Mathematical Statistics for Data Science

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Brian Greco

4:12:33

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1 - Introduction

1 - Course Introduction.mp4

01:01

2 - Probability Distributions

2 - Probability-Distribution-Notes.pdf

2 - Random variables PMFs and PDFs.mp4

07:23

3 - The Bernoulli Distribution.mp4

07:27

3 - bernoulli distribution wikipedia.zip

4 - The Uniform Distribution.mp4

06:51

4 - uniform distribution wikipedia.zip

5 - The Normal Distribution.mp4

04:32

5 - normal distribution wikipedia.zip

6 - Probability Distribution Recap.mp4

03:03

3 - Expected Values

7 - Expected-Value-Notes.pdf

7 - Sample mean and Expected Value.mp4

06:51

7 - expected value.zip

8 - Bernoulli Distribution Expected Value.mp4

02:12

9 - Uniform Distribution Expected Value.mp4

03:00

10 - Normal Distribution Expected Value.mp4

03:35

10 - proof of the mean of normal distribution using calculus.zip

11 - Expected Value Recap.mp4

01:56

12 - Expected Value Practice Problems and Solutions.html

12 - Expected-Value-Practice.pdf

4 - Estimators and the Method of Moments

13 - Estimators and the Method of Moments.mp4

06:30

13 - MOM-Notes.pdf

14 - Bernoulli Distribution MOM.mp4

03:37

15 - Uniform Distribution MOM.mp4

03:22

16 - Normal Distribution MOM.mp4

01:44

17 - Method of Moments Recap.mp4

01:50

18 - Method of Moments Practice and Solutions.html

18 - Method-of-Moments-Practice.pdf

5 - Unbiased Estimators

19 - Bias-Notes.pdf

19 - Sampling Distribution Evaluating Estimators Bias.mp4

05:51

20 - Properties of Expected Values.mp4

05:07

20 - expected value properties linearity.zip

21 - Bernoulli MOM Bias.mp4

04:00

22 - Uniform MOM Bias.mp4

03:19

23 - Normal MOM Bias.mp4

04:23

24 - Bias Recap.mp4

01:40

25 - Bias-Practice.pdf

25 - Unbiased Estimators Practice and Solutions.html

6 - Variance

26 - Variance.mp4

04:39

26 - Variance-Notes-2.pdf

27 - Bernoulli Distribution Variance.mp4

03:03

28 - Uniform Distribution Variance.mp4

03:31

29 - Normal Distribution Variance.mp4

01:52

30 - Variance of Estimators and Properties of Variance.mp4

03:47

31 - Bernoulli MOM Variance.mp4

06:31

32 - Uniform MOM Variance.mp4

05:35

33 - Normal MOM Variance.mp4

04:52

34 - Variance Recap.mp4

02:34

35 - Variance Practice and Solutions.html

35 - Variance-Practice.pdf

7 - Maximum Likelihood Estimation

36 - Likelihood Function and Maximum Likelihood Estimation Motivation.mp4

04:40

36 - MLE-Notes.pdf

36 - likelihood function.zip

37 - Joint pdf joint likelihood.mp4

07:05

38 - Loglikelihood and finding the MLE.mp4

04:05

39 - Properties of logarithms.mp4

01:50

40 - Bernoulli MLE.mp4

06:49

41 - Uniform MLE.mp4

10:28

42 - Mean Squared Error.mp4

03:16

43 - Normal MLE.mp4

06:53

44 - MLE Recap.mp4

03:21

45 - MLE Practice and Solutions.html

45 - MLE-Practice.pdf

8 - Fisher Information and the CramerRao Lower Bound

46 - CRLB-Notes.pdf

46 - The CramerRao Lower Bound CRLB and Fisher Information.mp4

04:21

46 - cramerrao lower bound.zip

47 - Bernoulli CRLB.mp4

04:53

48 - Uniform CRLB.mp4

02:37

49 - Normal CRLB.mp4

06:46

50 - Efficiency.mp4

02:45

50 - efficiency.zip

51 - CRLB Recap.mp4

01:30

52 - CRLB Practice and Solutions.html

52 - CRLB-practice.pdf

9 - Central Limit Theorem

53 - CLT-Notes.pdf

53 - Distribution of Estimators and Convergence in Distribution.mp4

06:33

54 - Bernoulli MOMMLE Distribution.mp4

06:57

55 - Uniform MOM Distribution.mp4

05:58

56 - Normal MOMMLE Distribution.mp4

04:19

57 - Consistency.mp4

02:13

58 - CLT Recap.mp4

02:54

10 - Confidence Intervals

59 - CI-Notes.pdf

59 - Confidence Intervals.mp4

09:20

59 - confidence intervals.zip

60 - Bernoulli Confidence Interval.mp4

06:42

61 - Uniform Confidence Interval based on MOM.mp4

04:33

62 - Normal Confidence Interval.mp4

04:25

63 - Confidence Interval Recap Link to Hypothesis Testing.mp4

01:42

64 - CI-practice.pdf

64 - Confidence Interval Practice and Solutions.html

Description

An introduction to mathematical statistics for data science, covering method of moments, maximum likelihood, and more

What You'll Learn?

Learn how to use the method of moments and maximum likelihood estimation to learn from data
Learn how to evaluate and compare different methods using notions such as bias, variance, and mean squared error.
Master the Bernoulli, Uniform and Normal Distributions
Learn about the Cramer-Rao lower bound and how to know if we have found the best possible estimator
Learn to evaluate asymptotic properties of estimators, including consistency and the central limit theorem.
Learn to create confidence intervals

Who is this for?

Anyone who has taken a basic statistics class and wants to dive into more mathematical detail

Data scientists looking to learn some basics of mathematical statistics

Undergraduate and graduate students looking for help in mathematical statistics courses

Academics and professionals wanting a strong foundation for further study in statistics

More details

Description
This course teaches the foundations of mathematical statistics, focusing on methods of estimation such as the method of moments and maximum likelihood estimators (MLEs), evaluating estimators by their bias, variance, and efficiency, and an introduction to asymptotic statistics including the central limit theorem and confidence intervals.

The course includes:
Over four hours of video lectures, using the innovative lightboard technology to deliver face-to-face lectures
Supplementary lecture notes with each lesson covering important vocabulary, examples and explanations from the video lessons
End of chapter practice problems to reinforce your understanding and develop skills from the course
You will learn about:
Three common probability distributions, the Bernoulli distribution, uniform distribution, and normal distribution
Expected value and its relation to the sample mean
The method of moments for creating estimators
Expected value of estimators and unbiased estimators
Variance of random variables and variance of estimators
Fisher information and the Cramer-Rao Lower Bound
The central limit theorem
Confidence intervals
This course is ideal for many types of students:
Students who have taken an introductory statistics class and who would like to dive into the mathematical details
Data science professionals who would like to refresh or expand their statistics knowledge to prepare for job interviews
Anyone who wants to learn how to think like a statistician
Pre-requisites
The course requires a good understanding of high school algebra and manipulating equations with variables.
Some chapters use concepts from introductory calculus like differentiation or integration. Â If you do not know calculus but otherwise have strong math skills, you can still follow along while only missing a few mathematical details.

Who this course is for:
Anyone who has taken a basic statistics class and wants to dive into more mathematical detail
Data scientists looking to learn some basics of mathematical statistics
Undergraduate and graduate students looking for help in mathematical statistics courses
Academics and professionals wanting a strong foundation for further study in statistics

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I am a statistician, data scientist, and teacher. I've worked as a data scientist at Google, where I analyzed data from over 1 billion users, and I've created new methods for analyzing genetic sequencing data. But most importantly, I love helping others learn statistics and have been teaching at top universities and online for over ten years. My goal is to help you obtain a deep understanding of statistics and to make it as easy as possible!

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