MACDONALD-KELCE LIBRARY
Understanding Advanced Statistical Methods by
Providing a much-needed bridge between elementary statistics courses and advanced research methods courses, Understanding Advanced Statistical Methodshelps students grasp the fundamental assumptions and machinery behind sophisticated statistical topics, such as logistic regression, maximum likelihood, bootstrapping, nonparametrics, and Bayesian methods. The book teaches students how to properly model, think critically, and design their own studies to avoid common errors. It leads them to think differently not only about math and statistics but also about general research and the scientific method. With a focus on statistical models as producersof data, the book enables students to more easily understand the machinery of advanced statistics. It also downplays the "population" interpretation of statistical models and presents Bayesian methods before frequentist ones. Requiring no prior calculus experience, the text employs a "just-in-time" approach that introduces mathematical topics, including calculus, where needed. Formulas throughout the text are used to explain why calculus and probability are essential in statistical modeling. The authors also intuitively explain the theory and logic behind real data analysis, incorporating a range of application examples from the social, economic, biological, medical, physical, and engineering sciences. Enabling your students to answer the whybehind statistical methods, this text teaches them how to successfully draw conclusions when the premises are flawed. It empowers them to use advanced statistical methods with confidence and develop their own statistical recipes. Ancillary materials are available on the book's website. he text employs a "just-in-time" approach that introduces mathematical topics, including calculus, where needed. Formulas throughout the text are used to explain why calculus and probability are essential in statistical modeling. The authors also intuitively explain the theory and logic behind real data analysis, incorporating a range of application examples from the social, economic, biological, medical, physical, and engineering sciences. Enabling your students to answer the whybehind statistical methods, this text teaches them how to successfully draw conclusions when the premises are flawed. It empowers them to use advanced statistical methods with confidence and develop their own statistical recipes. Ancillary materials are available on the book's website.
Lectures on Probability Theory and Mathematical Statistics - 2nd Edition by
This book is a collection of lectures on probability theory and mathematical statistics. It provides an accessible introduction to topics that are not usually found in elementary textbooks. It collects results and proofs, especially on probability distributions, that are hard to find in standard references and are scattered here and there in more specialistic books.The main topics covered by the book are as follows.PART 1 - MATHEMATICAL TOOLS: set theory, permutations, combinations, partitions, sequences and limits, review of differentiation and integration rules, the Gamma and Beta functions.PART 2 - FUNDAMENTALS OF PROBABILITY: events, probability, independence, conditional probability, Bayes' rule, random variables and random vectors, expected value, variance, covariance, correlation, covariance matrix, conditional distributions and conditional expectation, independent variables, indicator functions.PART 3 - ADDITIONAL TOPICS IN PROBABILITY THEORY: probabilistic inequalities, construction of probability distributions, transformations of probability distributions, moments and cross-moments, moment generating functions, characteristic functions.PART 4 - PROBABILITY DISTRIBUTIONS: Bernoulli, binomial, Poisson, uniform, exponential, normal, Chi-square, Gamma, Student's t, F, multinomial, multivariate normal, multivariate Student's t, Wishart.PART 5 - MORE DETAILS ABOUT THE NORMAL DISTRIBUTION: linear combinations, quadratic forms, partitions.PART 6 - ASYMPTOTIC THEORY: sequences of random vectors and random variables, pointwise convergence, almost sure convergence, convergence in probability, mean-square convergence, convergence in distribution, relations between modes of convergence, Laws of Large Numbers, Central Limit Theorems, Continuous Mapping Theorem, Slutski's Theorem.PART 7 - FUNDAMENTALS OF STATISTICS: statistical inference, point estimation, set estimation, hypothesis testing, statistical inferences about the mean, statistical inferences about the variance.
Cause and Correlation in Biology: a user's guide to path analysis, structural equations, and causal inference with R by
Many problems in biology require an understanding of the relationships among variables in a multivariate causal context. Exploring such cause-effect relationships through a series of statistical methods, this book explains how to test causal hypotheses when randomised experiments cannot be performed. This completely revised and updated edition features detailed explanations for carrying out statistical methods using the popular and freely available R statistical language. Sections on d-sep tests, latent constructs that are common in biology, missing values, phylogenetic constraints, and multilevel models are also an important feature of this new edition. Written for biologists and using a minimum of statistical jargon, the concept of testing multivariate causal hypotheses using structural equations and path analysis is demystified. Assuming only a basic understanding of statistical analysis, this new edition is a valuable resource for both students and practising biologists.
Practical Statistics for Environmental and Biological Scientists by
All students and researchers in environmental and biological sciences require statistical methods at some stage of their work. Many have a preconception that statistics are difficult and unpleasant and find that the textbooks available are difficult to understand. Practical Statistics for Environmental and Biological Scientists provides a concise, user-friendly, non-technical introduction to statistics. The book covers planning and designing an experiment, how to analyse and present data, and the limitations and assumptions of each statistical method. The text does not refer to a specific computer package but descriptions of how to carry out the tests and interpret the results are based on the approaches used by most of the commonly used packages, e.g. Excel, MINITAB and SPSS. Formulae are kept to a minimum and relevant examples are included throughout the text.
A Survival Guide to the Misinformation Age : Scientific Habits of Mind by
We live in the Information Age, with billions of bytes of data just two swipes away. Yet how much of this is mis- or even disinformation? A lot of it is, and your search engine can't tell the difference. As a result, an avalanche of misinformation threatens to overwhelm the discourse we so desperately need to address complex social problems such as climate change, the food and water crises, biodiversity collapse, and emerging threats to public health. This book provides an inoculation against the misinformation epidemic by cultivating scientific habits of mind. Anyone can do it--indeed, everyone must do it if our species is to survive on this crowded and finite planet. This survival guide supplies an essential set of apps for the prefrontal cortex while making science both accessible and entertaining. It will dissolve your fear of numbers, demystify graphs, and elucidate the key concepts of probability, all while celebrating the precise use of language and logic. David Helfand, one of our nation's leading astronomers and science educators, has taught scientific habits of mind to generations in the classroom, where he continues to wage a provocative battle against sloppy thinking and the encroachment of misinformation.
Principles of Uncertainty by
An intuitive and mathematical introduction to subjective probability and Bayesian statistics. An accessible, comprehensive guide to the theory of Bayesian statistics, Principles of Uncertainty presents the subjective Bayesian approach, which has played a pivotal role in game theory, economics, and the recent boom in Markov Chain Monte Carlo methods. Both rigorous and friendly, the book contains: Introductory chapters examining each new concept or assumption Just-in-time mathematics ¿ the presentation of ideas just before they are applied Summary and exercises at the end of each chapter Discussion of maximization of expected utility The basics of Markov Chain Monte Carlo computing techniques Problems involving more than one decision-maker Written in an appealing, inviting style, and packed with interesting examples, Principles of Uncertainty introduces the most compelling parts of mathematics, computing, and philosophy as they bear on statistics. Although many books present the computation of a variety of statistics and algorithms while barely skimming the philosophical ramifications of subjective probability, this book takes a different tack. By addressing how to think about uncertainty, this book gives readers the intuition and understanding required to choose a particular method for a particular purpose.
GIS Research Methods : incorporating spatial perspectives by 
The Analysis of Biological Data by
Learn the modern methods of statistics through the use of fascinating biological and medical cases as Analysis of Biological Data guides you through statistical methods one step at a time by providing a hefty amount of examples from medical and human health research.
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