Introduction to Statistics for Artificial Intelligence

Preface v

1 Introduction to Data 1
1.1 Statistics and artificial intelligence 1
1.2 Data and variables 3
1.3 Populations, samples, and study design 5

2 Summarizing Data 9
2.1 Examining numerical data 9
2.2 Considering categorical data 19

3 Probability 25
3.1 Defining probability 25
3.2 Conditional probability 30

4 Random Variables 37
4.1 Defining random variables 37
4.2 Expectation and variance 43
4.3 Joint distributions 47

5 Distributions 55
5.1 Uniform distribution 55
5.2 Normal distribution 57
5.3 Binomial distribution 62

6 Foundations for Inference 69
6.1 Point estimates and sampling variability 69
6.2 Confidence intervals for a proportion 73

7 Sampling Distribution and Point Estimation 77
7.1 Sampling distribution 77
7.2 Point estimation 86

8 Inference for Means 91
8.1 Confidence interval for a population mean 92
8.2 Hypothesis test for a population mean 99
8.3 Power calculations for a population mean 107
8.4 Paired data 109
8.5 Difference of two means: unequal variances 113
8.6 Difference of two means: equal variances 117
8.7 Power calculations for a difference of means 120
8.8 Comparing many means: ANOVA 123
8.9 Summary of tests for means 128

9 Linear Regression 131
9.1 Line fitting, residuals, and correlation 132
9.2 Fitting a line by least squares 140
9.3 Inference for linear regression 146
9.4 Multiple linear regression 152

10 Logistic Regression 159
10.1 Modeling a binary outcome 160
10.2 Fitting and interpreting logistic regression 163
10.3 Making and evaluating decisions 166
10.4 From regression to machine learning 171

A R Basics 175

B Statistical Tables 179

C Solutions to Exercises 187

References 215

Index 217

Yonghyun Kwon received B.S. degree in Statistics from Seoul National University, and Ph.D. degree in Statistics from Iowa State University. He is currently an assistant professor in the Department of Mathematics at Korea Military Academy.