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Probability and Statistics for Data Science: Math + R + Data > 데이터마이닝

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Probability and Statistics for Data Science: Math + R + Data
히트도서
판매가격 59,000원
저자 Matloff
도서종류 외국도서
출판사 Chapman & Hall
발행언어 영어
발행일 2019
페이지수 412
ISBN 9781138393295
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  • 도서 정보

    도서 상세설명

    Table of Contents
    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

    Multivariate pmfs

    Multivariate Distributions: Continuous Case

    Multivariate Densities

    Motivation and Definition

    Use of Multivariate Densities in Finding Probabilities and Expected Values

    Example: a Triangular Distribution

    Example: Train Rendezvous

    Multivariate Distributions: Mixed Discrete-Continuous Case

    Measuring Co-variation of Random Variables

    Covariance

    Example: the Committee Example Again

    Correlation

    Example: Correlation in the Triangular Distribution

    Sample Estimates

    Sets of Independent Random Variables

    Properties

    Expected Values Factor

    Covariance Is

    Variances Add

    Examples Involving Sets of Independent Random Variables

    Example: Dice

    Matrix Formulations

    Properties of Mean Vectors

    Covariance Matrices

    Covariance Matrices Linear Combinations of Random

    Vectors

    More on Sets of Independent Random Variables

    Probability Mass Functions and Densities Factor in the Independent Case

    Convolution

    Example: Ethernet

    Example: Backup Battery

    The Multivariate Normal Family of Distributions

    Densities

    Geometric Interpretation

    R Functions

    Special Case: New Variable Is a Single Linear Combination of a Random Vector

    Properties of Multivariate Normal Distributions

    The Multivariate Central Limit Theorem

    Iterated Expectations

    Conditional Distributions

    The Theorem

    Example: Flipping Coins with Bonuses

    Conditional Expectation as a Random Variable

    What about Variance?

    Mixture Distributions

    Derivation of Mean and Variance

    Mathematical Complements

    Transform Methods

    Generating Functions

    Sums of Independent Poisson Random Variables Are Poisson Distributed

    A Geometric View of Conditional Expectation

    Alternate Proof of E(UV) = EU EV for Independent U,V

    Computational Complements

    Generating Multivariate Normal Random Vectors

    Dimension Reduction
    Principal Components Analysis

    Intuition

    Properties of PCA

    Example: Turkish Teaching Evaluations

    Mathematical Complements

    Derivation of PCA

    Predictive Modeling
    Example: Heritage Health Prize

    The Goals: Prediction and Description

    Terminology

    What Does Relationship" Really Mean?

    Precise Definition

    Parametric Models for the Regression Function m()

    Estimation in Linear Parametric Regression Models

    Example: Baseball Data

    R Code

    Multiple Regression: More Than One Predictor Variable

    Example: Baseball Data (cont'd)

    Interaction Terms

    Parametric Estimation of Linear Regression Functions

    Meaning of Linear"

    Random-X and Fixed-X Regression

    Point Estimates and Matrix Formulation

    Approximate Confidence Intervals

    Example: Baseball Data (cont'd)

    Dummy Variables

    Classification

    Classification = Regression

    Logistic Regression

    The Logistic Model: Motivations

    Estimation and Inference for Logit Coefficients

    Example: Forest Cover Data

    R Code

    Analysis of the Results

    Multiclass Case

    Machine Learning Methods: Neural Networks

    Example: Predicting Vertebral Abnormalities

    But What Is Really Going On?

    R Packages

    Mathematical Complements

    Matrix Derivatives and Minimizing the Sum of Squares

    Computational Complements

    Some Computational Details in Section

    More Regarding glm()

    Model Parsimony and Overfitting
    What Is Overfitting?

    Example: Histograms

    Example: Polynomial Regression

    Can Anything Be Done about It?

    Cross-Validation

    A. R Quick Start

    A Correspondences

    A Starting R

    A First Sample Programming Session

    A Vectorization

    A Second Sample Programming Session

    A Recycling

    A More on Vectorization

    A Third Sample Programming Session

    A Default Argument Values

    A The R List Type

    A The Basics

    A S Classes

    A Some Workhorse Functions

    A Data Frames

    A Online Help

    A Debugging in R

    A Further Reading

    B. Matrix Algebra

    B Terminology and Notation

    B Matrix Addition and Multiplication

    B Matrix Transpose

    B Linear Independence

    B Determinants

    B Matrix Inverse

    B Eigenvalues and Eigenvectors

    B Matrix Algebra in R
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