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基本説明
This is a textbook for course in mathematical statistics taught at the senior undergraduate and graduate level. Simulations and computing - both SAS and R - are used throughout to help introduce and illoustrate topics.
Full Description
Providing a much-needed bridge between elementary statistics courses and advanced research methods courses, Understanding Advanced Statistical Methods helps 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 producers of 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 why behind 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.
Contents
Introduction: Probability, Statistics and Science. Random Variables and Their Probability Distributions. Probability Calculation and Simulation. Identifying Distributions. Conditional Distributions and Independence. Marginal Distributions, Joint Distributions, Independence, and Bayes' Theorem. Sampling from Populations and Processes. Expected Value and the Law of Large Numbers. Functions of Random Variables: Their Distributions and Expected Values. Distributions of Totals. Estimation: Unbiasedness, Consistency, and Efficiency. The Likelihood Function and Maximum Likelihood Estimates. Bayesian Statistics. Frequentist Statistical Methods. Are Your Results Explainable by Chance Alone? Chi-Squared, Student's t, and F-Distributions, with Applications. Likelihood Ratio Tests. Sample Size and Power. Robustness and Nonparametric Methods. Final Words. Index.
