This book provides a complete and comprehensive reference/guide to Pyomo (Python Optimization Modeling Objects) for both beginning and advanced modelers, including students at the undergraduate and graduate levels, academic researchers, and practitioners. The text illustrates the breadth of the modeling and analysis capabilities that are supported by the software and support of complex real-world applications. Pyomo is an open source software package for formulating and solving large-scale optimization and operations research problems. The text begins with a tutorial on simple linear and integer programming models. A detailed reference of Pyomo's modeling components is illustrated with extensive examples, including a discussion of how to load data from data sources like spreadsheets and databases. Chapters describing advanced modeling capabilities for nonlinear and stochastic optimization are also included. The Pyomo software provides familiar modeling features within Python, a powerful dynamic programming language that has a very clear, readable syntax and intuitive object orientation. Pyomo includes Python classes for defining sparse sets, parameters, and variables, which can be used to formulate algebraic expressions that define objectives and constraints. Moreover, Pyomo can be used from a command-line interface and within Python's interactive command environment, which makes it easy to create Pyomo models, apply a variety of optimizers, and examine solutions. The software supports a different modeling approach than commercial AML (Algebraic Modeling Languages) tools, and is designed for flexibility, extensibility, portability, and maintainability but also maintains the central ideas in modern AMLs.

This book was written to provide resource materials for teachers to use in their introductory or intermediate statistics class. The chapter content is ordered along the lines of many popular statistics books so it should be easy to supplement the content and exercises with class lecture materials. The book contains R script programs to demonstrate important topics and concepts covered in a statistics course, including probability, random sampling, population distribution types, role of the Central Limit Theorem, creation of sampling distributions for statistics, and more. The chapters contain T/F quizzes to test basic knowledge of the topics covered. In addition, the book chapters contain numerous exercises with answers or solutions to the exercises provided. The chapter exercises reinforce an understanding of the statistical concepts presented in the chapters. An instructor can select any of the supplemental materials to enhance lectures and/or provide additional coverage of concepts and topics in their statistics book.

Dynamical system theory has developed rapidly over the past fifty years. It is a subject upon which the theory of limit cycles has a significant impact for both theoretical advances and practical solutions to problems. Hopf bifurcation from a center or a focus is integral to the theory of bifurcation of limit cycles, for which normal form theory is a central tool. Although Hopf bifurcation has been studied for more than half a century, and normal form theory for over 100 years, efficient computation in this area is still a challenge with implications for Hilbert's 16th problem.

This book introduces the most recent developments in this field and provides major advances in fundamental theory of limit cycles. Split into two parts, the first focuses on the study of limit cycles bifurcating from Hopf singularity using normal form theory with later application to Hilbert's 16th problem, while the second considers near Hamiltonian systems using Melnikov function as the main mathematical tool.

Classic topics with new results are presented in a clear and concise manner and are accompanied by the liberal use of illustrations throughout. Containing a wealth of examples and structured algorithms that are treated in detail, a good balance between theoretical and applied topics is demonstrated. By including complete Maple programs within the text, this book also enables the reader to reconstruct the majority of formulas provided, facilitating the use of concrete models for study.

Through the adoption of an elementary and practical approach, this book will be of use to graduate mathematics students wishing to study the theory of limit cycles as well as scientists, across a number of disciplines, with an interest in the applications of periodic behavior."

The interaction of the solar and heat radiation with the atmosphere and surface is the subject of the book. It is useful also for wide circle scientists involved in environmental studies. The book contains the description of 17 computer studying programs supporting different topics of courses. It includes only the base ground for comprehension of key topics and provides the accomplishment of practical works with using specially elaborated computer programs. Themes of practical works reflect main sections of mentioned courses of lectures. The packet of computer programs is added for solution of direct and inverse problems. It promotes deep and reliable comprehension of corresponding topics by students. All described approaches and computer programs are valuable resources for solving radiative transfer problems and they could be used by students for courses and diploma studies concerned atmospheric optics.

The second edition of a bestselling textbook, Using R for Introductory Statistics guides students through the basics of R, helping them overcome the sometimes steep learning curve. The author does this by breaking the material down into small, task-oriented steps. The second edition maintains the features that made the first edition so popular, while updating data, examples, and changes to R in line with the current version.

See What’s New in the Second Edition:

Increased emphasis on more idiomatic R provides a grounding in the functionality of base R.

Discussions of the use of RStudio helps new R users avoid as many pitfalls as possible.

Use of knitr package makes code easier to read and therefore easier to reason about.

Additional information on computer-intensive approaches motivates the traditional approach.

Updated examples and data make the information current and topical.

The book has an accompanying package, UsingR, available from CRAN, R’s repository of user-contributed packages. The package contains the data sets mentioned in the text (data(package="UsingR")), answers to selected problems (answers()), a few demonstrations (demo()), the errata (errata()), and sample code from the text.

The topics of this text line up closely with traditional teaching progression; however, the book also highlights computer-intensive approaches to motivate the more traditional approach. The authors emphasize realistic data and examples and rely on visualization techniques to gather insight. They introduce statistics and R seamlessly, giving students the tools they need to use R and the information they need to navigate the sometimes complex world of statistical computing.

Table of Contents

DATA

What Is Data?

Some R Essentials

Accessing Data by Using Indices

Reading in Other Sources of Data

UNIVARIATE DATA

Categorical Data

Numeric Data

Shape of a Distribution

BIVARIATE DATA

Pairs of Categorical Variables

Comparing Independent Samples

Relationships in Numeric Data

Simple Linear Regression

MULTIVARIATE DATA

Viewing Multivariate Data

R Basics: Data Frames and Lists

Using Model Formula with Multivariate Data

Lattice Graphics

Types of Data in R

DESCRIBING POPULATIONS

Populations

Families of Distributions

The Central Limit Theorem

SIMULATION

The Normal Approximation for the Binomial

for loops

Simulations Related to the Central Limit Theorem

Defining a Function

Investigating Distributions

Bootstrap Samples

Alternates to for loops

CONFIDENCE INTERVALS

Confidence Interval Ideas

Confidence Intervals for a Population Proportion, p

Confidence Intervals for the Population Mean, µ

Other Confidence Intervals

Confidence Intervals for Differences

Confidence Intervals for the Median

SIGNIFICANCE TESTS

Significance Test for a Population Proportion

Significance Test for the Mean (t-Tests)

Significance Tests and Confidence Intervals

Significance Tests for the Median

Two-Sample Tests of Proportion

Two-Sample Tests of Center

GOODNESS OF FIT

The Chi-Squared Goodness-of-Fit Test

The Chi-Squared Test of Independence

Goodness-of-Fit Tests for Continuous Distributions

LINEAR REGRESSION

The Simple Linear Regression Model

Statistical Inference for Simple Linear Regression

Multiple Linear Regression

ANALYSIS OF VARIANCE

One-Way ANOVA

Using lm() for ANOVA

ANCOVA

Two-Way ANOVA

TWO EXTENSIONS OF THE LINEAR MODEL

Logistic Regression

Nonlinear Models

APPENDIX A: GETTING, INSTALLING, AND RUNNING R

Installing and Starting R

Extending R Using Additional Packages

APPENDIX B: GRAPHICAL USER INTERFACES AND R

The Windows GUI

The Mac OS X GUI

Rcdmr

APPENDIX C: TEACHING WITH R

APPENDIX D: MORE ON GRAPHICS WITH R

Low- and High-Level Graphic Functions

Creating New Graphics in R

APPENDIX E: PROGRAMMING IN R

Editing Functions

Using Functions

Using Files and a Better Editor

Object-Oriented Programming with R

INDEX

Rcpp is the glue that binds the power and versatility of R with the speed and efficiency of C++. With Rcpp, the transfer of data between R and C++ is nearly seamless, and high-performance statistical computing is finally accessible to most R users. Rcpp should be part of every statistician's toolbox. -- Michael Braun, MIT Sloan School of Management

"Seamless R and C++ integration with Rcpp" is simply a wonderful book. For anyone who uses C/C++ and R, it is an indispensable resource. The writing is outstanding. A huge bonus is the section on applications. This section covers the matrix packages Armadillo and Eigen and the GNU Scientific Library as well as RInside which enables you to use R inside C++. These applications are what most of us need to know to really do scientific programming with R and C++. I love this book. -- Robert McCulloch, University of Chicago Booth School of Business

Rcpp is now considered an essential package for anybody doing serious computational research using R. Dirk's book is an excellent companion and takes the reader from a gentle introduction to more advanced applications via numerous examples and efficiency enhancing gems. The book is packed with all you might have ever wanted to know about Rcpp, its cousins (RcppArmadillo, RcppEigen .etc.), modules, package development and sugar. Overall, this book is a must-have on your shelf. -- Sanjog Misra, UCLA Anderson School of Management

The Rcpp package represents a major leap forward for scientific computations with R. With very few lines of C++ code, one has R's data structures readily at hand for further computations in C++. Hence, high-level numerical programming can be made in C++ almost as easily as in R, but often with a substantial speed gain. Dirk is a crucial person in these developments, and his book takes the reader from the first fragile steps on to using the full Rcpp machinery. A very recommended book -- Soren Hojsgaard," "Department of Mathematical Sciences, Aalborg University, Denmark

"Seamless R and C ++ Integration with Rcpp" provides the first comprehensive introduction to Rcpp. Rcpp has become the most widely-used language extension for R, and is deployed by over one-hundred different CRAN and BioConductor packages. Rcpp permits users to pass scalars, vectors, matrices, list or entire R objects back and forth between R and C++ with ease. This brings the depth of the R analysis framework together with the power, speed, and efficiency of C++.

Dirk Eddelbuettel has been a contributor to CRAN for over a decade and maintains around twenty packages. He is the Debian/Ubuntu maintainer for R and other quantitative software, edits the CRAN Task Views for Finance and High-Performance Computing, is a co-founder of the annual R/Finance conference, and an editor of the Journal of Statistical Software. He holds a Ph.D. in Mathematical Economics from EHESS (Paris), and works in Chicago as a Senior Quantitative Analyst.

"

MATLAB is a high-level language and environment for numerical computation, visualization, and programming. Using MATLAB, you can analyze data, develop algorithms, and create models and applications. The language, tools, and built-in math functions enable you to explore multiple approaches and reach a solution faster than with spreadsheets or traditional programming languages, such as C/C++ or Java. MATLAB Optimization Techniques introduces you to the MATLAB language with practical hands-on instructions and results, allowing you to quickly achieve your goals. It begins by introducing the MATLAB environment and the structure of MATLAB programming before moving on to the mathematics of optimization. The central part of the book is dedicated to MATLAB's Optimization Toolbox, which implements state-of-the-art algorithms for solving multiobjective problems, non-linear minimization with boundary conditions and restrictions, minimax optimization, semi-infinitely constrained minimization and linear and quadratic programming. A wide range of exercises and examples are included, illustrating the most widely used optimization methods.

MATLAB is a high-level language and environment for numerical computation, visualization, and programming. Using MATLAB, you can analyze data, develop algorithms, and create models and applications. The language, tools, and built-in math functions enable you to explore multiple approaches and reach a solution faster than with spreadsheets or traditional programming languages, such as C/C++ or Java. This book is designed for use as a scientific/business calculator so that you can get numerical solutions to problems involving a wide array of mathematics using MATLAB. Just look up the function you want in the book and you are ready to use it in MATLAB or use the book to learn about the enormous range of options that MATLAB offers. MATLAB Numerical Calculations focuses on MATLAB capabilities to give you numerical solutions to problems you are likely to encounter in your professional or scholastic life. It introduces you to the MATLAB language with practical hands-on instructions and results, allowing you to quickly achieve your goals. Starting with a look at basic MATLAB functionality with integers, rational numbers and real and complex numbers, and MATLAB's relationship with Maple, you will learn how to solve equations in MATLAB, and how to simplify the results. You will see how MATLAB incorporates vector, matrix and character variables, and functions thereof. MATLAB is a powerful tool used to defined, manipulate and simplify complex algebraic expressions. With MATLAB you can also work with ease in matrix algebra, making use of commands which allow you to find eigenvalues, eigenvectors, determinants, norms and various matrix decompositions, among many other features. Lastly, you will see how you can write scripts and use MATLAB to explore numerical analysis, finding approximations of integrals, derivatives and numerical solutions of differential equations.

Through analysis of the European Union Emissions Trading Scheme (EU ETS) and the Clean Development Mechanism (CDM), this book demonstrates how to use a variety of econometric techniques to analyze the evolving and expanding carbon markets sphere, techniques that can be extrapolated to the worldwide marketplace. It features stylized facts about carbon markets from an economics perspective, as well as covering key aspects of pricing strategies, risk and portfolio management.

Engineering mechanics involves the development of mathematical models of the physical world. Statics addresses the forces acting on and in mechanical objects and systems. Statics with MATLAB (R) develops an understanding of the mechanical behavior of complex engineering structures and components using MATLAB (R) to execute numerical calculations and to facilitate analytical calculations. MATLAB (R) is presented and introduced as a highly convenient tool to solve problems for theory and applications in statics. Included are example problems to demonstrate the MATLAB (R) syntax and to also introduce specific functions dealing with statics. These explanations are reinforced through figures generated with MATLAB (R) and the extra material available online which includes the special functions described. This detailed introduction and application of MATLAB (R) to the field of statics makes Statics with MATLAB (R) a useful tool for instruction as well as self study, highlighting the use of symbolic MATLAB (R) for both theory and applications to find analytical and numerical solutions

This book provides anintroduction to multistate event history analysis. It is an extension of survival analysis, in which a single terminal event (endpoint) is considered and the time-to-event is studied. Multistate models focus on life histories or trajectories, conceptualized as sequences of states and sequences of transitions between states. Life histories are modeled as realizations of continuous-time Markov processes. The model parameters, transition rates, are estimated from data on event counts and populations at risk, using the statistical theory of counting processes.

The Comprehensive R Network Archive (CRAN) includes several packages for multistate modeling. This book is about "Biograph." The package is designed to (a) enhance exploratory analysis of life histories and (b) make multistate modeling accessible. The package incorporates utilities that connect to several packages for multistate modeling, including "survival," "eha," "Epi," "mvna," " etm," "mstate," "msm," and "TraMineR" for sequence analysis. The book is a hands-on presentation of "Biograph" and the packages listed. It is written from the perspective of the user. To help the user master the techniques and the software, a single data set is used to illustrate the methods and software. It is the subsample of the German Life History Survey, which was also used by Blossfeld and Rohwer in their popular textbook on event history modeling. Another data set, the Netherlands Family and Fertility Survey, is used to illustrate how "Biograph" can assist in answering questions on life paths of cohorts and individuals.

The book is suitable as a textbook for graduate courses on event history analysis and introductory courses on competing risks and multistate models. It may also be used as a self-study book. The R code used in the book is available online.

Frans Willekens is affiliated with the Max Planck Institute for Demographic Research (MPIDR) in Rostock, Germany. He is Emeritus Professor of Demography at the University of Groningen, a Honorary Fellow of the Netherlands Interdisciplinary Demographic Institute (NIDI) in the Hague, and a Research Associate of the International Institute for Applied Systems Analysis (IIASA), Laxenburg, Austria. He is a member of Royal Netherlands Academy of Arts and Sciences (KNAW). He has contributed to the modeling and simulation of life histories, mainly in the context of population forecasting."

The theme of the meeting was Statistical Methods for the Analysis of Large Data-Sets . In recent years there has been increasing interest in this subject; in fact a huge quantity of information is often available but standard statistical techniques are usually not well suited to managing this kind of data. The conference serves as an important meeting point for European researchers working on this topic and a number of European statistical societies participated in the organization of the event.
The book includes 45 papers from a selection of the 156 papers accepted for presentation and discussed at the conference on Advanced Statistical Methods for the Analysis of Large Data-sets. "

"Functional and Phylogenetic Ecology in R" is designed to teach readers to use R for phylogenetic and functional trait analyses. Over the past decade, a dizzying array of tools and methods were generated to incorporate phylogenetic and functional information into traditional ecological analyses. Increasingly these tools are implemented in R, thus greatly expanding their impact. Researchers getting started in R can use this volume as a step-by-step entryway into phylogenetic and functional analyses for ecology in R. More advanced users will be able to use this volume as a quick reference to understand particular analyses. The volume begins with an introduction to the R environment and handling relevant data in R. Chapters then cover phylogenetic and functional metrics of biodiversity; null modeling and randomizations for phylogenetic and functional trait analyses; integrating phylogenetic and functional trait information; and interfacing the R environment with a popular C-based program. This book presents a unique approach through its focus on ecological analyses and not macroevolutionary analyses. The author provides his own code, so that the reader is guided through the computational steps to calculate the desired metrics. This guided approach simplifies the work of determining which package to use for any given analysis. Example datasets are shared to help readers practice, and readers can then quickly turn to their own datasets.

This book collects the proceedings of the 10th Workshop on Model-Oriented Design and Analysis (mODa). A model-oriented view on the design of experiments, which is the unifying theme of all mODa meetings, assumes some knowledge of the form of the data-generating process and naturally leads to the so-called optimum experimental design. Its theory and practice have since become important in many scientific and technological fields, ranging from optimal designs for dynamic models in pharmacological research, to designs for industrial experimentation, to designs for simulation experiments in environmental risk management, to name but a few. The methodology has become even more important in recent years because of the increased speed of scientific developments, the complexity of the systems currently under investigation and the mounting pressure on businesses, industries and scientific researchers to reduce product and process development times. This increased competition requires ever increasing efficiency in experimentation, thus necessitating new statistical designs. This book presents a rich collection of carefully selected contributions ranging from statistical methodology to emerging applications. It primarily aims to provide an overview of recent advances and challenges in the field, especially in the context of new formulations, methods and state-of-the-art algorithms. The topics included in this volume will be of interest to all scientists and engineers and statisticians who conduct experiments.

Learn how to write R code with fewer bugs. The problem with programming is that you are always one typo away from writing something silly. Likewise with data analysis, a small mistake in your model can lead to a big mistake in your results. Combining the two disciplines means that it is all too easy for a missed minus sign to generate a false prediction that you don't spot until it's too late. Testing is the only way to be sure that your code, and your results, are correct. Testing R Code teaches you how to perform development-time testing using the testthat package, allowing you to ensure that your code works as intended. The book also teaches run-time testing using the assertive package; enabling your users to correctly run your code. After beginning with an introduction to testing in R, the book explores more advanced cases such as integrating tests into R packages; testing code that accesses databases; testing C++ code with Rcpp; and testing graphics. Each topic is explained with real-world examples, and has accompanying exercises for readers to practise their skills - only a small amount of experience with R is needed to get started!

This small book addresses different kinds of datafiles, as commonly encountered in clinical research, and their data-analysis on SPSS Software. Some 15 years ago serious statistical analyses were conducted by specialist statisticians using ma- frame computers. Nowadays, there is ready access to statistical computing using personal computers or laptops, and this practice has changed boundaries between basic statistical methods that can be conveniently carried out on a pocket calculator and more advanced statistical methods that can only be executed on a computer. Clinical researchers currently perform basic statistics without professional help from a statistician, including t-tests and chi-square tests. With help of user-friendly software the step from such basic tests to more complex tests has become smaller, and more easy to take. It is our experience as masters' and doctorate class teachers of the European College of Pharmaceutical Medicine (EC Socrates Project Lyon France) that s- dents are eager to master adequate command of statistical software for that purpose. However, doing so, albeit easy, still takes 20-50 steps from logging in to the final result, and all of these steps have to be learned in order for the procedures to be successful.

Python Algorithms, Second Edition explains the Python approach to algorithm analysis and design. Written by Magnus Lie Hetland, author of Beginning Python, this book is sharply focused on classical algorithms, but it also gives a solid understanding of fundamental algorithmic problem-solving techniques. The book deals with some of the most important and challenging areas of programming and computer science in a highly readable manner. It covers both algorithmic theory and programming practice, demonstrating how theory is reflected in real Python programs. Well-known algorithms and data structures that are built into the Python language are explained, and the user is shown how to implement and evaluate others.

This is an introduction to time series that emphasizes methods and analysis of data sets. The logic and tools of model-building for stationary and non-stationary time series are developed and numerous exercises, many of which make use of the included computer package, provide the reader with ample opportunity to develop skills. Statisticians and students will learn the latest methods in time series and forecasting, along with modern computational models and algorithms.

This volume presents theoretical developments, applications and computational methods for the analysis and modeling in behavioral and social sciences where data are usually complex to explore and investigate. The challenging proposals provide a connection between statistical methodology and the social domain with particular attention to computational issues in order to effectively address complicated data analysis problems.
The papers in this volume stem from contributions initially presented at the joint international meeting JCS-CLADAG held in Anacapri (Italy) where the Japanese Classification Society and the Classification and Data Analysis Group of the Italian Statistical Society had a stimulating scientific discussion and exchange.

Nonlinear physics continues to be an area of dynamic modern research, with applications to physics, engineering, chemistry, mathematics, computer science, biology, medicine and economics. In this text extensive use is made of the Mathematica computer algebra system. No prior knowledge of Mathematica or programming is assumed. This book includes 33 experimental activities that are designed to deepen and broaden the reader's understanding of nonlinear physics. These activities are correlated with Part I, the theoretical framework of the text.

Post-Optimal Analysis in Linear Semi-Infinite Optimization examines the following topics in regards to linear semi-infinite optimization: modeling uncertainty, qualitative stability analysis, quantitative stability analysis and sensitivity analysis. Linear semi-infinite optimization (LSIO) deals with linear optimization problems where the dimension of the decision space or the number of constraints is infinite. The authors compare the post-optimal analysis with alternative approaches to uncertain LSIO problems and provide readers with criteria to choose the best way to model a given uncertain LSIO problem depending on the nature and quality of the data along with the available software. This work also contains open problems which readers will find intriguing a challenging. Post-Optimal Analysis in Linear Semi-Infinite Optimization is aimed toward researchers, graduate and post-graduate students of mathematics interested in optimization, parametric optimization and related topics.

This proposed text appears to be a good introduction to evolutionary computation for use in applied statistics research. The authors draw from a vast base of knowledge about the current literature in both the design of evolutionary algorithms and statistical techniques. Modern statistical research is on the threshold of solving increasingly complex problems in high dimensions, and the generalization of its methodology to parameters whose estimators do not follow mathematically simple distributions is underway. Many of these challenges involve optimizing functions for which analytic solutions are infeasible. Evolutionary algorithms represent a powerful and easily understood means of approximating the optimum value in a variety of settings. The proposed text seeks to guide readers through the crucial issues of optimization problems in statistical settings and the implementation of tailored methods (including both stand-alone evolutionary algorithms and hybrid crosses of these procedures with standard statistical algorithms like Metropolis-Hastings) in a variety of applications. This book would serve as an excellent reference work for statistical researchers at an advanced graduate level or beyond, particularly those with a strong background in computer science.

Modern algorithmic techniques for summation, most of which were introduced in the 1990s, are developed here and carefully implemented in the computer algebra system Maple (TM). The algorithms of Fasenmyer, Gosper, Zeilberger, Petkovsek and van Hoeij for hypergeometric summation and recurrence equations, efficient multivariate summation as well as q-analogues of the above algorithms are covered. Similar algorithms concerning differential equations are considered. An equivalent theory of hyperexponential integration due to Almkvist and Zeilberger completes the book. The combination of these results gives orthogonal polynomials and (hypergeometric and q-hypergeometric) special functions a solid algorithmic foundation. Hence, many examples from this very active field are given. The materials covered are suitable for an introductory course on algorithmic summation and will appeal to students and researchers alike.

This book presents methods for computing correlation equations. All the topics treated hefe are eluci dated in terms of concrete examples, which have been chosen, for the most part, from the Held of analysis of the mechanical properties of steel, wood, and other materials. A necessary prerequisite for any study of correlation equations is so me knowledge of the moments of random variables. In the Appendix, there is provided a brief treatment of moments, as well as a discussion of the simplest methods of computing them. We have paid particular attention in this book to the techniques of computing correlation equations, and to the use of tables for alleviating the computationalload. The mathematical bases of the methods used in setting up correlation equations are expounded in the books cited at the end of this volume. A. M. December 1965 PIe ase note that the abbreviation 19 is used in this book to designate the logarithm to base ten, Note further that the comma has been retained as the decimal point in tabular material."

Sampling consists of selection, acquisition, and quantification of a part of the population. While selection and acquisition apply to physical sampling units of the population, quantification pertains only to the variable of interest, which is a particular characteristic of the sampling units. A sampling procedure is expected to provide a sample that is representative with respect to some specified criteria. Composite sampling, under idealized conditions, incurs no loss of information for estimating the population means. But an important limitation to the method has been the loss of information on individual sample values, such as, the extremely large value. In many of the situations where individual sample values are of interest or concern, composite sampling methods can be suitably modified to retrieve the information on individual sample values that may be lost due to compositing. This book presents statistical solutions to issues that arise in the context of applications of composite sampling.