Statistical Inference for Estimation in Data Science from Coursera

This course introduces statistical inference, sampling distributions, and confidence intervals. Students will learn how to define and construct good estimators, method of moments estimation, maximum likelihood estimation, and methods of constructing confidence intervals that will extend to more general settings.

This course can be taken for academic credit as part of CU Boulder’s Master of Science in Data Science (MS-DS) degree offered on the Coursera platform. The MS-DS is an interdisciplinary degree that brings together faculty from CU Boulder’s departments of Applied Mathematics, Computer Science, Information Science, and others. With performance-based admissions and no application process, the MS-DS is ideal for individuals with a broad range of undergraduate education and/or professional experience in computer science, information science, mathematics, and statistics. Learn more about the MS-DS program at https://www.coursera.org/degrees/master-of-science-data-science-boulder.

Logo adapted from photo by Christopher Burns on Unsplash.

What's inside

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.

Good to know

Know what's good

, what to watch for

, and possible dealbreakers

Develops statistical inference, sampling distributions, and confidence intervals, skills core to careers in research and science

Led by Jem Corcoran, an instructor with a proven track record in data science

Leverages a multimodal format that includes videos, discussions, assignments, and interactive materials

Provides a solid foundation for beginners without extensive prior exposure to statistics

Forms part of CU Boulder's Master of Science in Data Science (MS-DS) degree, adding to its credibility

Requires no application process, making it accessible to a broader audience

Reviews summary

Challenging but rewarding statistical inference course

Learners say this advanced course on statistical inference provides an engaging and challenging learning experience. Students describe the lectures as informative and well-paced, but recommend setting aside extra time to understand the material and complete difficult assignments. The instructor is praised for their expertise and clear explanations. While some students experienced technical issues or found the course difficult at times, many agree that they gained valuable knowledge and would recommend the course to others.

Knowledgeable Instructor

"The instrustor, Dr. Jem, is really interesting. She made the hard part of the Statistics easy to understand!"

"Jem Corcoran thruly wants you learn and share her experience with you."

"The instructor does not dumb the math down, which I respect."

Fast-Paced Material

"The first module of this course seems like it is supposed to be review of the topics covered in the previous one. But actually we are asked to do things that are much more complicated than the previous course covered, and we go through the material much more quickly."

Difficult Quizzes

"The professor goes through interesting examples in the videos but sometimes they are not closely related to the questions that show up in the quiz afterwards."

"I struggled my way through the quizzes, but I don't feel I have a good grasp of the material."

Occasional Technical Difficulties

"Quite a few technical issues with labs and programming assignments which prevent you from progressing in the course."

"There are SO many errors within the videos, the slides, the homeworks."

Challenging Homework Assignments

"The level of the Homework Questions and Programming assignments were far to difficult compared to what was taught in class."

"I felt confident coming out of the previous course in this series, but don't feel it prepared me for this course."

Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in Statistical Inference for Estimation in Data Science with these activities:

Organize your course materials

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Maintain a well-organized system for your notes, assignments, and other course materials to enhance your ability to review and retain information.

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Create folders for different course modules and topics.
File your notes, assignments, and any other relevant materials in the appropriate folders.
Review your organized materials regularly to reinforce your learning.

Review calculus concepts

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Refresh your memory on calculus concepts such as derivatives, integrals, and limits to strengthen your foundation for the course.

Browse courses on Calculus

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Review your notes from a previous calculus course.
Work through practice problems from a textbook or online resource.
Take a practice quiz or mock exam to assess your understanding.

Explore Python libraries for statistical analysis

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Become familiar with Python libraries like NumPy, SciPy, and Matplotlib, which will be used extensively in the course.

Browse courses on Python

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Follow tutorials on installing and using these libraries.
Work through examples and experiment with the library functions.
Create small Python scripts to perform basic statistical operations.

Five other activities

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Develop a cheat sheet of statistical formulas

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Create a concise reference document with essential statistical formulas and concepts, which can aid in quick recall during the course.

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Identify the key statistical formulas covered in the course.
Write down each formula clearly, along with its purpose and any relevant assumptions.
Organize the cheat sheet logically for easy reference.

Participate in online discussion forums

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Engage with fellow students by asking questions, sharing insights, and discussing course concepts to reinforce your understanding.

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Join the course discussion forum or create a study group.
Post questions or comments on topics you're struggling with.
Respond to other students' questions and offer your own perspectives.

Build a repository of statistical resources

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Gather and organize helpful resources such as online tutorials, articles, and datasets to supplement your learning throughout the course.

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Search for and bookmark online resources that cover course-related topics.
Download and save relevant articles and research papers.
Create a system to categorize and easily access these resources.

Read 'Statistical Inference' by George Casella and Roger L. Berger

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Delve into an advanced textbook that provides a comprehensive overview of statistical inference, complementing the course content.

View Statistical Inference (Chapman & Hall/CRC Texts... on Amazon

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Read the assigned chapters and take notes.
Work through the practice exercises to test your understanding.
Discuss the book's concepts with classmates or the instructor.

Solve statistical problems on online platforms

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Enhance your problem-solving skills by practicing statistical problems on platforms like LeetCode or HackerRank.

Browse courses on Data Analysis

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Choose a platform and register for an account.
Select problems related to the course topics.
Work through the problems and debug your solutions.

Career center

Learners who complete Statistical Inference for Estimation in Data Science will develop knowledge and skills that may be useful to these careers:

Data Scientist

Data Scientists are expected to be familiar with probability theory and be able to perform statistical analyses. This Statistical Inference for Estimation in Data Science course provides a solid foundation in statistics with a focus on estimation theory and techniques that are essential for data scientists. The course covers topics such as point estimation, maximum likelihood estimation, and confidence intervals, which are fundamental concepts for understanding and working with data.

See salaries and explore the career path for Data Scientist

Statistician

Statisticians are heavily involved in the design and analysis of statistical studies. They use their knowledge of statistical methods to collect, analyze, interpret, and present data. This course provides a comprehensive overview of statistical inference, covering topics such as sampling distributions, confidence intervals, and hypothesis testing. The knowledge and skills gained from this course are directly applicable to the work of a statistician.

See salaries and explore the career path for Statistician

Quantitative Analyst

Quantitative Analysts (Quants) use mathematical and statistical models to analyze data and make predictions. They play a crucial role in the financial industry, helping companies make informed decisions about investments and risk management. This course provides a solid foundation in statistical inference, which is essential for building and evaluating quantitative models. The course covers topics such as maximum likelihood estimation, confidence intervals, and hypothesis testing, which are commonly used in quantitative analysis.

See salaries and explore the career path for Quantitative Analyst

Machine Learning Engineer

Machine Learning Engineers design, develop, and deploy machine learning models. They use statistical methods to train and evaluate models, and they need to have a strong understanding of probability theory and statistical inference. This Statistical Inference for Estimation in Data Science course provides a comprehensive overview of statistical inference, covering topics such as point estimation, maximum likelihood estimation, and confidence intervals. The knowledge and skills gained from this course are essential for building and evaluating machine learning models.

See salaries and explore the career path for Machine Learning Engineer

Data Analyst

Data Analysts collect, clean, and analyze data to extract insights and inform decision-making. They use statistical methods to identify trends, patterns, and relationships in data. This course provides a solid foundation in statistical inference, covering topics such as point estimation, maximum likelihood estimation, and confidence intervals. The knowledge and skills gained from this course are essential for data analysts to effectively analyze and interpret data.

See salaries and explore the career path for Data Analyst

Market Researcher

Market Researchers collect and analyze data to understand consumer behavior and market trends. They use statistical methods to design and conduct surveys, analyze data, and draw conclusions. This course provides a solid foundation in statistical inference, covering topics such as point estimation, maximum likelihood estimation, and confidence intervals. The knowledge and skills gained from this course are essential for market researchers to effectively design and conduct market research studies.

See salaries and explore the career path for Market Researcher

Actuary

Actuaries use mathematical and statistical models to assess risk and uncertainty. They work in various industries, including insurance, finance, and healthcare. This course provides a solid foundation in statistical inference, covering topics such as point estimation, maximum likelihood estimation, and confidence intervals. The knowledge and skills gained from this course are essential for actuaries to effectively assess and manage risk.

See salaries and explore the career path for Actuary

Epidemiologist

Epidemiologists investigate the causes and distribution of diseases and other health conditions in populations. They use statistical methods to design and conduct studies, analyze data, and draw conclusions. This course provides a solid foundation in statistical inference, covering topics such as point estimation, maximum likelihood estimation, and confidence intervals. The knowledge and skills gained from this course are essential for epidemiologists to effectively investigate and prevent diseases.

See salaries and explore the career path for Epidemiologist

Biostatistician

Biostatisticians apply statistical methods to solve problems in the field of biology. They work in various settings, including academia, industry, and government. This course provides a solid foundation in statistical inference, covering topics such as point estimation, maximum likelihood estimation, and confidence intervals. The knowledge and skills gained from this course are essential for biostatisticians to effectively design and analyze biological studies.

See salaries and explore the career path for Biostatistician

Survey Researcher

Survey Researchers design, conduct, and analyze surveys to collect data on various topics. They use statistical methods to select samples, design questionnaires, and analyze data. This course provides a solid foundation in statistical inference, covering topics such as point estimation, maximum likelihood estimation, and confidence intervals. The knowledge and skills gained from this course are essential for survey researchers to effectively design and conduct surveys.

See salaries and explore the career path for Survey Researcher

Quality Control Inspector

Quality Control Inspectors ensure that products and services meet quality standards. They use statistical methods to collect and analyze data, and they make recommendations for improvements. This course provides a solid foundation in statistical inference, covering topics such as point estimation, maximum likelihood estimation, and confidence intervals. The knowledge and skills gained from this course are essential for quality control inspectors to effectively monitor and improve quality.

See salaries and explore the career path for Quality Control Inspector

Business Analyst

Business Analysts use data to solve business problems and improve decision-making. They use statistical methods to analyze data, identify trends, and develop recommendations. This course provides a solid foundation in statistical inference, covering topics such as point estimation, maximum likelihood estimation, and confidence intervals. The knowledge and skills gained from this course are essential for business analysts to effectively analyze data and make informed recommendations.

See salaries and explore the career path for Business Analyst

Operations Research Analyst

Operations Research Analysts use mathematical and statistical models to improve the efficiency and effectiveness of organizations. They work in various industries, including manufacturing, transportation, and healthcare. This course provides a solid foundation in statistical inference, covering topics such as point estimation, maximum likelihood estimation, and confidence intervals. The knowledge and skills gained from this course are essential for operations research analysts to effectively develop and evaluate models.

See salaries and explore the career path for Operations Research Analyst

Risk Analyst

Risk Analysts identify, assess, and manage risks for organizations. They use statistical methods to analyze data, identify risks, and develop mitigation strategies. This course provides a solid foundation in statistical inference, covering topics such as point estimation, maximum likelihood estimation, and confidence intervals. The knowledge and skills gained from this course are essential for risk analysts to effectively assess and manage risks.

See salaries and explore the career path for Risk Analyst

Financial Analyst

Financial Analysts evaluate the financial performance of companies and make recommendations on investments. They use statistical methods to analyze financial data, identify trends, and develop investment strategies. This course provides a solid foundation in statistical inference, covering topics such as point estimation, maximum likelihood estimation, and confidence intervals. The knowledge and skills gained from this course are essential for financial analysts to effectively analyze financial data and make informed investment recommendations.

See salaries and explore the career path for Financial Analyst