Statistical Inferences On High Frequency Financial Data And Quantum State Tomography

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Statistical Inferences on High-frequency Financial Data and Quantum State Tomography

Author : Donggyu Kim
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (968 download)

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Book Synopsis Statistical Inferences on High-frequency Financial Data and Quantum State Tomography by : Donggyu Kim

Download or read book Statistical Inferences on High-frequency Financial Data and Quantum State Tomography written by Donggyu Kim and published by . This book was released on 2016 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this dissertation, we study two topics, the volatility analysis based on the high-frequency financial data and quantum state tomography. In Part I, we study the volatility analysis based on the high-frequency financial data. We first investigate how to estimate large volatility matrices effectively and efficiently. For example, we introduce threshold rules to regularize kernel realized volatility, pre-averaging realized volatility, and multi-scale realized volatility. Their convergence rates are derived under sparsity on the large integrated volatility matrix. To account for the sparse structure well, we employ the factor-based Itô processes and under the proposed factor-based model, we develop an estimation scheme called "blocking and regularizing". Also, we establish a minimax lower bound for the eigenspace estimation problem and propose sparse principal subspace estimation methods by using the multi-scale realized volatility matrix estimator or the pre-averaging realized volatility matrix estimator. Finally, we introduce a unified model, which can accommodate both continuous-time Itô processes used to model high-frequency stock prices and GARCH processes employed to model low-frequency stock prices, by embedding a discrete-time GARCH volatility in its continuous-time instantaneous volatility. We adopt realized volatility estimators based on high-frequency financial data and the quasi-likelihood function for the low-frequency GARCH structure to develop parameter estimation methods for the combined high-frequency and low-frequency data. In Part II, we study the quantum state tomography with Pauli measurements. In the quantum science, the dimension of the quantum density matrix usually grows exponentially with the size of the quantum system, and thus it is important to develop effective and efficient estimation methods for the large quantum density matrices. We study large density matrix estimation methods and obtain the minimax lower bound under some sparse structures, for example, (i) the coefficients of the density matrix with respect to the Pauli basis are sparse; (ii) the rank is low; (iii) the eigenvectors are sparse. Their performances may depend on the sparse structure, and so it is essential to choose appropriate estimation methods according to the sparse structure. In light of this, we study how to conduct hypothesis tests for the sparse structure. Specifically, we propose hypothesis test procedures and develop central limit theorems for each test statistics. A simulation study is conducted to check the finite sample performances of proposed estimation methods and hypothesis tests.

Statistical Inferences on High-frequency Financial Data and Quantum State Tomography

Author :
Publisher :
ISBN 13 :
Total Pages : 368 pages
Book Rating : 4.:/5 (956 download)

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Book Synopsis Statistical Inferences on High-frequency Financial Data and Quantum State Tomography by :

Download or read book Statistical Inferences on High-frequency Financial Data and Quantum State Tomography written by and published by . This book was released on 2016 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this dissertation, we study two topics, the volatility analysis based on the high-frequency financial data and quantum state tomography. In Part I, we study the volatility analysis based on the high-frequency financial data. We first investigate how to estimate large volatility matrices effectively and efficiently. For example, we introduce threshold rules to regularize kernel realized volatility, pre-averaging realized volatility, and multi-scale realized volatility. Their convergence rates are derived under sparsity on the large integrated volatility matrix. To account for the sparse structure well, we employ the factor-based Itô processes and under the proposed factor-based model, we develop an estimation scheme called “blocking and regularizing". Also, we establish a minimax lower bound for the eigenspace estimation problem and propose sparse principal subspace estimation methods by using the multi-scale realized volatility matrix estimator or the pre-averaging realized volatility matrix estimator. Finally, we introduce a unified model, which can accommodate both continuous-time Itô processes used to model high-frequency stock prices and GARCH processes employed to model low-frequency stock prices, by embedding a discrete-time GARCH volatility in its continuous-time instantaneous volatility. We adopt realized volatility estimators based on high-frequency financial data and the quasi-likelihood function for the low-frequency GARCH structure to develop parameter estimation methods for the combined high-frequency and low-frequency data. In Part II, we study the quantum state tomography with Pauli measurements. In the quantum science, the dimension of the quantum density matrix usually grows exponentially with the size of the quantum system, and thus it is important to develop effective and efficient estimation methods for the large quantum density matrices. We study large density matrix estimation methods and obtain the minimax lower bound under some sparse structures, for example, (i) the coefficients of the density matrix with respect to the Pauli basis are sparse; (ii) the rank is low; (iii) the eigenvectors are sparse. Their performances may depend on the sparse structure, and so it is essential to choose appropriate estimation methods according to the sparse structure. In light of this, we study how to conduct hypothesis tests for the sparse structure. Specifically, we propose hypothesis test procedures and develop central limit theorems for each test statistics. A simulation study is conducted to check the finite sample performances of proposed estimation methods and hypothesis tests.

Handbook of Modeling High-Frequency Data in Finance

Author : Frederi G. Viens
Publisher : John Wiley & Sons
ISBN 13 : 1118204565
Total Pages : 468 pages
Book Rating : 4.1/5 (182 download)

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Book Synopsis Handbook of Modeling High-Frequency Data in Finance by : Frederi G. Viens

Download or read book Handbook of Modeling High-Frequency Data in Finance written by Frederi G. Viens and published by John Wiley & Sons. This book was released on 2011-11-16 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: CUTTING-EDGE DEVELOPMENTS IN HIGH-FREQUENCY FINANCIAL ECONOMETRICS In recent years, the availability of high-frequency data and advances in computing have allowed financial practitioners to design systems that can handle and analyze this information. Handbook of Modeling High-Frequency Data in Finance addresses the many theoretical and practical questions raised by the nature and intrinsic properties of this data. A one-stop compilation of empirical and analytical research, this handbook explores data sampled with high-frequency finance in financial engineering, statistics, and the modern financial business arena. Every chapter uses real-world examples to present new, original, and relevant topics that relate to newly evolving discoveries in high-frequency finance, such as: Designing new methodology to discover elasticity and plasticity of price evolution Constructing microstructure simulation models Calculation of option prices in the presence of jumps and transaction costs Using boosting for financial analysis and trading The handbook motivates practitioners to apply high-frequency finance to real-world situations by including exclusive topics such as risk measurement and management, UHF data, microstructure, dynamic multi-period optimization, mortgage data models, hybrid Monte Carlo, retirement, trading systems and forecasting, pricing, and boosting. The diverse topics and viewpoints presented in each chapter ensure that readers are supplied with a wide treatment of practical methods. Handbook of Modeling High-Frequency Data in Finance is an essential reference for academics and practitioners in finance, business, and econometrics who work with high-frequency data in their everyday work. It also serves as a supplement for risk management and high-frequency finance courses at the upper-undergraduate and graduate levels.

Handbook of High-Frequency Trading and Modeling in Finance

Author : Ionut Florescu
Publisher : John Wiley & Sons
ISBN 13 : 1118593324
Total Pages : 414 pages
Book Rating : 4.1/5 (185 download)

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Book Synopsis Handbook of High-Frequency Trading and Modeling in Finance by : Ionut Florescu

Download or read book Handbook of High-Frequency Trading and Modeling in Finance written by Ionut Florescu and published by John Wiley & Sons. This book was released on 2016-04-05 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: Reflecting the fast pace and ever-evolving nature of the financial industry, the Handbook of High-Frequency Trading and Modeling in Finance details how high-frequency analysis presents new systematic approaches to implementing quantitative activities with high-frequency financial data. Introducing new and established mathematical foundations necessary to analyze realistic market models and scenarios, the handbook begins with a presentation of the dynamics and complexity of futures and derivatives markets as well as a portfolio optimization problem using quantum computers. Subsequently, the handbook addresses estimating complex model parameters using high-frequency data. Finally, the handbook focuses on the links between models used in financial markets and models used in other research areas such as geophysics, fossil records, and earthquake studies. The Handbook of High-Frequency Trading and Modeling in Finance also features: • Contributions by well-known experts within the academic, industrial, and regulatory fields • A well-structured outline on the various data analysis methodologies used to identify new trading opportunities • Newly emerging quantitative tools that address growing concerns relating to high-frequency data such as stochastic volatility and volatility tracking; stochastic jump processes for limit-order books and broader market indicators; and options markets • Practical applications using real-world data to help readers better understand the presented material The Handbook of High-Frequency Trading and Modeling in Finance is an excellent reference for professionals in the fields of business, applied statistics, econometrics, and financial engineering. The handbook is also a good supplement for graduate and MBA-level courses on quantitative finance, volatility, and financial econometrics. Ionut Florescu, PhD, is Research Associate Professor in Financial Engineering and Director of the Hanlon Financial Systems Laboratory at Stevens Institute of Technology. His research interests include stochastic volatility, stochastic partial differential equations, Monte Carlo Methods, and numerical methods for stochastic processes. Dr. Florescu is the author of Probability and Stochastic Processes, the coauthor of Handbook of Probability, and the coeditor of Handbook of Modeling High-Frequency Data in Finance, all published by Wiley. Maria C. Mariani, PhD, is Shigeko K. Chan Distinguished Professor in Mathematical Sciences and Chair of the Department of Mathematical Sciences at The University of Texas at El Paso. Her research interests include mathematical finance, applied mathematics, geophysics, nonlinear and stochastic partial differential equations and numerical methods. Dr. Mariani is the coeditor of Handbook of Modeling High-Frequency Data in Finance, also published by Wiley. H. Eugene Stanley, PhD, is William Fairfield Warren Distinguished Professor at Boston University. Stanley is one of the key founders of the new interdisciplinary field of econophysics, and has an ISI Hirsch index H=128 based on more than 1200 papers. In 2004 he was elected to the National Academy of Sciences. Frederi G. Viens, PhD, is Professor of Statistics and Mathematics and Director of the Computational Finance Program at Purdue University. He holds more than two dozen local, regional, and national awards and he travels extensively on a world-wide basis to deliver lectures on his research interests, which range from quantitative finance to climate science and agricultural economics. A Fellow of the Institute of Mathematics Statistics, Dr. Viens is the coeditor of Handbook of Modeling High-Frequency Data in Finance, also published by Wiley.

High-frequency data analysis

Author : Nadine Hirte
Publisher : GRIN Verlag
ISBN 13 : 3638285227
Total Pages : 30 pages
Book Rating : 4.6/5 (382 download)

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Book Synopsis High-frequency data analysis by : Nadine Hirte

Download or read book High-frequency data analysis written by Nadine Hirte and published by GRIN Verlag. This book was released on 2004-06-23 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt: Seminar paper from the year 2003 in the subject Mathematics - Statistics, grade: 2.0 (B), European University Viadrina Frankfurt (Oder), language: English, abstract: Today the financial market becomes more complex and includes more competition. Reasons are trends like globalization, liberalization and lower-cost trading mechanism. The market microstructure research has the aim of an efficient market. It is focused on the structure of the financial market. The investigation becomes possible through the availability of high- frequency data. Those data exist especially in the United States and like that most of the research focuses this market. To explain the phenomena, which have been found adequate, models that fit the characteristics of high- frequency data have to be developed. The research is important to understand actions on the market as well as develop new efficient mechanism. One part of the market microstructure field is the bid-ask spread. It will be focus of this paper. In the first two parts it will be discussed theoretically. In the last part one model will be empirically analyzed and tested on its usefulness and validity. The second part of this paper explains the basic elements surrounding the research of bid-ask spread. Those are the financial market, market microstructure as well as high-frequency data. In the following part the bid-ask spread itself, approaches, researches and models focussing the spread will be discussed. The model of Roll (1984) will be explained in detail. The last part will be the empirical analysis of the model of Roll. It is analyzed with data from the NASDAQ.

Statistical Inferences and Computing for Diffusion Models in Finance

Author : Hai Xu
Publisher :
ISBN 13 :
Total Pages : 280 pages
Book Rating : 4.:/5 (746 download)

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Book Synopsis Statistical Inferences and Computing for Diffusion Models in Finance by : Hai Xu

Download or read book Statistical Inferences and Computing for Diffusion Models in Finance written by Hai Xu and published by . This book was released on 2006 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Separating Information Maximum Likelihood Method for High-Frequency Financial Data

Author : Naoto Kunitomo
Publisher : Springer
ISBN 13 : 9784431559283
Total Pages : 114 pages
Book Rating : 4.5/5 (592 download)

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Book Synopsis Separating Information Maximum Likelihood Method for High-Frequency Financial Data by : Naoto Kunitomo

Download or read book Separating Information Maximum Likelihood Method for High-Frequency Financial Data written by Naoto Kunitomo and published by Springer. This book was released on 2018-07-02 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a systematic explanation of the SIML (Separating Information Maximum Likelihood) method, a new approach to financial econometrics. Considerable interest has been given to the estimation problem of integrated volatility and covariance by using high-frequency financial data. Although several new statistical estimation procedures have been proposed, each method has some desirable properties along with some shortcomings that call for improvement. For estimating integrated volatility, covariance, and the related statistics by using high-frequency financial data, the SIML method has been developed by Kunitomo and Sato to deal with possible micro-market noises. The authors show that the SIML estimator has reasonable finite sample properties as well as asymptotic properties in the standard cases. It is also shown that the SIML estimator has robust properties in the sense that it is consistent and asymptotically normal in the stable convergence sense when there are micro-market noises, micro-market (non-linear) adjustments, and round-off errors with the underlying (continuous time) stochastic process. Simulation results are reported in a systematic way as are some applications of the SIML method to the Nikkei-225 index, derived from the major stock index in Japan and the Japanese financial sector.

Functional Data Based Inference for High Frequency Financial Data

Author : Bahaeddine Taoufik
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (971 download)

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Book Synopsis Functional Data Based Inference for High Frequency Financial Data by : Bahaeddine Taoufik

Download or read book Functional Data Based Inference for High Frequency Financial Data written by Bahaeddine Taoufik and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis is concerned with developing new functional data techniques for high frequency financial applications. Chapter 1 of the thesis introduces Functional Data Analysis (FDA) with examples of application to real data. In this chapter, we provide some theoretical foundations for FDA. We also present a general theory and basic properties of reproducing kernel Hilbert spaces (RKHS). Chapter 2 of the thesis explores the relationship between market returns and a number of financial factors by fitting functional regression models. We establish two estimation procedures based on the least squares and generalized least squares methods. We also present four hypothesis testing procedures on the functional regression coefficients based on the squared integral $L^2$ approach and the PCA approach for both least squares and generalized least squares methods. New asymptotic results are established allowing for minor departures from stationarity, to ensure convergence and asymptotic normality of our estimates. Our functional regression model is applied to cross-section returns data. Our data application results indicate a positive correlation between the volatility factor ``FVIX" and the higher returns and a negative correlation between the volatility factor ``FVIX" and the low and middle returns.Chapter 3 of the thesis develops a nonlinear function-on-function model using RKHS for real-valued functions. We establish the minimax rate of convergence of the excess prediction risk. Our simulation studies faced computational challenges due to the complexity of the estimation procedure. We examine the prediction performance accuracy of our model through a simulation study. Our nonlinear function-function model is applied to Cumulative intraday return (CIDR) data in order to investigate the prediction performance of Standard \& Poor's 500 Index (S\&P 500) and the Dow Jones Industrial Average (DJIA) for General Electric Company (GE) and International Business Machines Corp.(IBM) for the three periods defining the crisis: ``Before," `` During," and `` After''.

Optimal Statistical Inference in Financial Engineering

Author : Masanobu Taniguchi
Publisher : Chapman and Hall/CRC
ISBN 13 : 9781584885917
Total Pages : 384 pages
Book Rating : 4.8/5 (859 download)

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Book Synopsis Optimal Statistical Inference in Financial Engineering by : Masanobu Taniguchi

Download or read book Optimal Statistical Inference in Financial Engineering written by Masanobu Taniguchi and published by Chapman and Hall/CRC. This book was released on 2007-11-26 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: Until now, few systematic studies of optimal statistical inference for stochastic processes had existed in the financial engineering literature, even though this idea is fundamental to the field. Balancing statistical theory with data analysis, Optimal Statistical Inference in Financial Engineering examines how stochastic models can effectively describe actual financial data and illustrates how to properly estimate the proposed models. After explaining the elements of probability and statistical inference for independent observations, the book discusses the testing hypothesis and discriminant analysis for independent observations. It then explores stochastic processes, many famous time series models, their asymptotically optimal inference, and the problem of prediction, followed by a chapter on statistical financial engineering that addresses option pricing theory, the statistical estimation for portfolio coefficients, and value-at-risk (VaR) problems via residual empirical return processes. The final chapters present some models for interest rates and discount bonds, discuss their no-arbitrage pricing theory, investigate problems of credit rating, and illustrate the clustering of stock returns in both the New York and Tokyo Stock Exchanges. Basing results on a modern, unified optimal inference approach for various time series models, this reference underlines the importance of stochastic models in the area of financial engineering.

Large Volatility Matrix Inference Based on High-frequency Financial Data

Author :
Publisher :
ISBN 13 :
Total Pages : 142 pages
Book Rating : 4.:/5 (853 download)

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Book Synopsis Large Volatility Matrix Inference Based on High-frequency Financial Data by :

Download or read book Large Volatility Matrix Inference Based on High-frequency Financial Data written by and published by . This book was released on 2013 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: Financial practices often need to estimate an integrated volatility matrix of a large number of assets using noisy high-frequency financial data. This estimation problem is a challenging one for four reasons: (1) high-frequency financial data are discrete observations of the underlying assets' price processes; (2) due to market micro-structure noise, high-frequency data are observed with measurement errors; (3) different assets are traded at different time points, which is the so-called non-synchronization phenomenon in high-frequency financial data; (4) the number of assets may be comparable to or even exceed the observations, and hence many existing estimators of small size volatility matrices become inconsistent when the size of the matrix is close to or larger than the sample size. In this dissertation, we focus on large volatility matrix inference for high-frequency financial data, which can be summarized in three aspects. On the methodological aspect, we propose a new threshold MSRVM estimator of large volatility matrix. This estimator can deal with all the four challenges, and is consistent when both sample size and matrix size go to infinity. On the theoretical aspect, we study the optimal convergence rate for the volatility matrix estimation, by building the asymptotic theory for the proposed estimator and deriving a minimax lower bound for this estimation problem. The proposed threshold MSRVM estimator has a risk matching with the lower bound up to a constant factor, and hence it achieves an optimal convergence rate. As for the applications, we develop a novel approach to predict the volatility matrix. The approach extends the applicability of classical low-frequency models such as matrix factor models and vector autoregressive models to the high-frequency data. With this approach, we pool together the strengths of both classical low-frequency models and new high-frequency estimation methodologies. Furthermore, numerical studies are conducted to test the finite sample performance of the proposed estimators, to support the established asymptotic theories.

Application of Statistical and Machine Learning Techniques to Detect Rare Events in High Frequency Financial Data and Assess Corporate Credit Rating

Download Application of Statistical and Machine Learning Techniques to Detect Rare Events in High Frequency Financial Data and Assess Corporate Credit Rating PDF Online Free

Author : Parisa Golbayani
Publisher :
ISBN 13 : 9781392584958
Total Pages : 111 pages
Book Rating : 4.5/5 (849 download)

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Book Synopsis Application of Statistical and Machine Learning Techniques to Detect Rare Events in High Frequency Financial Data and Assess Corporate Credit Rating by : Parisa Golbayani

Download or read book Application of Statistical and Machine Learning Techniques to Detect Rare Events in High Frequency Financial Data and Assess Corporate Credit Rating written by Parisa Golbayani and published by . This book was released on with total page 111 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Contributions to Statistical Modelling of High-frequency Financial Data with Applications to Frankfurt Stock Exchange

Author : Ta-Chao Kao
Publisher :
ISBN 13 :
Total Pages : 240 pages
Book Rating : 4.:/5 (839 download)

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Book Synopsis Contributions to Statistical Modelling of High-frequency Financial Data with Applications to Frankfurt Stock Exchange by : Ta-Chao Kao

Download or read book Contributions to Statistical Modelling of High-frequency Financial Data with Applications to Frankfurt Stock Exchange written by Ta-Chao Kao and published by . This book was released on 2011 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt:

High-Frequency Trading

Author : Irene Aldridge
Publisher : John Wiley & Sons
ISBN 13 : 1118343506
Total Pages : 326 pages
Book Rating : 4.1/5 (183 download)

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Book Synopsis High-Frequency Trading by : Irene Aldridge

Download or read book High-Frequency Trading written by Irene Aldridge and published by John Wiley & Sons. This book was released on 2013-04-22 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: A fully revised second edition of the best guide to high-frequency trading High-frequency trading is a difficult, but profitable, endeavor that can generate stable profits in various market conditions. But solid footing in both the theory and practice of this discipline are essential to success. Whether you're an institutional investor seeking a better understanding of high-frequency operations or an individual investor looking for a new way to trade, this book has what you need to make the most of your time in today's dynamic markets. Building on the success of the original edition, the Second Edition of High-Frequency Trading incorporates the latest research and questions that have come to light since the publication of the first edition. It skillfully covers everything from new portfolio management techniques for high-frequency trading and the latest technological developments enabling HFT to updated risk management strategies and how to safeguard information and order flow in both dark and light markets. Includes numerous quantitative trading strategies and tools for building a high-frequency trading system Address the most essential aspects of high-frequency trading, from formulation of ideas to performance evaluation The book also includes a companion Website where selected sample trading strategies can be downloaded and tested Written by respected industry expert Irene Aldridge While interest in high-frequency trading continues to grow, little has been published to help investors understand and implement this approach—until now. This book has everything you need to gain a firm grip on how high-frequency trading works and what it takes to apply it to your everyday trading endeavors.

Feynman-Kac Formulae

Author : Pierre Del Moral
Publisher : Springer Science & Business Media
ISBN 13 : 1468493930
Total Pages : 567 pages
Book Rating : 4.4/5 (684 download)

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Book Synopsis Feynman-Kac Formulae by : Pierre Del Moral

Download or read book Feynman-Kac Formulae written by Pierre Del Moral and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 567 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text takes readers in a clear and progressive format from simple to recent and advanced topics in pure and applied probability such as contraction and annealed properties of non-linear semi-groups, functional entropy inequalities, empirical process convergence, increasing propagations of chaos, central limit, and Berry Esseen type theorems as well as large deviation principles for strong topologies on path-distribution spaces. Topics also include a body of powerful branching and interacting particle methods.

Statistical Rethinking

Author : Richard McElreath
Publisher : CRC Press
ISBN 13 : 1315362619
Total Pages : 488 pages
Book Rating : 4.3/5 (153 download)

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Book Synopsis Statistical Rethinking by : Richard McElreath

Download or read book Statistical Rethinking written by Richard McElreath and published by CRC Press. This book was released on 2018-01-03 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: Statistical Rethinking: A Bayesian Course with Examples in R and Stan builds readers’ knowledge of and confidence in statistical modeling. Reflecting the need for even minor programming in today’s model-based statistics, the book pushes readers to perform step-by-step calculations that are usually automated. This unique computational approach ensures that readers understand enough of the details to make reasonable choices and interpretations in their own modeling work. The text presents generalized linear multilevel models from a Bayesian perspective, relying on a simple logical interpretation of Bayesian probability and maximum entropy. It covers from the basics of regression to multilevel models. The author also discusses measurement error, missing data, and Gaussian process models for spatial and network autocorrelation. By using complete R code examples throughout, this book provides a practical foundation for performing statistical inference. Designed for both PhD students and seasoned professionals in the natural and social sciences, it prepares them for more advanced or specialized statistical modeling. Web Resource The book is accompanied by an R package (rethinking) that is available on the author’s website and GitHub. The two core functions (map and map2stan) of this package allow a variety of statistical models to be constructed from standard model formulas.

Ubiquitous Quantum Structure

Author : Andrei Y. Khrennikov
Publisher : Springer Science & Business Media
ISBN 13 : 3642051014
Total Pages : 226 pages
Book Rating : 4.6/5 (42 download)

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Book Synopsis Ubiquitous Quantum Structure by : Andrei Y. Khrennikov

Download or read book Ubiquitous Quantum Structure written by Andrei Y. Khrennikov and published by Springer Science & Business Media. This book was released on 2010-01-23 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum-like structure is present practically everywhere. Quantum-like (QL) models, i.e. models based on the mathematical formalism of quantum mechanics and its generalizations can be successfully applied to cognitive science, psychology, genetics, economics, finances, and game theory. This book is not about quantum mechanics as a physical theory. The short review of quantum postulates is therefore mainly of historical value: quantum mechanics is just the first example of the successful application of non-Kolmogorov probabilities, the first step towards a contextual probabilistic description of natural, biological, psychological, social, economical or financial phenomena. A general contextual probabilistic model (Växjö model) is presented. It can be used for describing probabilities in both quantum and classical (statistical) mechanics as well as in the above mentioned phenomena. This model can be represented in a quantum-like way, namely, in complex and more general Hilbert spaces. In this way quantum probability is totally demystified: Born's representation of quantum probabilities by complex probability amplitudes, wave functions, is simply a special representation of this type.

Probability and Statistics

Author : Michael J. Evans
Publisher : Macmillan
ISBN 13 : 9780716747420
Total Pages : 704 pages
Book Rating : 4.7/5 (474 download)

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Book Synopsis Probability and Statistics by : Michael J. Evans

Download or read book Probability and Statistics written by Michael J. Evans and published by Macmillan. This book was released on 2004 with total page 704 pages. Available in PDF, EPUB and Kindle. Book excerpt: Unlike traditional introductory math/stat textbooks, Probability and Statistics: The Science of Uncertainty brings a modern flavor based on incorporating the computer to the course and an integrated approach to inference. From the start the book integrates simulations into its theoretical coverage, and emphasizes the use of computer-powered computation throughout.* Math and science majors with just one year of calculus can use this text and experience a refreshing blend of applications and theory that goes beyond merely mastering the technicalities. They'll get a thorough grounding in probability theory, and go beyond that to the theory of statistical inference and its applications. An integrated approach to inference is presented that includes the frequency approach as well as Bayesian methodology. Bayesian inference is developed as a logical extension of likelihood methods. A separate chapter is devoted to the important topic of model checking and this is applied in the context of the standard applied statistical techniques. Examples of data analyses using real-world data are presented throughout the text. A final chapter introduces a number of the most important stochastic process models using elementary methods. *Note: An appendix in the book contains Minitab code for more involved computations. The code can be used by students as templates for their own calculations. If a software package like Minitab is used with the course then no programming is required by the students.