APPA 5003: Statistical Estimation for Data Science and AI
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- Course Type: Pathway | Breadth
- Specialization: Foundations of Probability and Statistics
- Instructor:Dr.Jem Corcoran,Associate Professor in Applied Mathematics
- Prior knowledge needed:
- Programming languages: Intro to R programming
- Math: Calculus 1 and 2
- Technical requirements:
Learning Outcomes
- Identify characteristics of “good” estimators and be able to compare competing estimators.
- Construct sound estimators using the techniques of maximum likelihood and method of moments estimation.
- Construct and interpret confidence intervals for one and two population means, one and two population proportions, and a population variance.
Course Grading Policy
| Assignment | Percentage of Grade |
|---|---|
| Week 1 | |
| Quiz: Recognizing Discrete Distributions | 4% |
| Quiz: Calculations with Continuous Distributions | 4% |
| Quiz: Probability, Expectation, and Variance | 4% |
| Quiz: Method of Moments Estimation | 4% |
| Programming Assignment: Point Estimation | 6.5% |
| Week 2 | |
| Quiz: Finding MLEs | 4% |
| Quiz: Invariance, Mean-Squared Error, and Efficiency | 4% |
| Programming Assignment: Maximum Likelihood Estimation | 6.5% |
| Week 3 | |
| Quiz: The Cramer-Rao Lower Bound | 4% |
| Quiz: Further Computations with MLEs | 4% |
| Programming Assignment: Large Sample Properties of MLEs | 6.5% |
| Week 4 | |
| Quiz: Confidence Intervals Involving the Normal Distribution | 4% |
| Quiz: Confidence Intervals for Differences Between Means | 4% |
| Programming Assignment: Normal Distribution Confidence Intervals | 6.5% |
| Week 5 | |
| Quiz: Confidence Intervals for Proportions and Variances | 4% |
| Quiz: Build Your Own Confidence Intervals | 4% |
| Programming Assignment: Confidence Intervals Unleashed | 6% |
| Final Exam | |
| DTSA 5002 Statistical Inference for Estimation in Data Science Final Exam | 20% |
Course Content
Duration: 7hours
In this module you will learn how to estimate parameters from a large population based only on information from a small sample. You will learn about desirable properties that can be used to help you to differentiate between good and bad estimators. We will review the concepts of expectation, variance, and covariance, and you will be introduced to a formal, yet intuitive, method of estimation known as the "method of moments".
Duration: 5 hours
In this module we will learn what a likelihood function is and the concept of maximum likelihood estimation. We will construct maximum likelihood estimators (MLEs) for one and two parameter examples and functions of parameters using the invariance property of MLEs.
Duration: 5 hours
In this module we will explore large sample properties of maximum likelihood estimators including asymptotic unbiasedness and asymptotic normality. We will learn how to compute the “Cramér–Rao lower bound” which gives us a benchmark for the smallest possible variance for an unbiased estimator.
Duration: 7 hours
In this module we learn about the theory of “interval estimation”. We will learn the definition and correct interpretation of a confidence interval and how to construct one for the mean of an unseen population based on both large and small samples. We will look at the cases where the variance is known and unknown.
Duration: 4 hours
In this module, we will generalize the lessons of Module 4 so that we can develop confidence intervals for other quantities of interest beyond the distribution mean and for other distributions entirely. This module covers two sample confidence intervals in more depth, and confidence intervals for population variances and proportions. We will also learn how to develop confidence intervals for parameters of interest in non-normal distributions.
Duration: 2 hour
Final Exam Format: Proctored Exam
You will complete a proctored exam worth 20% of your grade made up of multiple choice and free response questions. You must attempt the final in order to earn a grade in the course.If you've upgraded to the for-credit version of this course, please make sure you review the additional for-credit materials in the Introductory module and anywhere else they may be found.
Notes
- Cross-listed Courses: Coursesthat are offered under two or more programs. Considered equivalent when evaluating progress toward degree requirements. You may not earn credit for more than one version of a cross-listed course.
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