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E-raamat: Statistics with Julia: Fundamentals for Data Science, Machine Learning and Artificial Intelligence

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This monograph uses the Julia language to guide the reader through an exploration of the fundamental concepts of probability and statistics, all with a view of mastering machine learning, data science, and artificial intelligence. The text does not require any prior statistical knowledge and only assumes a basic understanding of programming and mathematical notation. It is accessible to practitioners and researchers in data science, machine learning, bio-statistics, finance, or engineering who may wish to solidify their knowledge of probability and statistics. 

The book progresses through ten independent chapters starting with an introduction of Julia, and moving through basic probability, distributions, statistical inference, regression analysis, machine learning methods, and the use of Monte Carlo simulation for dynamic stochastic models. Ultimately this text introduces the Julia programming language as a computational tool, uniquely addressing end-users rather than developers. It makes heavy use of over 200 code examples to illustrate dozens of key statistical concepts. The Julia code, written in a simple format with parameters that can be easily modified, is also available for download from the book’s associated GitHub repository online.

See what co-creators of the Julia language are saying about the book:

Professor Alan Edelman, MIT: With “Statistics with Julia”, Yoni and Hayden have written an easy to read, well organized, modern introduction to statistics.  The code may be looked at, and understood on the static pages of a book, or even better, when running live on a computer.  Everything you need is here in one nicely written self-contained reference.  

Dr. Viral Shah, CEO of Julia Computing: Yoni and Hayden provide a modern way to learn statistics with the Julia programming language. This book has been perfected through iteration over several semesters in the classroom. It prepares the reader with two complementary skills - statistical reasoning with hands on experience and working with large datasets through training in Julia.
Preface vii
1 Introducing Julia
1(44)
1.1 Language Overview
4(9)
1.2 Setup and Interface
13(5)
1.3 Crash Course by Example
18(8)
1.4 Plots, Images, and Graphics
26(7)
1.5 Random Numbers and Monte Carlo Simulation
33(7)
1.6 Integration with Other Languages
40(5)
2 Basic Probability
45(28)
2.1 Random Experiments
46(11)
2.2 Working with Sets
57(7)
2.3 Independence
64(1)
2.4 Conditional Probability
65(2)
2.5 Bayes' Rule
67(6)
3 Probability Distributions
73(56)
3.1 Random Variables
73(4)
3.2 Moment-Based Descriptors
77(5)
3.3 Functions Describing Distributions
82(6)
3.4 Distributions and Related Packages
88(5)
3.5 Families of Discrete Distributions
93(11)
3.6 Families of Continuous Distributions
104(16)
3.7 Joint Distributions and Covariance
120(9)
4 Processing and Summarizing Data
129(50)
4.1 Working with Data Frames
133(11)
4.2 Summarizing Data
144(7)
4.3 Plots for Single Samples and Time Series
151(13)
4.4 Plots for Comparing Two or More Samples
164(3)
4.5 Plots for Multivariate and High-Dimensional Data
167(6)
4.6 Plots for the Board Room
173(2)
4.7 Working with Files and Remote Servers
175(4)
5 Statistical Inference Concepts
179(46)
5.1 A Random Sample
180(2)
5.2 Sampling from a Normal Population
182(9)
5.3 The Central Limit Theorem
191(2)
5.4 Point Estimation
193(12)
5.5 Confidence Interval as a Concept
205(2)
5.6 Hypothesis Tests Concepts
207(8)
5.7 A Taste of Bayesian Statistics
215(10)
6 Confidence Intervals
225(30)
6.1 Single Sample Confidence Intervals for the Mean
226(2)
6.2 Two Sample Confidence Intervals for the Difference in Means
228(6)
6.3 Confidence Intervals for Proportions
234(7)
6.4 Confidence Interval for the Variance of a Normal Population
241(4)
6.5 Bootstrap Confidence Intervals
245(3)
6.6 Prediction Intervals
248(2)
6.7 Credible Intervals
250(5)
7 Hypothesis Testing
255(44)
7.1 Single Sample Hypothesis Tests for the Mean
256(8)
7.2 Two Sample Hypothesis Tests for Comparing Means
264(6)
7.3 Analysis of Variance (ANOVA)
270(9)
7.4 Independence and Goodness of Fit
279(13)
7.5 More on Power
292(7)
8 Linear Regression and Extensions
299(62)
8.1 Clouds of Points and Least Squares
301(10)
8.2 Linear Regression with One Variable
311(17)
8.3 Multiple Linear Regression
328(5)
8.4 Model Adaptations
333(10)
8.5 Model Selection
343(6)
8.6 Logistic Regression and the Generalized Linear Model
349(4)
8.7 A Taste of Time Series and Forecasting
353(8)
9 Machine Learning Basics
361(62)
9.1 Training, Testing, and Tricks of the Trade
363(16)
9.2 Supervised Learning Methods
379(15)
9.3 Bias, Variance, and Regularization
394(7)
9.4 Unsupervised Learning Methods
401(10)
9.5 Markov Decision Processes and Reinforcement Learning
411(8)
9.6 Generative Adversarial Networks
419(4)
10 Simulation of Dynamic Models
423(52)
10.1 Deterministic Dynamical Systems
424(7)
10.2 Markov Chains
431(17)
10.3 Discrete Event Simulation
448(7)
10.4 Models with Additive Noise
455(7)
10.5 Network Reliability
462(6)
10.6 Common Random Numbers and Multiple RNGs
468(7)
Appendix A How-to in Julia 475(18)
Appendix B Additional Julia Features 493(4)
Appendix C Additional Packages 497(8)
Bibliography 505(4)
List of Julia Code 509(6)
Index 515
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