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Statistical Inference for Estimation in Data Science

Jem Corcoran

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.

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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".

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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

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Reviews summary

Core statistical inference for data science

According to students, this course offers a rigorous and foundational understanding of statistical inference, crucial for data science. Learners appreciate the clear explanations of complex topics like maximum likelihood estimation and confidence intervals. While providing a strong theoretical grounding, some mention the course can be mathematically intensive, requiring a solid background in probability and calculus. The lectures are generally well-received for their depth, though prospective students should be prepared for a conceptual challenge that may require additional study.

Strong theory, less emphasis on direct coding application.

"While the theoretical aspects are strong, I would have liked more hands-on coding exercises using Python or R."

"It's very theory-heavy, which is good for a deep dive, but don't expect extensive practical implementations within the course itself."

"I found myself supplementing the course with my own coding projects to bridge the gap between theory and direct application."

Provides essential skills for a data science career.

"This course provided a critical understanding of estimation methods directly applicable to real-world data science problems."

"I can now better interpret and choose appropriate estimators for various datasets in my projects."

"Understanding these inferential techniques is fundamental for any serious data scientist, and this course delivers on that."

Instructor effectively clarifies complex statistical ideas.

"The instructor's ability to break down complex statistical concepts into digestible lectures was a highlight."

"I appreciated how clearly the likelihood function and its properties were explained, making them less intimidating."

"Even difficult topics like asymptotic normality were presented in a way that made them understandable."

Excellent for building a strong theoretical base.

"I found the course invaluable for solidifying my understanding of point estimation and confidence intervals."

"It truly built a robust theoretical foundation for statistical inference, which I needed for my data science career."

"This course gave me the essential concepts and framework for estimation that I can apply later in my work."

Course can be challenging, requiring strong math skills.

"The mathematical derivations, especially for MLEs and Cramér–Rao bounds, were quite demanding."

"I felt a strong background in calculus and linear algebra was essential to keep up with the pace."

"While the content is deep, it definitely assumes a certain level of mathematical maturity from students."

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

Reading list

We've selected 13 books that we think will supplement your learning. Use these to develop background knowledge, enrich your coursework, and gain a deeper understanding of the topics covered in Statistical Inference for Estimation in Data Science.

Statistical Inference

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This widely used graduate-level textbook serves as an excellent resource for the core statistical inference material covered in this course.

Statistical Inference

Hardcover

$$$

Statistical Inference

Hardcover