Probability And Statistics For Data Science - Matloff Norman | Libro Chapman And Hall/Crc 07/2019 -

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matloff norman - probability and statistics for data science

Probability and Statistics for Data Science Math + R + Data

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Lingua: Inglese
Pubblicazione: 07/2019
Edizione: 1° edizione

Note Editore

This text is designed for a one-semester junior/senior/graduate-level calculus-based course on probability and statistics, aimed specifically at data science students (including computer science). In addition to calculus, the text assumes basic knowledge of matrix algebra and rudimentary computer programming. The key difference is the consistently applied approach, pervasive throughout the book. The overriding goal is to stay mathematically precise, yet emphasize intuition, modeling and applications.


Basic Probability Models Example: Bus Ridership A \Notebook" View: the Notion of a Repeatable Experiment Theoretical Approaches A More Intuitive Approach Our Definitions "Mailing Tubes" Example: Bus Ridership Model (cont'd) Example: ALOHA Network ALOHA Network Model Summary ALOHA Network Computations ALOHA in the Notebook Context Example: A Simple Board Game Bayes' Rule General Principle Example: Document Classification Random Graph Models Example: Preferential Attachment Model Combinatorics-Based Probability Computation Which Is More Likely in Five Cards, One King or Two Hearts? Example: Random Groups of Students Example: Lottery Tickets Example: \Association Rules" Example: Gaps between Numbers Multinomial Coefficients Example: Probability of Getting Four Aces in a Bridge Hand Monte Carlo Simulation Example: Rolling Dice First Improvement Second Improvement Third Improvement Example: Dice Problem Use of runif() for Simulating Events Example: ALOHA Network (cont'd) Example: Bus Ridership (cont'd) Example: Board Game (cont'd) Example: Broken Rod How Long Should We Run the Simulation? Computational Complements More on the replicate() Function Discrete Random Variables: Expected Value Random Variables Discrete Random Variables Independent Random Variables Example: The Monty Hall Problem Expected Value Generality|Not Just for Discrete Random Variables Misnomer Definition and Notebook View Properties of Expected Value Computational Formula Further Properties of Expected Value Finding Approximate Expected Values via Simulation Casinos, Insurance Companies and \Sum Users," Compared to Others Mathematical Complements Proof of Property E: Discrete Random Variables: Variance Variance Definition Central Importance of the Concept of Variance Intuition Regarding the Size of Var(X) Chebychev's Inequality The Coefficient of Variation A Useful Fact Covariance Indicator Random Variables, and Their Means and Variances Example: Return Time for Library Books, Version I Example: Return Time for Library Books, Version II Example: Indicator Variables in a Committee Problem Skewness Mathematical Complements Proof of Chebychev's Inequality Discrete Parametric Distribution Families Distributions Example: Toss Coin Until First Head Example: Sum of Two Dice Example: Watts-Strogatz Random Graph Model The Model Parametric Families of Distributions The Case of Importance to Us: Parameteric Families of pmfs Distributions Based on Bernoulli Trials The Geometric Family of Distributions R Functions Example: a Parking Space Problem The Binomial Family of Distributions R Functions Example: Parking Space Model The Negative Binomial Family of Distributions R Functions Example: Backup Batteries Two Major Non-Bernoulli Models The Poisson Family of Distributions R Functions Example: Broken Rod Fitting the Poisson and Power Law Models to Data Example: the Bus Ridership Problem Example: Flipping Coins with Bonuses Example: Analysis of Social Networks Mathematical Complements Computational Complements Graphics and Visualization in R Introduction to Discrete Markov Chains Matrix Formulation Example: Die Game Long-Run State Probabilities Stationary Distribution Calculation of _ Simulation Calculation of _ Example: -Heads-in-a-Row Game Example: Bus Ridership Problem Hidden Markov Models Example: Bus Ridership Computation Google PageRank Continuous Probability Models A Random Dart Individual Values Now Have Probability Zero But Now We Have a Problem Our Way Out of the Problem: Cumulative Distribution Functions CDFs Non-Discrete, Non-Continuous Distributions Density Functions Properties of Densities Intuitive Meaning of Densities Expected Values A First Example Famous Parametric Families of Continuous Distributions The Uniform Distributions Density and Properties R Functions Example: Modeling of Disk Performance Example: Modeling of Denial-of-Service Attack The Normal (Gaussian) Family of Continuous Distributions Density and Properties R Functions Importance in Modeling The Exponential Family of Distributions Density and Properties R Functions Example: Garage Parking Fees Memoryless Property of Exponential Distributions Importance in Modeling The Gamma Family of Distributions Density and Properties Example: Network Buffer Importance in Modeling The Beta Family of Distributions Density Etc Importance in Modeling Mathematical Complements Duality of the Exponential Family with the Poisson Family Computational Complements Inverse Method for Sampling from a Density Sampling from a Poisson Distribution Statistics: Prologue Importance of This Chapter Sampling Distributions Random Samples The Sample Mean | a Random Variable Toy Population Example Expected Value and Variance of X Toy Population Example Again Interpretation Notebook View Simple Random Sample Case The Sample Variance|Another Random Variable Intuitive Estimation of _ Easier Computation Special Case: X Is an Indicator Variable To Divide by n or n-? Statistical Bias The Concept of a \Standard Error" Example: Pima Diabetes Study Don't Forget: Sample = Population! Simulation Issues Sample Estimates Infinite Populations? Observational Studies The Bayesian Philosophy How Does It Work? Arguments for and Against Computational Complements R's split() and tapply() Functions Fitting Continuous Models Estimating a Density from Sample Data Example: BMI Data The Number of Bins The Bias-Variance Tradeo_ The Bias-Variance Tradeo_ in the Histogram Case A General Issue: Choosing the Degree of Smoothing Parameter Estimation Method of Moments Example: BMI Data The Method of Maximum Likelihood Example: Humidity Data MM vs MLE Advanced Methods for Density Estimation Assessment of Goodness of Fit Mathematical Complements Details of Kernel Density Estimators Computational Complements Generic Functions The gmm Package The gmm() Function Example: Bodyfat Data The Family of Normal Distributions Density and Properties Closure Under Affine Transformation Closure Under Independent Summation A Mystery R Functions The Standard Normal Distribution Evaluating Normal cdfs Example: Network Intrusion Example: Class Enrollment Size The Central Limit Theorem Example: Cumulative Roundo_ Error Example: Coin Tosses Example: Museum Demonstration A Bit of Insight into the Mystery X Is Approximately Normal|No Matter What the Population Distribution Is Approximate Distribution of (Centered and Scaled) X Improved Assessment of Accuracy of X Importance in Modeling The Chi-Squared Family of Distributions Density and Properties Example: Error in Pin Placement Importance in Modeling Relation to Gamma Family Mathematical Complements Convergence in Distribution, and the Precisely-Stated CLT Computational Complements Example: Generating Normal Random Numbers Introduction to Statistical Inference The Role of Normal Distributions Confidence Intervals for Means Basic Formulation Example: Pima Diabetes Study Example: Humidity Data Meaning of Confidence Intervals A Weight Survey in Davis Confidence Intervals for Proportions Example: Machine Classification of Forest Covers The Student-t Distribution Introduction to Significance Tests The Proverbial Fair Coin The Basics General Testing Based on Normally Distributed Estimators The Notion of \p-Values" What's Random and What Is Not Example: the Forest Cover Data Problems with Significance Testing History of Significance Testing, and Where We Are Today The Basic Issues Alternative Approach The Problem of \P-hacking" A Thought Experiment Multiple Inference Methods Philosophy of Statistics More about Interpretation of CIs The Bayesian View of Confidence Intervals Multivariate Distributions Multivariate Distributions: Discrete Case Example: Marbles in a Bag Multivariat


Dr. Norm Matloff is a professor of computer science at the University of California at Davis and formerly a professor of statistics at that university. He is a recipient of the campus-wide Distinguished Teaching Award and Distinguished Public Service Award at UC Davis. Dr. Matloff has a PhD in pure mathematics from UCLA, specializing in probability theory and statistics. He has published numerous papers in computer science and statistics, with current research interests in parallel processing, regression methodology, recommender systems, and machine learning. Dr. Matloff is the author of several widely-used Web tutorials on computer topics such as the Linux operating system and the Python programming language. He and Dr. Peter Salzman are authors of The Art of Debugging with GDB, DDD, and Eclipse. He is also author of The Art of R Programming (2011), Parallel Computation for Data Science (2015), and Statistical Regression and Classification: from Linear Models to Machine Learning (2017). The latter was selected for the 2017 Ziegel Prize awarded annually to an outstanding new book reviewed in Technometrics.

Altre Informazioni



Condizione: Nuovo
Collana: Chapman & Hall/CRC Texts in Statistical Science
Dimensioni: 9.25 x 6.125 in
Formato: Brossura
Pagine Arabe: 500

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