Mathematical Statistics For Data Science
Published 2/2023
MP4 | Video: h264, 1280x720 | Audio: AAC, 44.1 KHz
Language: English | Size: 5.43 GB | Duration: 4h 13m
An introduction to mathematical statistics for data science, covering method of moments, maximum likelihood, and more
What you'll learn
Learn how to estimate statistical parameters using the method of moments and maximum likelihood
Learn how to evaluate and compare different estimators using notions such as bias, variance, and mean squared error.
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
Requirements
High school algebra, including manipulating functions with variables
Basic knowledge of calculus (integration and differentiation) is recommended for some chapters.
Prior experience with probability or statistics will be useful, but we cover everything assuming no previous knowledge!
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 lecturesSupplementary lecture notes with each lesson covering important vocabulary, examples and explanations from the video lessonsEnd of chapter practice problems to reinforce your understanding and develop skills from the courseYou will learn about:Three common probability distributions, the Bernoulli distribution, uniform distribution, and normal distributionExpected value and its relation to the sample meanThe method of moments for creating estimatorsExpected value of estimators and unbiased estimatorsVariance of random variables and variance of estimatorsFisher information and the Cramer-Rao Lower BoundThe central limit theoremConfidence intervalsThis 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 detailsData science professionals who would like to refresh or expand their statistics knowledge to prepare for job interviewsAnyone who wants to learn how to think like a statisticianPre-requisitesThe 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. If you do not know calculus but otherwise have strong math skills, you can still follow along while only missing a few mathematical details.
Overview
Section 1: Introduction
Lecture 1 Course Introduction
Section 2: Probability Distributions
Lecture 2 Random variables, PMFs and PDFs
Lecture 3 The Bernoulli Distribution
Lecture 4 The Uniform Distribution
Lecture 5 The Normal Distribution
Lecture 6 Probability Distribution Recap
Section 3: Expected Values
Lecture 7 Sample mean and Expected Value
Lecture 8 Bernoulli Distribution Expected Value
Lecture 9 Uniform Distribution Expected Value
Lecture 10 Normal Distribution Expected Value
Lecture 11 Expected Value Recap
Lecture 12 Expected Value Practice Problems and Solutions
Section 4: Estimators and the Method of Moments
Lecture 13 Estimators and the Method of Moments
Lecture 14 Bernoulli Distribution MOM
Lecture 15 Uniform Distribution MOM
Lecture 16 Normal Distribution MOM
Lecture 17 Method of Moments Recap
Lecture 18 Method of Moments Practice and Solutions
Section 5: Unbiased Estimators
Lecture 19 Sampling Distribution, Evaluating Estimators, Bias
Lecture 20 Properties of Expected Values
Lecture 21 Bernoulli MOM Bias
Lecture 22 Uniform MOM Bias
Lecture 23 Normal MOM Bias
Lecture 24 Bias Recap
Lecture 25 Unbiased Estimators Practice and Solutions
Section 6: Variance
Lecture 26 Variance
Lecture 27 Bernoulli Distribution Variance
Lecture 28 Uniform Distribution Variance
Lecture 29 Normal Distribution Variance
Lecture 30 Variance of Estimators and Properties of Variance
Lecture 31 Bernoulli MOM Variance
Lecture 32 Uniform MOM Variance
Lecture 33 Normal MOM Variance
Lecture 34 Variance Recap
Lecture 35 Variance Practice and Solutions
Section 7: Maximum Likelihood Estimation
Lecture 36 Likelihood Function and Maximum Likelihood Estimation - Motivation
Lecture 37 Joint pdf, joint likelihood
Lecture 38 Log-likelihood and finding the MLE
Lecture 39 Properties of logarithms
Lecture 40 Bernoulli MLE
Lecture 41 Uniform MLE
Lecture 42 Mean Squared Error
Lecture 43 Normal MLE
Lecture 44 MLE Recap
Lecture 45 MLE Practice and Solutions
Section 8: Fisher Information and the Cramer-Rao Lower Bound
Lecture 46 The Cramer-Rao Lower Bound (CRLB) and Fisher Information
Lecture 47 Bernoulli CRLB
Lecture 48 Uniform CRLB
Lecture 49 Normal CRLB
Lecture 50 Efficiency
Lecture 51 CRLB Recap
Lecture 52 CRLB Practice and Solutions
Section 9: Central Limit Theorem
Lecture 53 Distribution of Estimators and Convergence in Distribution
Lecture 54 Bernoulli MOM/MLE Distribution
Lecture 55 Uniform MOM Distribution
Lecture 56 Normal MOM/MLE Distribution
Lecture 57 Consistency
Lecture 58 CLT Recap
Section 10: Confidence Intervals
Lecture 59 Confidence Intervals
Lecture 60 Bernoulli Confidence Interval
Lecture 61 Uniform Confidence Interval based on MOM
Lecture 62 Normal Confidence Interval
Lecture 63 Confidence Interval Recap, Link to Hypothesis Testing
Lecture 64 Confidence Interval Practice and Solutions
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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