Stable Non-Gaussian Random Processes: Stochastic Models with Infinite Variance (Stochastic Modeling Series)
This book serves as a standard reference, making this area accessible not only to researchers in probability and statistics, but also to graduate students and practitioners. The book assumes only a first-year graduate course in probability. Each chapter begins with a brief overview and concludes with a wide range of exercises at varying levels of difficulty. The authors supply detailed hints for the more challenging problems, and cover many advances made in recent years.
Published by: Routledge | Publication date: 11/22/2017Kindle book details: Kindle Edition, 632 pages
Stochastic Analysis of Mixed Fractional Gaussian Processes presents the main tools necessary to characterize Gaussian processes. The book focuses on the particular case of the linear combination of independent fractional and sub-fractional Brownian motions with different Hurst indices. Stochastic integration with respect to these processes is considered, as is the study of the existence and uniqueness of solutions of related SDE's. Applications in finance and statistics are also explored, with each chapter supplying a number of exercises to illustrate key concepts.
- Presents both mixed fractional and sub-fractional Brownian motions
- Provides an accessible description for mixed fractional gaussian processes that is ideal for Master's and PhD students
- Includes different Hurst indices
Published by: ISTE Press - Elsevier | Publication date: 05/26/2018Kindle book details: Kindle Edition, 201 pages
This book examines non-Gaussian distributions. It addresses the causes and consequences of non-normality and time dependency in both asset returns and option prices. The book is written for non-mathematicians who want to model financial market prices so the emphasis throughout is on practice. There are abundant empirical illustrations of the models and techniques described, many of which could be equally applied to other financial time series.
Published by: Springer | Publication date: 04/05/2007Kindle book details: Kindle Edition, 541 pages
The purpose of this handbook is to provide comprehensive tables of percentage points of the inverse Gaussian distribution. There is no other publication available today which condenses these tables - to such extent-in a concise, straightforward manner. The inverse Gaussian distribution is not only important for determining boundary crossing probabilities of Brownian Motion, which probabilities determine the operating characteristics of many sequential sampling procedures in statistics. It is also used in quality control procedures. This one-of-a-kind work includes a brief introductory section which outlines the inverse Gaussian distribution and explains the tables. The tables are produced in a fine grid of cumulative probabilities, and uses the closed form expression for the cumulative distribution function. This easy-to-use table reference also includes an excellent discussion of searching ordered tables. This handbook is a helpful, indispensable guide for all who are involved with statistics, mathematics, and computers. Mechanical engineers and physicists will find it useful also.
Published by: CRC Press | Publication date: 01/18/2018Kindle book details: Kindle Edition, 306 pages
First derived within the context of life-testing, inverse Gaussian distribution has become one of the most important and widely employed distributions, and is often used to model the lifetimes of components. It is also used as a model in many varied applications, including fatigue analysis, economic prediction analysis, and the analysis of extreme events such as rainfall and flood levels. The interesting features and properties of this distribution make it an important and realistic model in a variety of problems across numerous disciplines.Because of the broad range of applications, this handbook will be useful not only to members of the statistical community but will also appeal to applied scientists, engineers, econometricians, and anyone who desires a thorough evaluation of this important topic.
Published by: Routledge | Publication date: 11/22/2017Kindle book details: Kindle Edition, 704 pages
A comprehensive introduction to machine learning that uses probabilistic models and inference as a unifying approach.Today's Web-enabled deluge of electronic data calls for automated methods of data analysis. Machine learning provides these, developing methods that can automatically detect patterns in data and then use the uncovered patterns to predict future data. This textbook offers a comprehensive and self-contained introduction to the field of machine learning, based on a unified, probabilistic approach.The coverage combines breadth and depth, offering necessary background material on such topics as probability, optimization, and linear algebra as well as discussion of recent developments in the field, including conditional random fields, L1 regularization, and deep learning. The book is written in an informal, accessible style, complete with pseudo-code for the most important algorithms. All topics are copiously illustrated with color images and worked examples drawn from such application domains as biology, text processing, computer vision, and robotics. Rather than providing a cookbook of different heuristic methods, the book stresses a principled model-based approach, often using the language of graphical models to specify models in a concise and intuitive way. Almost all the models described have been implemented in a MATLAB software package—PMTK (probabilistic modeling toolkit)—that is freely available online. The book is suitable for upper-level undergraduates with an introductory-level college math background and beginning graduate students.
Published by: The MIT Press | Publication date: 09/07/2012Kindle book details: Kindle Edition, 1104 pages
Unsupervised Machine Learning in Python: Master Data Science and Machine Learning with Cluster Analysis, Gaussian Mixture Models, and Principal Components Analysis
In a real-world environment, you can imagine that a robot or an artificial intelligence won’t always have access to the optimal answer, or maybe there isn’t an optimal correct answer. You’d want that robot to be able to explore the world on its own, and learn things just by looking for patterns.Think about the large amounts of data being collected today, by the likes of the NSA, Google, and other organizations. No human could possibly sift through all that data manually. It was reported recently in the Washington Post and Wall Street Journal that the National Security Agency collects so much surveillance data, it is no longer effective.Could automated pattern discovery solve this problem?Do you ever wonder how we get the data that we use in our supervised machine learning algorithms?Kaggle always seems to provide us with a nice CSV, complete with Xs and corresponding Ys.If you haven’t been involved in acquiring data yourself, you might not have thought about this, but someone has to make this data!A lot of the time this involves manual labor. Sometimes, you don’t have access to the correct information or it is infeasible or costly to acquire.You still want to have some idea of the structure of the data.This is where unsupervised machine learning comes into play.In this book we are first going to talk about clustering. This is where instead of training on labels, we try to create our own labels. We’ll do this by grouping together data that looks alike.The 2 methods of clustering we’ll talk about: k-means clustering and hierarchical clustering.Next, because in machine learning we like to talk about probability distributions, we’ll go into Gaussian mixture models and kernel density estimation, where we talk about how to learn the probability distribution of a set of data.One interesting fact is that under certain conditions, Gaussian mixture models and k-means clustering are exactly the same! We’ll prove how this is the case.Lastly, we’ll look at the theory behind principal components analysis or PCA. PCA has many useful applications: visualization, dimensionality reduction, denoising, and de-correlation. You will see how it allows us to take a different perspective on latent variables, which first appear when we talk about k-means clustering and GMMs.All the algorithms we’ll talk about in this course are staples in machine learning and data science, so if you want to know how to automatically find patterns in your data with data mining and pattern extraction, without needing someone to put in manual work to label that data, then this book is for you.All of the materials required to follow along in this book are free: You just need to able to download and install Python, Numpy, Scipy, Matplotlib, and Sci-kit Learn.
Publication date: 05/22/2016Kindle book details: Kindle Edition, 38 pages
Gaussian Processes on Trees: From Spin Glasses to Branching Brownian Motion (Cambridge Studies in Advanced Mathematics)
Branching Brownian motion (BBM) is a classical object in probability theory with deep connections to partial differential equations. This book highlights the connection to classical extreme value theory and to the theory of mean-field spin glasses in statistical mechanics. Starting with a concise review of classical extreme value statistics and a basic introduction to mean-field spin glasses, the author then focuses on branching Brownian motion. Here, the classical results of Bramson on the asymptotics of solutions of the F-KPP equation are reviewed in detail and applied to the recent construction of the extremal process of BBM. The extension of these results to branching Brownian motion with variable speed are then explained. As a self-contained exposition that is accessible to graduate students with some background in probability theory, this book makes a good introduction for anyone interested in accessing this exciting field of mathematics.
Published by: Cambridge University Press | Publication date: 10/20/2016Kindle book details: Kindle Edition, 211 pages
Physical Sciences Data, Volume 16: Gaussian Basis Sets for Molecular Calculations provides information pertinent to the Gaussian basis sets, with emphasis on lithium, radon, and important ions. This book discusses the polarization functions prepared for lithium through radon for further improvement of the basis sets.Organized into three chapters, this volume begins with an overview of the basis set for the most stable negative and positive ions. This text then explores the total atomic energies given by the basis sets. Other chapters consider the distinction between diffuse functions and polarization function. This book presents as well the exponents of polarization function. The final chapter deals with the Gaussian basis sets.This book is a valuable resource for chemists, scientists, and research workers.
Published by: Elsevier Science | Publication date: 12/02/2012Kindle book details: Kindle Edition, 434 pages
Gaussian Markov Random Fields: Theory and Applications (Chapman & Hall/CRC Monographs on Statistics & Applied Probability)
Gaussian Markov Random Field (GMRF) models are most widely used in spatial statistics - a very active area of research in which few up-to-date reference works are available. This is the first book on the subject that provides a unified framework of GMRFs with particular emphasis on the computational aspects. This book includes extensive case-studies and, online, a c-library for fast and exact simulation. With chapters contributed by leading researchers in the field, this volume is essential reading for statisticians working in spatial theory and its applications, as well as quantitative researchers in a wide range of science fields where spatial data analysis is important.
Published by: Chapman and Hall/CRC | Publication date: 02/18/2005Kindle book details: Kindle Edition, 280 pages