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
Written with persons of all ages and abilities in mind, 'Understanding the Normal Distribution' is your perfect companion for understanding the rudiments of the most widely used distribution in statistics. Concepts are simply explained in a conversational style, and there are lots of questions to practice with answers provided for evaluation purposes. Enjoy!!
Published by: Christian A.Hume | Publication date: 06/21/2016Kindle book details: Kindle Edition, 541 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
This is the physical chemistry textbook for students with an affinity for computers! It offers basic and advanced knowledge for students in the second year of chemistry masters studies and beyond. In seven chapters, the book presents thermodynamics, chemical kinetics, quantum mechanics and molecular structure (including an introduction to quantum chemical calculations), molecular symmetry and crystals. The application of physical-chemical knowledge and problem solving is demonstrated in a chapter on water, treating both the water molecule as well as water in condensed phases.Instead of a traditional textbook top-down approach, this book presents the subjects on the basis of examples, exploring and running computer programs (Mathematica®), discussing the results of molecular orbital calculations (performed using Gaussian) on small molecules and turning to suitable reference works to obtain thermodynamic data. Selected Mathematica® codes are explained at the end of each chapter and cross-referenced with the text, enabling students to plot functions, solve equations, fit data, normalize probability functions, manipulate matrices and test physical models. In addition, the book presents clear and step-by-step explanations and provides detailed and complete answers to all exercises. In this way, it creates an active learning environment that can prepare students for pursuing their own research projects further down the road.Students who are not yet familiar with Mathematica® or Gaussian will find a valuable introduction to computer-based problem solving in the molecular sciences. Other computer applications can alternatively be used. For every chapter learning goals are clearly listed in the beginning, so that readers can easily spot the highlights, and a glossary in the end of the chapter offers a quick look-up of important terms.
Published by: Springer | Publication date: 01/16/2017Kindle book details: Kindle Edition, 457 pages
Stable Non-Gaussian Random Processes: Stochastic Models with Infinite Variance (Stochastic Modeling Series Book 1)
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
Tough Test Questions? Missed Lectures? Not Enough Time?Fortunately, there's Schaum's. This all-in-one-package includes 738 fully solved problems, examples, and practice exercises to sharpen your problem-solving skills. Plus, you will have access to 30 detailed videos featuring Math instructors who explain how to solve the most commonly tested problems--it's just like having your own virtual tutor! You'll find everything you need to build confidence, skills, and knowledge for the highest score possible.More than 40 million students have trusted Schaum's to help them succeed in the classroom and on exams. Schaum's is the key to faster learning and higher grades in every subject. Each Outline presents all the essential course information in an easy-to-follow, topic-by-topic format. You also get hundreds of examples, solved problems, and practice exercises to test your skills.This Schaum's Outline gives you
- 738 fully solved problems
- The latest course scope and sequences, with complete coverage of limits, continuity, and derivatives
- Succinct explanation of all precalculus concepts
Published by: McGraw-Hill Education | Publication date: 11/16/2012Kindle book details: Kindle Edition, 408 pages
Statistical Rethinking: A Bayesian Course with Examples in R and Stan (Chapman & Hall/CRC Texts in Statistical Science Book 122)
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 ResourceThe 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.
Published by: Chapman and Hall/CRC | Publication date: 01/03/2018Kindle book details: Kindle Edition, 487 pages
This monograph is devoted to a completely new approach to geometric problems arising in the study of random fields. The groundbreaking material in Part III, for which the background is carefully prepared in Parts I and II, is of both theoretical and practical importance, and striking in the way in which problems arising in geometry and probability are beautifully intertwined."Random Fields and Geometry" will be useful for probabilists and statisticians, and for theoretical and applied mathematicians who wish to learn about new relationships between geometry and probability. It will be helpful for graduate students in a classroom setting, or for self-study. Finally, this text will serve as a basic reference for all those interested in the companion volume of the applications of the theory.
Published by: Springer | Publication date: 01/29/2009Kindle book details: Kindle Edition, 454 pages
This superb text by David Bohm, formerly Princeton University and Emeritus Professor of Theoretical Physics at Birkbeck College, University of London, provides a formulation of the quantum theory in terms of qualitative and imaginative concepts that have evolved outside and beyond classical theory. Although it presents the main ideas of quantum theory essentially in nonmathematical terms, it follows these with a broad range of specific applications that are worked out in considerable mathematical detail. Addressed primarily to advanced undergraduate students, the text begins with a study of the physical formulation of the quantum theory, from its origin and early development through an analysis of wave vs. particle properties of matter. In Part II, Professor Bohm addresses the mathematical formulation of the quantum theory, examining wave functions, operators, Schrödinger's equation, fluctuations, correlations, and eigenfunctions.Part III takes up applications to simple systems and further extensions of quantum theory formulation, including matrix formulation and spin and angular momentum. Parts IV and V explore the methods of approximate solution of Schrödinger's equation and the theory of scattering. In Part VI, the process of measurement is examined along with the relationship between quantum and classical concepts.Throughout the text, Professor Bohm places strong emphasis on showing how the quantum theory can be developed in a natural way, starting from the previously existing classical theory and going step by step through the experimental facts and theoretical lines of reasoning which led to replacement of the classical theory by the quantum theory.
Published by: Dover Publications | Publication date: 04/25/2012Kindle book details: Kindle Edition, 673 pages
Gaussian Markov Random Fields: Theory and Applications (Chapman & Hall/CRC Monographs on Statistics and Applied Probability Book 104)
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-studie
Published by: Chapman and Hall/CRC | Publication date: 02/18/2005Kindle book details: Kindle Edition, 280 pages