastic volatility models driven by fractional Levy processes. By incorporating jumps and long memory into the volatility process, these new methods will help better predict option pricing and stock market crash risk. Some simulation algorithms for numerical experiments are provided.
Book Synopsis An Introduction to Sequential Monte Carlo by : Nicolas Chopin
Download or read book An Introduction to Sequential Monte Carlo written by Nicolas Chopin and published by Springer Nature. This book was released on 2020-10-01 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a general introduction to Sequential Monte Carlo (SMC) methods, also known as particle filters. These methods have become a staple for the sequential analysis of data in such diverse fields as signal processing, epidemiology, machine learning, population ecology, quantitative finance, and robotics. The coverage is comprehensive, ranging from the underlying theory to computational implementation, methodology, and diverse applications in various areas of science. This is achieved by describing SMC algorithms as particular cases of a general framework, which involves concepts such as Feynman-Kac distributions, and tools such as importance sampling and resampling. This general framework is used consistently throughout the book. Extensive coverage is provided on sequential learning (filtering, smoothing) of state-space (hidden Markov) models, as this remains an important application of SMC methods. More recent applications, such as parameter estimation of these models (through e.g. particle Markov chain Monte Carlo techniques) and the simulation of challenging probability distributions (in e.g. Bayesian inference or rare-event problems), are also discussed. The book may be used either as a graduate text on Sequential Monte Carlo methods and state-space modeling, or as a general reference work on the area. Each chapter includes a set of exercises for self-study, a comprehensive bibliography, and a “Python corner,” which discusses the practical implementation of the methods covered. In addition, the book comes with an open source Python library, which implements all the algorithms described in the book, and contains all the programs that were used to perform the numerical experiments.
Book Synopsis Backward Stochastic Differential Equations by : N El Karoui
Download or read book Backward Stochastic Differential Equations written by N El Karoui and published by CRC Press. This book was released on 1997-01-17 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the texts of seminars presented during the years 1995 and 1996 at the Université Paris VI and is the first attempt to present a survey on this subject. Starting from the classical conditions for existence and unicity of a solution in the most simple case-which requires more than basic stochartic calculus-several refinements on the hypotheses are introduced to obtain more general results.
Book Synopsis Applied Stochastic Differential Equations by : Simo Särkkä
Download or read book Applied Stochastic Differential Equations written by Simo Särkkä and published by Cambridge University Press. This book was released on 2019-05-02 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: With this hands-on introduction readers will learn what SDEs are all about and how they should use them in practice.
Book Synopsis Pattern Recognition in Bioinformatics by : Tjeerd M.H. Dijkstra
Download or read book Pattern Recognition in Bioinformatics written by Tjeerd M.H. Dijkstra and published by Springer Science & Business Media. This book was released on 2010-09-20 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 5th International Conference on Pattern Recognition in Bioinformatics, PRIB 2010, held in Nijmegen, The Netherlands, in September 2010. The 38 revised full papers presented were carefully reviewed and selected from 46 submissions. The field of bioinformatics has two main objectives: the creation and maintenance of biological databases and the analysis of life sciences data in order to unravel the mysteries of biological function. Computer science methods such as pattern recognition, machine learning, and data mining have a great deal to offer the field of bioinformatics.
Book Synopsis Network Bioscience, 2nd Edition by : Marco Pellegrini
Download or read book Network Bioscience, 2nd Edition written by Marco Pellegrini and published by Frontiers Media SA. This book was released on 2020-03-27 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: Network science has accelerated a deep and successful trend in research that influences a range of disciplines like mathematics, graph theory, physics, statistics, data science and computer science (just to name a few) and adapts the relevant techniques and insights to address relevant but disparate social, biological, technological questions. We are now in an era of 'big biological data' supported by cost-effective high-throughput genomic, transcriptomic, proteomic, metabolomic data collection techniques that allow one to take snapshots of the cells' molecular profiles in a systematic fashion. Moreover recently, also phenotypic data, data on diseases, symptoms, patients, etc. are being collected at nation-wide level thus giving us another source of highly related (causal) 'big data'. This wealth of data is usually modeled as networks (aka binary relations, graphs or webs) of interactions, (including protein-protein, metabolic, signaling and transcription-regulatory interactions). The network model is a key view point leading to the uncovering of mesoscale phenomena, thus providing an essential bridge between the observable phenotypes and 'omics' underlying mechanisms. Moreover, network analysis is a powerful 'hypothesis generation' tool guiding the scientific cycle of 'data gathering', 'data interpretation, 'hypothesis generation' and 'hypothesis testing'. A major challenge in contemporary research is the synthesis of deep insights coming from network science with the wealth of data (often noisy, contradictory, incomplete and difficult to replicate) so to answer meaningful biological questions, in a quantifiable way using static and dynamic properties of biological networks.
Book Synopsis Verification, Model Checking, and Abstract Interpretation by : Cezara Dragoi
Download or read book Verification, Model Checking, and Abstract Interpretation written by Cezara Dragoi and published by Springer Nature. This book was released on 2023-01-16 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 24th International Conference on Verification, Model Checking, and Abstract Interpretation, VMCAI 2023, which took place in Boston, USA, in January 2023. The 17 full papers presented in this book were carefully reviewed and selected from 34 submissions. The contributions deal with program verification, model checking, abstract interpretation, program synthesis, static analysis, type systems, deductive methods, decision procedures, theorem proving, program certification, debugging techniques, program transformation, optimization, and hybrid and cyber-physical systems.
Book Synopsis Statistical Methods for Stochastic Differential Equations by : Mathieu Kessler
Download or read book Statistical Methods for Stochastic Differential Equations written by Mathieu Kessler and published by CRC Press. This book was released on 2012-05-17 with total page 509 pages. Available in PDF, EPUB and Kindle. Book excerpt: The seventh volume in the SemStat series, Statistical Methods for Stochastic Differential Equations presents current research trends and recent developments in statistical methods for stochastic differential equations. Written to be accessible to both new students and seasoned researchers, each self-contained chapter starts with introductions to the topic at hand and builds gradually towards discussing recent research. The book covers Wiener-driven equations as well as stochastic differential equations with jumps, including continuous-time ARMA processes and COGARCH processes. It presents a spectrum of estimation methods, including nonparametric estimation as well as parametric estimation based on likelihood methods, estimating functions, and simulation techniques. Two chapters are devoted to high-frequency data. Multivariate models are also considered, including partially observed systems, asynchronous sampling, tests for simultaneous jumps, and multiscale diffusions. Statistical Methods for Stochastic Differential Equations is useful to the theoretical statistician and the probabilist who works in or intends to work in the field, as well as to the applied statistician or financial econometrician who needs the methods to analyze biological or financial time series.
Book Synopsis Modeling and Parameter Estimation for Heterogeneous Cell Populations by : Jan Hasenauer
Download or read book Modeling and Parameter Estimation for Heterogeneous Cell Populations written by Jan Hasenauer and published by Logos Verlag Berlin GmbH. This book was released on 2013 with total page 143 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most of the modeling performed in biology aims at achieving a quantitative description and understanding of the intracellular signaling pathways within a "typical cell". However, in many biologically important situations even genetically identical cell populations show a heterogeneous response. This means that individual members of the cell population behave differently. Such situations require the study of cell-to-cell variability and the development of models for heterogeneous cell populations. The main contribution of this thesis is the development of unifying modeling frameworks for signal transduction and proliferation processes in heterogeneous cell populations. These modeling frameworks allow for the detailed description of individual cells as well as differences between them. In contrast to many existing modeling approaches, the proposed frameworks allow for a direct comparison of model predictions with available data. Beyond this, the proposed population models can be simulated efficiently and, by exploiting the model structures, we are able to develop model-tailored Bayesian parameter estimation methods. These methods enable the calculation of the optimal parameter estimates, as well as the evaluation of the parameter and prediction uncertainties. The proposed tools allow for novel insights in population dynamics, in particular the model-based characterization of population heterogeneity and cellular subgroups. This is illustrated for two different application examples: pro- and anti-apoptotic signaling, which is interesting in the context of cancer therapy, and immune cell proliferation.
Book Synopsis Model Calibration and Parameter Estimation by : Ne-Zheng Sun
Download or read book Model Calibration and Parameter Estimation written by Ne-Zheng Sun and published by Springer. This book was released on 2015-07-01 with total page 638 pages. Available in PDF, EPUB and Kindle. Book excerpt: This three-part book provides a comprehensive and systematic introduction to these challenging topics such as model calibration, parameter estimation, reliability assessment, and data collection design. Part 1 covers the classical inverse problem for parameter estimation in both deterministic and statistical frameworks, Part 2 is dedicated to system identification, hyperparameter estimation, and model dimension reduction, and Part 3 considers how to collect data and construct reliable models for prediction and decision-making. For the first time, topics such as multiscale inversion, stochastic field parameterization, level set method, machine learning, global sensitivity analysis, data assimilation, model uncertainty quantification, robust design, and goal-oriented modeling, are systematically described and summarized in a single book from the perspective of model inversion, and elucidated with numerical examples from environmental and water resources modeling. Readers of this book will not only learn basic concepts and methods for simple parameter estimation, but also get familiar with advanced methods for modeling complex systems. Algorithms for mathematical tools used in this book, such as numerical optimization, automatic differentiation, adaptive parameterization, hierarchical Bayesian, metamodeling, Markov chain Monte Carlo, are covered in details. This book can be used as a reference for graduate and upper level undergraduate students majoring in environmental engineering, hydrology, and geosciences. It also serves as an essential reference book for professionals such as petroleum engineers, mining engineers, chemists, mechanical engineers, biologists, biology and medical engineering, applied mathematicians, and others who perform mathematical modeling.
Book Synopsis Computational Methods in Finance by : Ali Hirsa
Download or read book Computational Methods in Finance written by Ali Hirsa and published by CRC Press. This book was released on 2016-04-19 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: Helping readers accurately price a vast array of derivatives, this self-contained text explains how to solve complex functional equations through numerical methods. It addresses key computational methods in finance, including transform techniques, the finite difference method, and Monte Carlo simulation. Developed from his courses at Columbia University and the Courant Institute of New York University, the author also covers model calibration and optimization and describes techniques, such as Kalman and particle filters, for parameter estimation.
Book Synopsis Advances in Mathematical Sciences by : Bahar Acu
Download or read book Advances in Mathematical Sciences written by Bahar Acu and published by Springer Nature. This book was released on 2020-07-16 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume highlights the mathematical research presented at the 2019 Association for Women in Mathematics (AWM) Research Symposium held at Rice University, April 6-7, 2019. The symposium showcased research from women across the mathematical sciences working in academia, government, and industry, as well as featured women across the career spectrum: undergraduates, graduate students, postdocs, and professionals. The book is divided into eight parts, opening with a plenary talk and followed by a combination of research paper contributions and survey papers in the different areas of mathematics represented at the symposium: algebraic combinatorics and graph theory algebraic biology commutative algebra analysis, probability, and PDEs topology applied mathematics mathematics education
Book Synopsis Bayesian Time Series Models by : David Barber
Download or read book Bayesian Time Series Models written by David Barber and published by Cambridge University Press. This book was released on 2011-08-11 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first unified treatment of time series modelling techniques spanning machine learning, statistics, engineering and computer science.
Book Synopsis Health Assessment of Engineered Structures by : Achintya Haldar
Download or read book Health Assessment of Engineered Structures written by Achintya Haldar and published by World Scientific. This book was released on 2013 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers some of the most recent developments and application potentials in structural health assessment for non-experts in the subject. Among topics addressed are sensor types, platforms and data conditioning for practical applications, wireless collection of sensor data, sensor power needs and on-site energy harvesting, long-term monitoring of structures, uncertainty in collected data, and future directions in structural health assessment.
Download or read book Data Assimilation written by Geir Evensen and published by Springer Science & Business Media. This book was released on 2006-12-22 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book reviews popular data-assimilation methods, such as weak and strong constraint variational methods, ensemble filters and smoothers. The author shows how different methods can be derived from a common theoretical basis, as well as how they differ or are related to each other, and which properties characterize them, using several examples. Readers will appreciate the included introductory material and detailed derivations in the text, and a supplemental web site.
Book Synopsis Bayesian Risk Management by : Matt Sekerke
Download or read book Bayesian Risk Management written by Matt Sekerke and published by John Wiley & Sons. This book was released on 2015-08-19 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: A risk measurement and management framework that takes model risk seriously Most financial risk models assume the future will look like the past, but effective risk management depends on identifying fundamental changes in the marketplace as they occur. Bayesian Risk Management details a more flexible approach to risk management, and provides tools to measure financial risk in a dynamic market environment. This book opens discussion about uncertainty in model parameters, model specifications, and model-driven forecasts in a way that standard statistical risk measurement does not. And unlike current machine learning-based methods, the framework presented here allows you to measure risk in a fully-Bayesian setting without losing the structure afforded by parametric risk and asset-pricing models. Recognize the assumptions embodied in classical statistics Quantify model risk along multiple dimensions without backtesting Model time series without assuming stationarity Estimate state-space time series models online with simulation methods Uncover uncertainty in workhorse risk and asset-pricing models Embed Bayesian thinking about risk within a complex organization Ignoring uncertainty in risk modeling creates an illusion of mastery and fosters erroneous decision-making. Firms who ignore the many dimensions of model risk measure too little risk, and end up taking on too much. Bayesian Risk Management provides a roadmap to better risk management through more circumspect measurement, with comprehensive treatment of model uncertainty.
