Bayesian Statistics: From Concept to Data Analysis

Go to Course: https://www.coursera.org/learn/bayesian-statistics

Introduction

### Course Review: Bayesian Statistics: From Concept to Data Analysis If you're eager to delve into the world of Bayesian statistics, the Coursera course "Bayesian Statistics: From Concept to Data Analysis" is an excellent choice. This course, designed to both educate and transform your approach to data analysis, offers a comprehensive and accessible introduction to Bayesian methods, making it a great fit for beginners and seasoned statisticians alike. #### Overview of the Course The course provides learners with a solid foundation in Bayesian statistics, emphasizing its contemporary relevance in data analysis. The course begins with the philosophical underpinnings of the Bayesian approach, focusing on how it stands in contrast with the more traditional Frequentist statistics. One of the primary benefits of Bayesian statistics is its ability to handle uncertainty in a more nuanced way, providing clearer insights through the lens of probability. #### Structure and Syllabus Breakdown The curriculum is structured into four key modules, each focusing on critical aspects of Bayesian statistics: 1. **Probability and Bayes' Theorem**: - The course opens with a foundational review of probability concepts and Bayes' theorem. This section is pivotal, as it introduces different paradigms of probability and details why this framework is crucial for understanding uncertainty. It discusses the rules of conditional probability and introduces common probability distributions essential for both discrete and continuous contexts. 2. **Statistical Inference**: - The course then transitions to statistical inference. Here, students will explore both Frequentist and Bayesian perspectives. This module is particularly interesting for those who wish to appreciate the contrasts between the two approaches, with maximum likelihood estimation and confidence intervals covered from the Frequentist angle before diving deep into Bayesian inference using binomial likelihoods and prior probabilities. 3. **Priors and Models for Discrete Data**: - This section focuses on selecting prior distributions and formulating models for discrete data. Lessons are thorough, offering insights into Bernoulli data analysis and the efficient use of conjugate priors. The detailed guidance on selecting prior hyperparameters is invaluable for learners aiming to apply Bayesian methods effectively. 4. **Models for Continuous Data**: - The final module tackles Bayesian analysis for continuous data, emphasizing essential statistical techniques like Bayesian linear regression. This part of the course highlights how to utilize non-informative priors, equipping students with tools comparable to classical regression while still embracing the Bayesian framework. #### Key Benefits of the Course - **Comprehensive Learning**: The course methodically leads learners from foundational concepts to more complex analyses, which builds confidence as you progress. - **Real-World Application**: With practical examples and discussions, the course prepares students to effectively apply Bayesian statistics in various fields. - **Comparison of Approaches**: Understanding the differences and overlaps between Bayesian and Frequentist statistics deepens your statistical thinking and enhances analytical skills. - **Supportive Learning Environment**: Coursera fosters a community learning experience, enabling discussions with peers and access to resources, which enhances understanding. #### Recommendation I highly recommend "Bayesian Statistics: From Concept to Data Analysis" to anyone looking to enrich their statistical toolkit. Whether you're a student, a professional transitioning into data analysis, or someone keen to grasp the intricacies of Bayesian methods, this course provides a well-rounded, practical approach that meets diverse learning needs. With its combination of theory, practical analyses, and theoretical comparisons, learners will walk away with actionable insights, making them not just consumers of data but informed analysts capable of making robust predictions and decisions. Enroll today and embark on your journey into the expansive realm of Bayesian statistics!

Syllabus

Probability and Bayes' Theorem

In this module, we review the basics of probability and Bayes’ theorem. In Lesson 1, we introduce the different paradigms or definitions of probability and discuss why probability provides a coherent framework for dealing with uncertainty. In Lesson 2, we review the rules of conditional probability and introduce Bayes’ theorem. Lesson 3 reviews common probability distributions for discrete and continuous random variables.

This module introduces concepts of statistical inference from both frequentist and Bayesian perspectives. Lesson 4 takes the frequentist view, demonstrating maximum likelihood estimation and confidence intervals for binomial data. Lesson 5 introduces the fundamentals of Bayesian inference. Beginning with a binomial likelihood and prior probabilities for simple hypotheses, you will learn how to use Bayes’ theorem to update the prior with data to obtain posterior probabilities. This framework is extended with the continuous version of Bayes theorem to estimate continuous model parameters, and calculate posterior probabilities and credible intervals.

In this module, you will learn methods for selecting prior distributions and building models for discrete data. Lesson 6 introduces prior selection and predictive distributions as a means of evaluating priors. Lesson 7 demonstrates Bayesian analysis of Bernoulli data and introduces the computationally convenient concept of conjugate priors. Lesson 8 builds a conjugate model for Poisson data and discusses strategies for selection of prior hyperparameters.

This module covers conjugate and objective Bayesian analysis for continuous data. Lesson 9 presents the conjugate model for exponentially distributed data. Lesson 10 discusses models for normally distributed data, which play a central role in statistics. In Lesson 11, we return to prior selection and discuss ‘objective’ or ‘non-informative’ priors. Lesson 12 presents Bayesian linear regression with non-informative priors, which yield results comparable to those of classical regression.