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Inference and Learning from Data: Volume 2 : Inference
This extraordinary three-volume work, written in an engaging and rigorous style by a world authority in the field, provides an accessible, comprehensive introduction to the full spectrum of mathematical and statistical techniques underpinning contemporary methods in data-driven learning and inference.This second volume, Inference, builds on the foundational topics established in volume I to introduce students to techniques for inferring unknown variables and quantities, including Bayesian inference, Monte Carlo Markov Chain methods, maximum-likelihood estimation, hidden Markov models, Bayesian networks, and reinforcement learning.A consistent structure and pedagogy is employed throughout this volume to reinforce student understanding, with over 350 end-of-chapter problems (including solutions for instructors), 180 solved examples, almost 200 figures, datasets and downloadable Matlab code.Supported by sister volumes Foundations and Learning, and unique in its scale and depth, this textbook sequence is ideal for early-career researchers and graduate students across many courses in signal processing, machine learning, statistical analysis, data science and inference.
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Statistical Inference
This book builds theoretical statistics from the first principles of probability theory.Starting from the basics of probability, the authors develop the theory of statistical inference using techniques, definitions, and concepts that are statistical and are natural extensions and consequences of previous concepts.Intended for first-year graduate students, this book can be used for students majoring in statistics who have a solid mathematics background.It can also be used in a way that stresses the more practical uses of statistical theory, being more concerned with understanding basic statistical concepts and deriving reasonable statistical procedures for a variety of situations, and less concerned with formal optimality investigations.
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Statistical Inference
This classic textbook builds theoretical statistics from the first principles of probability theory.Starting from the basics of probability, the authors develop the theory of statistical inference using techniques, definitions, and concepts that are statistical and natural extensions, and consequences, of previous concepts.It covers all topics from a standard inference course including: distributions, random variables, data reduction, point estimation, hypothesis testing, and interval estimation. Features The classic graduate-level textbook on statistical inferenceDevelops elements of statistical theory from first principles of probabilityWritten in a lucid style accessible to anyone with some background in calculusCovers all key topics of a standard course in inferenceHundreds of examples throughout to aid understandingEach chapter includes an extensive set of graduated exercisesStatistical Inference, Second Edition is primarily aimed at graduate students of statistics, but can be used by advanced undergraduate students majoring in statistics who have a solid mathematics background.It also stresses the more practical uses of statistical theory, being more concerned with understanding basic statistical concepts and deriving reasonable statistical procedures, while less focused on formal optimality considerations. This is a reprint of the second edition originally published by Cengage Learning, Inc. in 2001.
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Nonparametric Statistical Inference
Praise for previous editions:"… a classic with a long history." – Statistical Papers"The fact that the first edition of this book was published in 1971 … [is] testimony to the book’s success over a long period." – ISI Short Book Reviews"… one of the best books available for a theory course on nonparametric statistics. … very well written and organized … recommended for teachers and graduate students." – Biometrics"… There is no competitor for this book and its comprehensive development and application of nonparametric methods.Users of one of the earlier editions should certainly consider upgrading to this new edition." – Technometrics"… Useful to students and research workers … a good textbook for a beginning graduate-level course in nonparametric statistics." – Journal of the American Statistical AssociationSince its first publication in 1971, Nonparametric Statistical Inference has been widely regarded as the source for learning about nonparametrics.The Sixth Edition carries on this tradition and incorporates computer solutions based on R.Features Covers the most commonly used nonparametric procedures States the assumptions, develops the theory behind the procedures, and illustrates the techniques using realistic examples from the social, behavioral, and life sciences Presents tests of hypotheses, confidence-interval estimation, sample size determination, power, and comparisons of competing procedures Includes an Appendix of user-friendly tables needed for solutions to all data-oriented examples Gives examples of computer applications based on R, MINITAB, STATXACT, and SAS Lists over 100 new referencesNonparametric Statistical Inference, Sixth Edition, has been thoroughly revised and rewritten to make it more readable and reader-friendly.All of the R solutions are new and make this book much more useful for applications in modern times.It has been updated throughout and contains 100 new citations, including some of the most recent, to make it more current and useful for researchers.
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What is inference in linear regression?
Inference in linear regression refers to the process of drawing conclusions about the relationships between variables based on the estimated coefficients of the regression model. It involves testing hypotheses about the significance of these coefficients and making predictions about the dependent variable. Inference helps us understand the strength and direction of the relationships between the independent and dependent variables, as well as the overall fit of the model to the data. It is an important aspect of linear regression analysis that allows us to make informed decisions and interpretations based on the statistical results.
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What exactly is a mathematical inference in mathematics and computer science?
A mathematical inference in mathematics and computer science is the process of drawing conclusions or making predictions based on existing information or data. In mathematics, this often involves using logical reasoning and mathematical principles to make deductions or prove the validity of a statement. In computer science, mathematical inference can be used in areas such as artificial intelligence and machine learning to make predictions or decisions based on patterns and data. Overall, mathematical inference is a fundamental concept in both fields that allows for the application of logic and reasoning to solve problems and make decisions.
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How are logical inference, the Gentzen calculus, and De Morgan's laws correctly derived?
Logical inference is the process of deriving new information from existing knowledge using valid reasoning. The Gentzen calculus is a formal system for representing and manipulating logical inference in a rigorous way. De Morgan's laws, which describe the relationships between logical conjunction and disjunction, can be correctly derived using the rules of the Gentzen calculus, which ensures that the inference process is sound and valid. By following the rules of the Gentzen calculus, one can systematically derive De Morgan's laws and other logical principles in a mathematically rigorous manner.
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Where did the indulgence money from the indulgence letters go?
The indulgence money from the indulgence letters went to the Catholic Church. It was used to fund various projects and initiatives, including the construction of St. Peter's Basilica in Rome. The sale of indulgences was a significant source of revenue for the church during the Renaissance period. This practice was one of the issues that Martin Luther and other reformers criticized, leading to the Protestant Reformation.
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Causal Inference in Python : Applying Causal Inference in the Tech Industry
How many buyers will an additional dollar of online marketing bring in?Which customers will only buy when given a discount coupon?How do you establish an optimal pricing strategy? The best way to determine how the levers at our disposal affect the business metrics we want to drive is through causal inference. In this book, author Matheus Facure, senior data scientist at Nubank, explains the largely untapped potential of causal inference for estimating impacts and effects.Managers, data scientists, and business analysts will learn classical causal inference methods like randomized control trials (A/B tests), linear regression, propensity score, synthetic controls, and difference-in-differences.Each method is accompanied by an application in the industry to serve as a grounding example. With this book, you will:Learn how to use basic concepts of causal inferenceFrame a business problem as a causal inference problemUnderstand how bias gets in the way of causal inferenceLearn how causal effects can differ from person to personUse repeated observations of the same customers across time to adjust for biasesUnderstand how causal effects differ across geographic locationsExamine noncompliance bias and effect dilution
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Bayesian inference with INLA
The integrated nested Laplace approximation (INLA) is a recent computational method that can fit Bayesian models in a fraction of the time required by typical Markov chain Monte Carlo (MCMC) methods.INLA focuses on marginal inference on the model parameters of latent Gaussian Markov random fields models and exploits conditional independence properties in the model for computational speed. Bayesian Inference with INLA provides a description of INLA and its associated R package for model fitting.This book describes the underlying methodology as well as how to fit a wide range of models with R.Topics covered include generalized linear mixed-effects models, multilevel models, spatial and spatio-temporal models, smoothing methods, survival analysis, imputation of missing values, and mixture models.Advanced features of the INLA package and how to extend the number of priors and latent models available in the package are discussed.All examples in the book are fully reproducible and datasets and R code are available from the book website. This book will be helpful to researchers from different areas with some background in Bayesian inference that want to apply the INLA method in their work.The examples cover topics on biostatistics, econometrics, education, environmental science, epidemiology, public health, and the social sciences.
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Theory of Statistical Inference
Theory of Statistical Inference is designed as a reference on statistical inference for researchers and students at the graduate or advanced undergraduate level.It presents a unified treatment of the foundational ideas of modern statistical inference, and would be suitable for a core course in a graduate program in statistics or biostatistics.The emphasis is on the application of mathematical theory to the problem of inference, leading to an optimization theory allowing the choice of those statistical methods yielding the most efficient use of data.The book shows how a small number of key concepts, such as sufficiency, invariance, stochastic ordering, decision theory and vector space algebra play a recurring and unifying role.The volume can be divided into four sections. Part I provides a review of the required distribution theory.Part II introduces the problem of statistical inference.This includes the definitions of the exponential family, invariant and Bayesian models.Basic concepts of estimation, confidence intervals and hypothesis testing are introduced here.Part III constitutes the core of the volume, presenting a formal theory of statistical inference.Beginning with decision theory, this section then covers uniformly minimum variance unbiased (UMVU) estimation, minimum risk equivariant (MRE) estimation and the Neyman-Pearson test.Finally, Part IV introduces large sample theory. This section begins with stochastic limit theorems, the d-method, the Bahadur representation theorem for sample quantiles, large sample U-estimation, the Cramér-Rao lower bound and asymptotic efficiency.A separate chapter is then devoted to estimating equation methods.The volume ends with a detailed development of large sample hypothesis testing, based on the likelihood ratio test (LRT), Rao score test and the Wald test.Features This volume includes treatment of linear and nonlinear regression models, ANOVA models, generalized linear models (GLM) and generalized estimating equations (GEE). An introduction to decision theory (including risk, admissibility, classification, Bayes and minimax decision rules) is presented.The importance of this sometimes overlooked topic to statistical methodology is emphasized. The volume emphasizes throughout the important role that can be played by group theory and invariance in statistical inference. Nonparametric (rank-based) methods are derived by the same principles used for parametric models and are therefore presented as solutions to well-defined mathematical problems, rather than as robust heuristic alternatives to parametric methods. Each chapter ends with a set of theoretical and applied exercises integrated with the main text.Problems involving R programming are included. Appendices summarize the necessary background in analysis, matrix algebra and group theory.
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Causal Inference : The Mixtape
An accessible, contemporary introduction to the methods for determining cause and effect in the social sciences “Causation versus correlation has been the basis of arguments—economic and otherwise—since the beginning of time.Causal Inference: The Mixtape uses legit real-world examples that I found genuinely thought-provoking.It’s rare that a book prompts readers to expand their outlook; this one did for me.”—Marvin Young (Young MC) Causal inference encompasses the tools that allow social scientists to determine what causes what.In a messy world, causal inference is what helps establish the causes and effects of the actions being studied—for example, the impact (or lack thereof) of increases in the minimum wage on employment, the effects of early childhood education on incarceration later in life, or the influence on economic growth of introducing malaria nets in developing regions.Scott Cunningham introduces students and practitioners to the methods necessary to arrive at meaningful answers to the questions of causation, using a range of modeling techniques and coding instructions for both the R and the Stata programming languages.
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What is an indulgence?
An indulgence is a way for Catholics to reduce the punishment for sins that have already been forgiven. It is believed to help cleanse the soul of the temporal punishment due to sin. Indulgences can be obtained through prayer, acts of charity, or other spiritual practices, and are granted by the Church. They are seen as a way to encourage spiritual growth and penance.
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What is delicacy rattlesnake meat?
Delicacy rattlesnake meat refers to the meat of a rattlesnake, which is considered a delicacy in some cultures. It is often described as having a mild, slightly sweet flavor and a texture similar to chicken or fish. Rattlesnake meat is low in fat and high in protein, making it a popular choice for those looking for a lean and healthy meat option. It is often prepared by grilling, frying, or baking, and is commonly served in dishes such as tacos, stews, or even as a standalone appetizer.
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What is this delicacy called?
This delicacy is called a macaron. It is a sweet meringue-based confection made with egg white, icing sugar, granulated sugar, almond meal, and food coloring. The macaron is typically filled with ganache, buttercream, or jam to create a delicious and colorful treat. It is often enjoyed as a dessert or a special treat for celebrations.
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What delicacy could this be?
Based on the description provided, the delicacy in question could be a traditional French dish called coq au vin. This dish typically consists of chicken braised with red wine, mushrooms, onions, and bacon, resulting in a rich and flavorful stew. The use of red wine and the slow cooking process gives the dish a deep, complex flavor that is often associated with French cuisine.
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