English | MP4 | AVC 1920×1080 | AAC 44KHz 2ch | 36 Hours | 11.7 GB

A rigorous and engaging deep-dive into statistics and machine-learning, with hands-on applications in Python and MATLAB.

Statistics and probability control your life. I don’t just mean What YouTube’s algorithm recommends you to watch next, and I don’t just mean the chance of meeting your future significant other in class or at a bar. Human behavior, single-cell organisms, Earthquakes, the stock market, whether it will snow in the first week of December, and countless other phenomena are probabilistic and statistical. Even the very nature of the most fundamental deep structure of the universe is governed by probability and statistics.

You need to understand statistics.

Nearly all areas of human civilization are incorporating code and numerical computations. This means that many jobs and areas of study are based on applications of statistical and machine-learning techniques in programming languages like Python and MATLAB. This is often called ‘data science’ and is an increasingly important topic.

If you want to make yourself a future-proof employee, employer, data scientist, or researcher in any technical field — ranging from data scientist to engineering to research scientist to deep learning modeler — you’ll need to know statistics and machine-learning. And you’ll need to know how to implement concepts like probability theory and confidence intervals, k-means clustering and PCA, Spearman correlation and logistic regression, in computer languages like Python or MATLAB.

There are six reasons why you should take this course:

- This course covers everything you need to understand the fundamentals of statistics, machine learning, and data science, from bar plots to ANOVAs, regression to k-means, t-test to non-parametric permutation testing.
- After completing this course, you will be able to understand a wide range of statistical and machine-learning analyses, even specific advanced methods that aren’t taught here. That’s because you will learn the foundations upon which advanced methods are build.
- This course balances mathematical rigor with intuitive explanations, and hands-on explorations in code.
- Enrolling in the course gives you access to the Q&A, in which I actively participate every day.
- I’ve been studying, developing, and teaching statistics for 20 years, and I’m, like, really great at math.

What you’ll learn

- Descriptive statistics (mean, variance, etc)
- Inferential statistics
- T-tests, correlation, ANOVA, regression, clustering
- The math behind the “black box” statistical methods
- How to implement statistical methods in code
- How to interpret statistics correctly and avoid common misunderstandings
- Coding techniques in Python and MATLAB/Octave
- Machine learning methods like clustering, predictive analysis, classification, and data cleaning

**+ Table of Contents**

**Introductions**

1 [Important] Getting the most out of this course

2 About using MATLAB or Python

3 Statistics guessing game!

4 Using the Q&A forum

5 (optional) Entering time-stamped notes in the Udemy video player

**Math prerequisites**

6 Should you memorize statistical formulas

7 Arithmetic and exponents

8 Scientific notation

9 Summation notation

10 Absolute value

11 Natural exponent and logarithm

12 The logistic function

13 Rank and tied-rank

**IMPORTANT Download course materials**

14 Download materials for the entire course!

**What are (is ) data **

15 Is data singular or plural ! !! !

16 Where do data come from and what do they mean

17 Types of data categorical, numerical, etc

18 Code representing types of data on computers

19 Sample vs. population data

20 Samples, case reports, and anecdotes

21 The ethics of making up data

**Visualizing data**

22 Bar plots

23 Code bar plots

24 Box-and-whisker plots

25 Code box plots

26 Unsupervised learning Boxplots of normal and uniform noise

27 Histograms

28 Code histograms

29 Unsupervised learning Histogram proportion

30 Pie charts

31 Code pie charts

32 When to use lines instead of bars

33 Linear vs. logarithmic axis scaling

34 Code line plots

35 Unsupervised learning log-scaled plots

**Descriptive statistics**

36 Descriptive vs. inferential statistics

37 Accuracy, precision, resolution

38 Data distributions

39 Code data from different distributions

40 Unsupervised learning histograms of distributions

41 The beauty and simplicity of Normal

42 Measures of central tendency (mean)

43 Measures of central tendency (median, mode)

44 Code computing central tendency

45 Unsupervised learning central tendencies with outliers

46 Measures of dispersion (variance, standard deviation)

47 Code Computing dispersion

48 Interquartile range (IQR)

49 Code IQR

50 QQ plots

51 Code QQ plots

52 Statistical moments

53 Histograms part 2 Number of bins

54 Code Histogram bins

55 Violin plots

56 Code violin plots

57 Unsupervised learning asymmetric violin plots

58 Shannon entropy

59 Code entropy

60 Unsupervised learning entropy and number of bins

**Data normalizations and outliers**

61 Garbage in, garbage out (GIGO)

62 Z-score standardization

63 Code z-score

64 Min-max scaling

65 Code min-max scaling

66 Unsupervised learning Invert the min-max scaling

67 What are outliers and why are they dangerous

68 Removing outliers z-score method

69 The modified z-score method

70 Code z-score for outlier removal

71 Unsupervised learning z vs. modified-z

72 Multivariate outlier detection

73 Code Euclidean distance for outlier removal

74 Removing outliers by data trimming

75 Code Data trimming to remove outliers

76 Non-parametric solutions to outliers

77 An outlier lecture on personal accountability

**Probability theory**

78 What is probability

79 Probability vs. proportion

80 Computing probabilities

81 Code compute probabilities

82 Probability and odds

83 Unsupervised learning probabilities of odds-space

84 Probability mass vs. density

85 Code compute probability mass functions

86 Cumulative probability distributions

87 Code cdfs and pdfs

88 Unsupervised learning cdf’s for various distributions

89 Creating sample estimate distributions

90 Monte Carlo sampling

91 Sampling variability, noise, and other annoyances

92 Code sampling variability

93 Expected value

94 Conditional probability

95 Code conditional probabilities

96 Tree diagrams for conditional probabilities

97 The Law of Large Numbers

98 Code Law of Large Numbers in action

99 The Central Limit Theorem

100 Code the CLT in action

101 Unsupervised learning Averaging pairs of numbers

**Hypothesis testing**

102 IVs, DVs, models, and other stats lingo

103 What is an hypothesis and how do you specify one

104 Sample distributions under null and alternative hypotheses

105 P-values definition, tails, and misinterpretations

106 P-z combinations that you should memorize

107 Degrees of freedom

108 Type 1 and Type 2 errors

109 Parametric vs. non-parametric tests

110 Multiple comparisons and Bonferroni correction

111 Statistical vs. theoretical vs. clinical significance

112 Cross-validation

113 Statistical significance vs. classification accuracy

**The t-test family**

114 Purpose and interpretation of the t-test

115 One-sample t-test

116 Code One-sample t-test

117 Unsupervised learning The role of variance

118 Two-samples t-test

119 Code Two-samples t-test

120 Unsupervised learning Importance of N for t-test

121 Wilcoxon signed-rank (nonparametric t-test)

122 Code Signed-rank test

123 Mann-Whitney U test (nonparametric t-test)

124 Code Mann-Whitney U test

125 Permutation testing for t-test significance

126 Code permutation testing

127 Unsupervised learning How many permutations

**Confidence intervals on parameters**

128 What are confidence intervals and why do we need them

129 Computing confidence intervals via formula

130 Code compute confidence intervals by formula

131 Confidence intervals via bootstrapping (resampling)

132 Code bootstrapping confidence intervals

133 Unsupervised learning Confidence intervals for variance

134 Misconceptions about confidence intervals

**Correlation**

135 Motivation and description of correlation

136 Covariance and correlation formulas

137 Code correlation coefficient

138 Code Simulate data with specified correlation

139 Correlation matrix

140 Code correlation matrix

141 Unsupervised learning average correlation matrices

142 Unsupervised learning correlation to covariance matrix

143 Partial correlation

144 Code partial correlation

145 The problem with Pearson

146 Nonparametric correlation Spearman rank

147 Fisher-Z transformation for correlations

148 Code Spearman correlation and Fisher-Z

149 Unsupervised learning Spearman correlation

150 Unsupervised learning confidence interval on correlation

151 Kendall’s correlation for ordinal data

152 Code Kendall correlation

153 Unsupervised learning Does Kendall vs. Pearson matter

154 Cosine similarity

155 Code Cosine similarity vs. Pearson correlation

**Analysis of Variance (ANOVA)**

156 ANOVA intro, part1

157 ANOVA intro, part 2

158 Sum of squares

159 The F-test and the ANOVA table

160 The omnibus F-test and post-hoc comparisons

161 The two-way ANOVA

162 One-way ANOVA example

163 Code One-way ANOVA (independent samples)

164 Code One-way repeated-measures ANOVA

165 Two-way ANOVA example

166 Code Two-way mixed ANOVA

**Regression**

167 Introduction to GLM regression

168 Least-squares solution to the GLM

169 Evaluating regression models R2 and F

170 Simple regression

171 Code simple regression

172 Unsupervised learning Compute R2 and F

173 Multiple regression

174 Standardizing regression coefficients

175 Code Multiple regression

176 Polynomial regression models

177 Code polynomial modeling

178 Unsupervised learning Polynomial design matrix

179 Logistic regression

180 Code Logistic regression

181 Under- and over-fitting

182 Unsupervised learning Overfit data

183 Comparing nested models

184 What to do about missing data

**Statistical power and sample sizes**

185 What is statistical power and why is it important

186 Estimating statistical power and sample size

187 Compute power and sample size using G Power

**Clustering and dimension-reduction**

188 K-means clustering

189 Code k-means clustering

190 Unsupervised learning K-means and normalization

191 Unsupervised learning K-means on a Gauss blur

192 Clustering via dbscan

193 Code dbscan

194 Unsupervised learning dbscan vs. k-means

195 K-nearest neighbor classification

196 Code KNN

197 Principal components analysis (PCA)

198 Code PCA

199 Unsupervised learning K-means on PC data

200 Independent components analysis (ICA)

201 Code ICA

**Signal detection theory**

202 The two perspectives of the world

203 d-prime

204 Code d-prime

205 Response bias

206 Code Response bias

207 Receiver operating characteristics (ROC)

208 Code ROC curves

209 Unsupervised learning Make this plot look nicer!

**Bonus section**

210 About deep learning

211 Bonus content

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