Basic Statistics

This concise, self-contained and cohesive book focuses on commonly used and recently developed methods for designing and analyzing high-throughput screening (HTS) experiments from a statistically sound basis. Combining ideas from biology, computing and statistics, the author explains experimental designs and analytic methods that are amenable to rigorous analysis and interpretation of RNAi HTS experiments. The opening chapters are carefully presented to be accessible both to biologists with training only in basic statistics and to computational scientists and statisticians with basic biological knowledge. Biologists will see how new experiment designs and rudimentary data-handling strategies for RNAi HTS experiments can improve their results, whereas analysts will learn how to apply recently developed statistical methods to interpret HTS experiments.

This concise, self-contained and cohesive book focuses on commonly used and recently developed methods for designing and analyzing high-throughput screening (HTS) experiments from a statistically sound basis. Combining ideas from biology, computing and statistics, the author explains experimental designs and analytic methods that are amenable to rigorous analysis and interpretation of RNAi HTS experiments. The opening chapters are carefully presented to be accessible both to biologists with training only in basic statistics and to computational scientists and statisticians with basic biological knowledge. Biologists will see how new experiment designs and rudimentary data-handling strategies for RNAi HTS experiments can improve their results, whereas analysts will learn how to apply recently developed statistical methods to interpret HTS experiments.

Association schemes are of interest to both mathematicians and statisticians and this book was written with both audiences in mind. For statisticians, it shows how to construct designs for experiments in blocks, how to compare such designs, and how to analyse data from them. The reader is only assumed to know very basic abstract algebra. For pure mathematicians, it tells why association schemes are important and develops the theory to the level of advanced research. This book arose from a course successfully taught by the author and as such the material is thoroughly class-tested. There are a great number of examples and exercises that will increase the book's appeal to both graduate students and their instructors. It is ideal for those coming either from pure mathematics or statistics backgrounds who wish to develop their understanding of association schemes.

ELEMENTARY STATISTICS: A STEP BY STEP APPROACH is for general beginning statistics courses with a basic algebra prerequisite. The book is non-theoretical, explaining concepts intuitively and teaching

This book is aimed primarily at microbiologists who are undertaking research, and who require a basic knowledge of statistics to analyse their experimental data. Computer software employing a wide ra

Bayesian decision analysis supports principled decision making in complex domains. This textbook takes the reader from a formal analysis of simple decision problems to a careful analysis of the sometimes very complex and data rich structures confronted by practitioners. The book contains basic material on subjective probability theory and multi-attribute utility theory, event and decision trees, Bayesian networks, influence diagrams and causal Bayesian networks. The author demonstrates when and how the theory can be successfully applied to a given decision problem, how data can be sampled and expert judgements elicited to support this analysis, and when and how an effective Bayesian decision analysis can be implemented. Evolving from a third-year undergraduate course taught by the author over many years, all of the material in this book will be accessible to a student who has completed introductory courses in probability and mathematical statistics.

Discover what you can do with R! Introducing the R system, covering standard regression methods, then tackling more advanced topics, this book guides users through the practical, powerful tools that the R system provides. The emphasis is on hands-on analysis, graphical display, and interpretation of data. The many worked examples, from real-world research, are accompanied by commentary on what is done and why. The companion website has code and datasets, allowing readers to reproduce all analyses, along with solutions to selected exercises and updates. Assuming basic statistical knowledge and some experience with data analysis (but not R), the book is ideal for research scientists, final-year undergraduate or graduate-level students of applied statistics, and practising statisticians. It is both for learning and for reference. This third edition expands upon topics such as Bayesian inference for regression, errors in variables, generalized linear mixed models, and random forests.

This textbook for a second course in basic statistics for undergraduates or first-year graduate students introduces linear regression models and describes other linear models including Poisson regression, logistic regression, proportional hazards regression, and nonparametric regression. Numerous examples drawn from the news and current events with an emphasis on health issues illustrate these concepts. Assuming only a pre-calculus background, the author keeps equations to a minimum and demonstrates all computations using SAS. Most of the programs and output are displayed in a self-contained way, with an emphasis on the interpretation of the output in terms of how it relates to the motivating example. Plenty of exercises conclude every chapter. All of the datasets and SAS programs are available from the book's website, along with other ancillary material.

While there is a wide selection of 'by experts, for experts’ books in statistics and molecular biology, there is a distinct need for a book that presents the basic principles of proper statistical ana

Scary headlines and scarier statistics tell the story of a financial crisis on a scale not seen in decades—certainly not within the lifetime of most Americans. Moreover, this is a worldwide fin

In recent years cosmologists have advanced from largely qualitative models of the Universe to precision modelling using Bayesian methods, in order to determine the properties of the Universe to high accuracy. This timely book is the only comprehensive introduction to the use of Bayesian methods in cosmological studies, and is an essential reference for graduate students and researchers in cosmology, astrophysics and applied statistics. The first part of the book focuses on methodology, setting the basic foundations and giving a detailed description of techniques. It covers topics including the estimation of parameters, Bayesian model comparison, and separation of signals. The second part explores a diverse range of applications, from the detection of astronomical sources (including through gravitational waves), to cosmic microwave background analysis and the quantification and classification of galaxy properties. Contributions from 24 highly regarded cosmologists and statisticians make

Steganography, the art of hiding of information in apparently innocuous objects or images, is a field with a rich heritage, and an area of rapid current development. This clear, self-contained guide shows you how to understand the building blocks of covert communication in digital media files and how to apply the techniques in practice, including those of steganalysis, the detection of steganography. Assuming only a basic knowledge in calculus and statistics, the book blends the various strands of steganography, including information theory, coding, signal estimation and detection, and statistical signal processing. Experiments on real media files demonstrate the performance of the techniques in real life, and most techniques are supplied with pseudo-code, making it easy to implement the algorithms. The book is ideal for students taking courses on steganography and information hiding, and is also a useful reference for engineers and practitioners working in media security and informati

This book was created for students and teachers interested in mastering the basic applications of algebra, geometry, trigonometry, and statistics. This text has been proven to improve learning for stu

This book presents the basic procedures for utilizing SAS Enterprise Guide to analyze statistical data. SAS Enterprise Guide is a graphical user interface (point and click) to the main SAS application. Each chapter contains a brief conceptual overview and then guides the reader through concrete step-by-step examples to complete the analyses. The eleven sections of the book cover a wide range of statistical procedures including descriptive statistics, correlation and simple regression, t tests, one-way chi square, data transformations, multiple regression, analysis of variance, analysis of covariance, multivariate analysis of variance, factor analysis, and canonical correlation analysis. Designed to be used either as a stand-alone resource or as an accompaniment to a statistics course, the book offers a smooth path to statistical analysis with SAS Enterprise Guide for advanced undergraduate and beginning graduate students, as well as professionals in psychology, education, business, hea

This book presents the basic procedures for utilizing SAS Enterprise Guide to analyze statistical data. SAS Enterprise Guide is a graphical user interface (point and click) to the main SAS application. Each chapter contains a brief conceptual overview and then guides the reader through concrete step-by-step examples to complete the analyses. The eleven sections of the book cover a wide range of statistical procedures including descriptive statistics, correlation and simple regression, t tests, one-way chi square, data transformations, multiple regression, analysis of variance, analysis of covariance, multivariate analysis of variance, factor analysis, and canonical correlation analysis. Designed to be used either as a stand-alone resource or as an accompaniment to a statistics course, the book offers a smooth path to statistical analysis with SAS Enterprise Guide for advanced undergraduate and beginning graduate students, as well as professionals in psychology, education, business, hea

Making a substantiated choice of the most efficient statistical test is one of the basic problems of statistics. Asymptotic efficiency is an indispensable technique for comparing and ordering statistical tests in large samples. It is especially useful in nonparametric statistics where it is usually necessary to rely on heuristic tests. This monograph presents a unified treatment of the analysis and calculation of the asymptotic efficiencies of nonparametric tests. Powerful new methods are developed to evaluate explicitly different kinds of efficiencies. Of particular interest is the description of domains of the Bahadur local optimality and related characterisation problems based on recent research by the author. Other Russian results are also published here for the first time in English. Researchers, professionals and students in statistics will find this book invaluable.

Elements of Spatial Structure is a contribution to the literature on spatial series. Written by a group with varied backgrounds in engineering, geography and statistics, who collaborated at Bristol University in the early 1970s, the book analyses certain basic properties of spatial structure. It shows how spatial elements form an essential part of the real-world problems of population distribution, of urban and regional economies, and of diffusion processes. The book is divided into three parts. Part one is concerned with a static cross-sectional approach to spatial structure and explores some aspects of the central geographical problems of region-building and trend-surface mapping. Part two moves to a dynamic framework and extends time-series analysis in a regional framework. It includes two chapters on the application of the models presented to diffusion and unemployment data in south-west England. Part three links the first two parts together through a consideration of spatial autoc

Robust statistics is an extension of classical statistics that specifically takes into account the concept that the underlying models used to describe data are only approximate. Its basic philosophy i

Instead of taking somebody's word for it about the basic size and distance statistics for the solar system, this book shows amateur astronomers how to measure these things for themselves. This is an

This book approaches the study of patterns by emphasising the processes responsible for them; it emphasises the logical format of process-to-pattern rather than the more wasteful pattern-to-process approach. The concern is primarily with two-dimensional surfaces, which is the way most maps are used for analysis. The material is organised into sections on process models responsible for point patterns, for line patterns and then for area patterns. It represents a synthesis of the work done on patterns in a number of fields and a large literature is reviewed in the process of the synthesis. In many respects this book represents a translation of complex mathematical materials into a readable and relatively simple verbal approach to the subject and thus brings the more sophisticated aspects to a larger number of students than has been done before. The reader need only have an elementary background in statistics. The basic probability theory required by the text is given in an appendix.

The theory of generalized hypergeometric functions is fundamental in the field of mathematical physics, since all the commonly used functions of analysis (Besse] Functions, Legendre Functions, etc.) are special cases of the general functions. The unified theory provides a means for the analysis of the simpler functions and can be used to solve the more complicated equations in physics. The generalized Gauss function is also used in mathematical statistics and the basic analogues of the Gauss functions have applications in the field of number theory. Dr Slater's treatment leads on from a discussion of the Gauss functions to the basic hypergeometric functions, the hypergeometric integrals, bilateral series and Appel series. This book was planned jointly with the late Professor W. N. Bailey as an extended revision of his Cambridge Mathematical Tract (1935) on the subject and Dr Slater has continued it single-handed since Professor Bailey's death, incorporating in it the results of many of

The authors believe that a proper treatment of probability theory requires an adequate background in the theory of finite measures in general spaces. The first part of their book sets out this material in a form that not only provides an introduction for intending specialists in measure theory but also meets the needs of students of probability. The theory of measure and integration is presented for general spaces, with Lebesgue measure and the Lebesgue integral considered as important examples whose special properties are obtained. The introduction to functional analysis which follows covers the material (such as the various notions of convergence) which is relevant to probability theory and also the basic theory of L2-spaces, important in modern physics. The second part of the book is an account of the fundamental theoretical ideas which underlie the applications of probability in statistics and elsewhere, developed from the results obtained in the first part. A large number of examp

This unique book develops the classical subjects of geometric probability and integral geometry, and the more modern one of stochastic geometry, in rather a novel way to provide a unifying framework in which they can be studied. The author focuses on factorisation properties of measures and probabilities implied by the assumption of their invariance with respect to a group, in order to investigate non-trivial factors. The study of these properties is the central theme of the book. Basic facts about integral geometry and random point process theory are developed in a simple geometric way, so that the whole approach is suitable for a non-specialist audience. Even in the later chapters, where the factorisation principles are applied to geometrical processes, the prerequisites are only standard courses on probability and analysis. The main ideas presented here have application to such areas as stereology and tomography, geometrical statistics, pattern and texture analysis. This book will b

This updated textbook is an excellent way to introduce probability and information theory to new students in mathematics, computer science, engineering, statistics, economics, or business studies. Only requiring knowledge of basic calculus, it starts by building a clear and systematic foundation to the subject: the concept of probability is given particular attention via a simplified discussion of measures on Boolean algebras. The theoretical ideas are then applied to practical areas such as statistical inference, random walks, statistical mechanics and communications modelling. Topics covered include discrete and continuous random variables, entropy and mutual information, maximum entropy methods, the central limit theorem and the coding and transmission of information, and added for this new edition is material on Markov chains and their entropy. Lots of examples and exercises are included to illustrate how to use the theory in a wide range of applications, with detailed solutions to

This updated textbook is an excellent way to introduce probability and information theory to new students in mathematics, computer science, engineering, statistics, economics, or business studies. Only requiring knowledge of basic calculus, it starts by building a clear and systematic foundation to the subject: the concept of probability is given particular attention via a simplified discussion of measures on Boolean algebras. The theoretical ideas are then applied to practical areas such as statistical inference, random walks, statistical mechanics and communications modelling. Topics covered include discrete and continuous random variables, entropy and mutual information, maximum entropy methods, the central limit theorem and the coding and transmission of information, and added for this new edition is material on Markov chains and their entropy. Lots of examples and exercises are included to illustrate how to use the theory in a wide range of applications, with detailed solutions to

A practical, quick reference guide for the basic sciences (physics, physiology, pharmacology and statistics) required by anaesthetists preparing for the primary or final FRCA. Provides all key graphs,

Statistical design is one of the fundamentals of our subject, being at the core of the growth of statistics during the previous century. In this book the basic theoretical underpinnings are covered. I

This concise book presents evidence-based medicine to neophytes in simplified, friendly language. Basic concepts and application of research statistics are presented in simple sequences that are non-t

This practical guide to survival data and its analysis for readers with a minimal background in statistics shows why the analytic methods work and how to effectively analyze and interpret epidemiologic and medical survival data with the help of modern computer systems. The introduction presents a review of a variety of statistical methods that are not only key elements of survival analysis but are also central to statistical analysis in general. Techniques such as statistical tests, transformations, confidence intervals, and analytic modeling are presented in the context of survival data but are, in fact, statistical tools that apply to understanding the analysis of many kinds of data. Similarly, discussions of such statistical concepts as bias, confounding, independence, and interaction are presented in the context of survival analysis and also are basic components of a broad range of applications. These topics make up essentially a 'second-year', one-semester biostatistics course in

This practical guide to survival data and its analysis for readers with a minimal background in statistics shows why the analytic methods work and how to effectively analyze and interpret epidemiologic and medical survival data with the help of modern computer systems. The introduction presents a review of a variety of statistical methods that are not only key elements of survival analysis but are also central to statistical analysis in general. Techniques such as statistical tests, transformations, confidence intervals, and analytic modeling are presented in the context of survival data but are, in fact, statistical tools that apply to understanding the analysis of many kinds of data. Similarly, discussions of such statistical concepts as bias, confounding, independence, and interaction are presented in the context of survival analysis and also are basic components of a broad range of applications. These topics make up essentially a 'second-year', one-semester biostatistics course in

A team of experts in the area of baseball statistics addresses the question as to why teams win pennant races, drawing on in-depth statistical analyses to reveal the secrets behind a team's long-term

Algebraic geometry, central to pure mathematics, has important applications in such fields as engineering, computer science, statistics and computational biology, which exploit the computational algorithms that the theory provides. Users get the full benefit, however, when they know something of the underlying theory, as well as basic procedures and facts. This book is a systematic introduction to the central concepts of algebraic geometry most useful for computation. Written for advanced undergraduate and graduate students in mathematics and researchers in application areas, it focuses on specific examples and restricts development of formalism to what is needed to address these examples. In particular, it introduces the notion of Gröbner bases early on and develops algorithms for almost everything covered. It is based on courses given over the past five years in a large interdisciplinary programme in computational algebraic geometry at Rice University, spanning mathematics, computer

Since the baseball statistics revolution began in the 1970s, no one had written the book that reveals, across every area of strategy and management, how the best practitioners of statistical analysis

Boland's (University College Dublin, Ireland) text covers many of the diverse methods in applied probability and statistics, building on the reader's existing basic knowledge of probability and statis

Aiming to provide scientifically sound advice on ecological risk assessment to environmental decision makers (who have a basic knowledge of biology, chemistry, mathematics, and statistics), Sutter (sc

Suitable for a first year graduate course, this textbook unites the applications of numerical mathematics and scientific computing to the practice of chemical engineering. Written in a pedagogic style, the book describes basic linear and nonlinear algebric systems all the way through to stochastic methods, Bayesian statistics and parameter estimation. These subjects are developed at a level of mathematics suitable for graduate engineering study without the exhaustive level of the theoretical mathematical detail. The implementation of numerical methods in MATLAB is integrated within each chapter and numerous examples in chemical engineering are provided, with a library of corresponding MATLAB programs. This book will provide the graduate student with essential tools required by industry and research alike. Supplementary material includes solutions to homework problems set in the text, MATLAB programs and tutorial, lecture slides, and complicated derivations for the more advanced reader.

This book is about the coordinate-free, or geometric, approach to the theory of linear models; more precisely, Model I ANOVA and linear regression models with non-random predictors in a finite-dimensional setting. This approach is more insightful, more elegant, more direct, and simpler than the more common matrix approach to linear regression, analysis of variance, and analysis of covariance models in statistics. The book discusses the intuition behind and optimal properties of various methods of estimating and testing hypotheses about unknown parameters in the models. Topics covered range from linear algebra, such as inner product spaces, orthogonal projections, book orthogonal spaces, Tjur experimental designs, basic distribution theory, the geometric version of the Gauss-Markov theorem, optimal and non-optimal properties of Gauss-Markov, Bayes, and shrinkage estimators under assumption of normality, the optimal properties of F-test, and the analysis of covariance and missing observa

In its first six chapters this 2006 text seeks to present the basic ideas and properties of the Jacobi elliptic functions as an historical essay, an attempt to answer the fascinating question: 'what would the treatment of elliptic functions have been like if Abel had developed the ideas, rather than Jacobi?' Accordingly, it is based on the idea of inverting integrals which arise in the theory of differential equations and, in particular, the differential equation that describes the motion of a simple pendulum. The later chapters present a more conventional approach to the Weierstrass functions and to elliptic integrals, and then the reader is introduced to the richly varied applications of the elliptic and related functions. Applications spanning arithmetic (solution of the general quintic, the functional equation of the Riemann zeta function), dynamics (orbits, Euler's equations, Green's functions), and also probability and statistics, are discussed.

In its first six chapters this 2006 text seeks to present the basic ideas and properties of the Jacobi elliptic functions as an historical essay, an attempt to answer the fascinating question: 'what would the treatment of elliptic functions have been like if Abel had developed the ideas, rather than Jacobi?' Accordingly, it is based on the idea of inverting integrals which arise in the theory of differential equations and, in particular, the differential equation that describes the motion of a simple pendulum. The later chapters present a more conventional approach to the Weierstrass functions and to elliptic integrals, and then the reader is introduced to the richly varied applications of the elliptic and related functions. Applications spanning arithmetic (solution of the general quintic, the functional equation of the Riemann zeta function), dynamics (orbits, Euler's equations, Green's functions), and also probability and statistics, are discussed.

Within this detailed book you will find 90 superb original color photographs, brief background history of the company and full story of the LI series. Basic specification and statistics quotes, and in