Statistical Inference for Estimation in Data Science

University of Colorado Boulder via Coursera

Go to Course: https://www.coursera.org/learn/statistical-inference-for-estimation-in-data-science

Introduction

## Course Review: Statistical Inference for Estimation in Data Science ### Overview In an era where data drives decision-making across sectors, understanding statistical inference is essential for data scientists. Coursera’s course "Statistical Inference for Estimation in Data Science," offered as part of the University of Colorado Boulder’s Master of Science in Data Science (MS-DS), is a comprehensive introduction to the principles and techniques necessary for making informed estimations based on data. ### Content and Structure The course is designed with an emphasis on practical application and theoretical understanding, making it suitable for both budding data scientists and experienced practitioners seeking to sharpen their skills. **Module Highlights:** 1. **Start Here!** The introductory module sets the stage by providing logistical information essential for navigating the course smoothly. It encourages learners to engage openly and emphasizes the course's participatory nature. 2. **Point Estimation** This module dives right into defining what it means to estimate parameters from sample data. It highlights the desirable properties of estimators, teaching students to differentiate between good and bad estimates. Core statistical concepts like expectation, variance, and covariance are revisited, along with the intuitive "method of moments" for estimation. 3. **Maximum Likelihood Estimation (MLE)** Students explore the concept of likelihood functions and learn to compute MLEs for various parameters. This module's practical approach—through one and two-parameter examples—enables students to grasp how powerful MLEs can be in real-world data scenarios. 4. **Large Sample Properties of MLEs** This module delves into asymptotic properties, such as unbiasedness and normality of MLEs, providing benchmarks like the Cramér–Rao lower bound—the cornerstone for evaluating estimator efficiency. 5. **Confidence Intervals Involving the Normal Distribution** Here, students learn how to construct and interpret confidence intervals—an essential tool for making informed decisions. The module covers scenarios for both large and small samples, with cases of known and unknown variance. 6. **Beyond Normality: Confidence Intervals Unleashed!** The final module broadens the scope, teaching how to develop confidence intervals for various statistics beyond just means. It covers two-sample intervals and delves into non-normal distributions, equipping students with the versatility to tackle different statistical scenarios. ### Learning Experience The course is well-structured and interactive, utilizing a mixture of instructional videos, quizzes, and hands-on programming assignments using statistical software, which encourages active engagement. The comprehensive nature of the syllabus ensures that students not only acquire theoretical knowledge but also apply concepts through real-life data challenges. Membership in the MS-DS program also provides the added benefit of access to a network of peers and professionals, enhancing the learning experience through community engagement. ### Recommendation For anyone pursuing a career in data science or related fields, "Statistical Inference for Estimation in Data Science" is an invaluable addition to your learning portfolio. The course excels in demystifying complex statistical concepts and provides the tools necessary for effective data analysis. The strong foundation built in statistical inference will be beneficial whether you are involved in policy formation, business analytics, or machine learning. I highly recommend this course as it not only lays the groundwork for advanced statistical learning but also enhances critical thinking skills essential for a successful career as a data scientist. ### Conclusion In summary, "Statistical Inference for Estimation in Data Science" on Coursera is a must-take course that fulfills both academic credit requirements and practical learning ambitions. It empowers students with crucial statistical tools that support data-driven decision-making. Enroll today to boost your statistical acumen and elevate your data science capabilities!

Syllabus

Start Here!

Welcome to the course! This module contains logistical information to get you started!

Point Estimation

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".

Maximum Likelihood Estimation

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.

Large Sample Properties of Maximum Likelihood Estimators

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.

Confidence Intervals Involving the Normal Distribution

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.

Beyond Normality: Confidence Intervals Unleashed!

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.