Fundamentals Of Bayesian Statistics
 

Learn Bayesian Inference, Probability Distributions, MCMC Methods, and Statistical Modeling Step by Step with Examples
What you'll learn
The fundamental differences between Bayesian and frequentist statistics and how they approach probability and inference
Key probability concepts, including marginal and conditional probability, and their role in Bayesian reasoning
Bayes' Theorem and its application in statistical inference
How to specify a prior and understand different types of priors, including Jeffrey's prior, reference priors, and Zellner's G-priors
The probability of data given model choice and how it impacts inference
An introduction to probability distributions commonly used in Bayesian data analysis, including Beta, Normal, Poisson, and Gamma distributions
Conjugate priors and their significance in simplifying Bayesian inference
Credible intervals and highest density posterior intervals (HDPI) as Bayesian alternatives to confidence intervals
Objective Bayesian data analysis and its role in making unbiased inferences
Forecasting in Bayesian systems using posterior predictive distributions
Markov Chain Monte Carlo (MCMC) methods, including grid approximations, Metropolis-Hastings sampling, and Gibbs sampling
Hypothesis testing using Bayesian methods, including classical test analogues and pure Bayesian approaches
Hierarchical models and hyperpriors, and how they allow for multi-level Bayesian inference
Bayesian linear regression and its application in predictive modeling
Requirements
No prior knowledge of Bayesian statistics is required, but familiarity with probability concepts will be helpful.
Description
Bayesian statistics is a powerful and intuitive framework for statistical inference, widely used in data science, machine learning, economics, medicine, and many other fields. This course provides a structured and in-depth introduction to Bayesian reasoning, covering fundamental concepts, key mathematical principles, and practical applications.This course provides a complete introduction to the field of Bayesian Statistics. It assumes very little prior knowledge and, in particular, aims to provide explanations of concepts with as little maths as possible. The lectures are designed to be clear, engaging, and practical. Each topic is broken down step by step, ensuring that learners understand both the intuition behind Bayesian methods and the mathematical principles that support them. The course includes real-world examples, case studies, and problem-solving exercises to reinforce key concepts.The course covers the following topics:The fundamental differences between Bayesian and frequentist statistics and how they approach probability and inferenceKey probability concepts, including marginal and conditional probability, and their role in Bayesian reasoningBayes' Theorem and its application in statistical inferenceHow to specify a prior and understand different types of priors, including Jeffrey's prior, reference priors, and Zellner's G-priorsThe probability of data given model choice and how it impacts inferenceAn introduction to probability distributions commonly used in Bayesian data analysis, including Beta, Normal, Poisson, and Gamma distributionsConjugate priors and their significance in simplifying Bayesian inferenceCredible intervals and highest density posterior intervals (HDPI) as Bayesian alternatives to confidence intervalsObjective Bayesian data analysis and its role in making unbiased inferencesForecasting in Bayesian systems using posterior predictive distributionsMarkov Chain Monte Carlo (MCMC) methods, including grid approximations, Metropolis-Hastings sampling, and Gibbs samplingHypothesis testing using Bayesian methods, including classical test analogues and pure Bayesian approachesHierarchical models and hyperpriors, and how they allow for multi-level Bayesian inferenceBayesian linear regression and its application in predictive modelingCourse Structure:The course begins with an exploration of Bayesian vs. frequentist statistics, followed by an in-depth discussion of probability distributions, Bayes' theorem, and inference techniques. It introduces priors and posterior distributions, explores conjugate priors and credible intervals, and covers forecasting, hypothesis testing, and Bayesian regression. The course also includes an introduction to MCMC methods, with a focus on Metropolis-Hastings and Gibbs sampling for practical Bayesian computation.Instructor Expertise and Teaching ApproachThis course is developed by an experienced instructor with a strong background in probability, statistics, and data analysis. The instructor emphasizes both theoretical understanding and practical application, making the course suitable for learners who want to develop a strong foundation in Bayesian statistics.A Balanced Mix of Theory and ApplicationWhile the course provides a rigorous introduction to Bayesian methods, it also focuses on their practical implementation. Topics such as posterior and predictive distributions, Bayesian hypothesis testing, and statistical modeling are covered in detail, ensuring learners gain both theoretical insights and hands-on experience with Bayesian approaches.This course is designed to be accessible to learners with a basic understanding of probability and statistics. Whether you are a student, researcher, or professional looking to expand your statistical knowledge, this course will equip you with the tools needed to confidently apply Bayesian reasoning to real-world problems.By the end of this course, you will have a solid understanding of Bayesian inference and the ability to apply Bayesian techniques to real-world problems.No prior knowledge of Bayesian statistics is required, but familiarity with probability concepts will be helpful.Enroll now to start your journey into Bayesian reasoning!
Who this course is for
Students of statistics, data science, and machine learning
Researchers seeking a strong theoretical foundation in Bayesian methods
Analysts and decision-makers interested in probabilistic reasoning and forecasting
Anyone with a basic understanding of probability and statistics who wants to learn Bayesian statistics step by step
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