Free online courseBayesian statistics: a comprehensive course
Duration of the online course: 5 hours and 3 minutes
New course
Explore Bayesian statistics with Ox educ's online course, covering essentials from marginal probabilities to practical inference examples in various contexts.
In this free course, learn about
- Foundations of Probability and Bayes' Rule
- Bayesian Inference Basics and Exchangeability
- Conjugate Priors and Beta–Binomial Models
- Bayesian Inference for Disease Prevalence and Predictive Distributions
- Normal–Normal Conjugate Models and Predictive Analysis
- Poisson–Gamma Models and Count Data
Course Description
Embark on a journey into Bayesian statistics with this comprehensive online course offered by Ox educ, ideal for those looking to deepen their understanding of statistical methodologies. Delve into various aspects of marginal and conditional probability for continuous variables.
The course introduces Bayes' rule, offering both a derivation and intuitive explanation. Explore its application in statistical inference, from understanding likelihoods, priors, and denominators to real-world examples like posterior distribution.
Grasp the concept of exchangeability and its significance to independent identically distributed (iid) variables. Learn about the intricacies of Bayes' rule's denominator for discrete and continuous variables, and why likelihood isn't a probability.
Discover sequential Bayes and data order invariance, and familiarize yourself with conjugate priors, Bernoulli, Binomial, and Beta distributions. Witness Bayesian inference in action with a thorough examination of disease prevalence cases.
Gain insights into predictive distributions, examine normal priors, likelihoods, and their conjugations, including examples with known variance and population mean test scores. Explore probability distributions like Poisson and Gamma, and see real-world examples in crime count modeling.
The course provides a full spectrum of Bayesian inference concepts and applications, laying the groundwork for practical understanding and application in various fields. Ideal for students and professionals in basic studies wanting to enhance their statistics knowledge.
Course content
- Video class: 1 - Marginal probability for continuous variables 06m
- Exercise: What is the process to find the marginal probability of a continuous random variable?
- Video class: 2 Conditional probability continuous rvs 06m
- Exercise: What is the probability of height ≤ 1.5m given weight ≤ 50kg?
- Video class: A derivation of Bayes' rule 02m
- Exercise: What is Bayes' Rule derived from the given probabilities?
- Video class: 4 - Bayes' rule - an intuitive explanation 06m
- Exercise: What does Bayes' Rule Help Determine?
- Video class: 5 - Bayes' rule in statistics 08m
- Exercise: What is the ultimate goal of Bayesian statistics?
- Video class: 6 - Bayes' rule in inference - likelihood 07m
- Exercise: What is the probability that all three individuals are uninfected given theta?
- Video class: 7 Bayes' rule in inference the prior and denominator 06m
- Exercise: What is the likelihood probability for theta equals 0?
- Video class: 8 - Bayes' rule in inference - example: the posterior distribution 03m
- Exercise: What is the posterior probability that Theta equals zero?
- Video class: 9 - Bayes' rule in inference - example: forgetting the denominator 04m
- Exercise: Why can the denominator be ignored in Bayesian computations?
- Video class: 10 - Bayes' rule in inference - example: graphical intuition 05m
- Exercise: What is the probability that theta equals 0 given the data and model choice?
- Video class: 11 The definition of exchangeability 04m
- Exercise: What defines exchangeability in a sequence of random variables?
- Video class: 12 exchangeability and iid 07m
- Exercise: What does exchangeability imply about random variables?
- Video class: 13 exchangeability what is its significance? 06m
- Exercise: Why is exchangeability important in Bayesian statistics?
- Video class: 14 - Bayes' rule denominator: discrete and continuous 04m
- Exercise: How is the denominator in the probability calculation determined in the context of Bayesian inference?
- Video class: 15 Bayes' rule: why likelihood is not a probability 04m
- Exercise: Why shouldn't likelihood be considered identical to probability?
- Video class: 15a - Maximum likelihood estimator - short introduction 07m
- Exercise: What is the primary goal of Maximum Likelihood Estimation?
- Video class: 16 Sequential Bayes: Data order invariance 04m
- Exercise: What does Bayes' Rule imply about the order of independent data points?
- Video class: 17 - Conjugate priors - an introduction 05m
- Exercise: What is a key advantage of using a conjugate prior in Bayesian inference?
- Video class: 18 - Bernoulli and Binomial distributions - an introduction 08m
- Exercise: What is the purpose of the Bernoulli and binomial distributions?
- Video class: 19 - Beta distribution - an introduction 10m
- Exercise: What is a key characteristic of the Beta distribution?
- Video class: 20 - Beta conjugate prior to Binomial and Bernoulli likelihoods 05m
- Exercise: What are the parameters of a beta distribution?
- Video class: 21 - Beta conjugate to Binomial and Bernoulli likelihoods - full proof 05m
- Exercise: What is the role of the gamma function in the proof of conjugate distributions?
- Video class: 22 - Beta conjugate to Binomial and Bernoulli likelihoods - full proof 2 04m
- Exercise: What is the conjugate prior for a Binomial distribution?
- Video class: 23 - Beta conjugate to Binomial and Bernoulli likelihoods - full proof 3 02m
- Exercise: What is demonstrated in the proof relating to the beta distribution and binomial likelihood?
- Video class: 24 - Bayesian inference in practice - posterior distribution: example Disease prevalence 07m
- Exercise: What is a key advantage of having more data in a Bayesian inference model?
- Video class: 25 - Bayesian inference in practice - Disease prevalence 06m
- Exercise: How does an increase in parameters 'a' and 'b' affect the posterior mean in Bayesian inference?
- Video class: 26 - Prior and posterior predictive distributions - an introduction 05m
- Exercise: What is the difference between prior and posterior predictive distributions?
- Video class: 27 - Prior predictive distribution: example Disease - 1 07m
- Exercise: How does changing parameters affect the prior predictive distribution in the disease model?
- Video class: 27 - Prior predictive distribution: example Disease - 2 06m
- Exercise: What happens to the prior predictive distribution when a = b = 1?
- Video class: 29 - Posterior predictive distribution: example Disease 09m
- Exercise: How does the posterior predictive probability change?
- Video class: 30 - Normal prior and likelihood - known variance 06m
- Exercise: What is the mean of the professor's prior belief distribution?
- Video class: 31 - Normal prior conjugate to normal likelihood - proof 1 05m
- Exercise: What makes a normal prior density conjugate to a normal likelihood?
- Video class: 32 - Normal prior conjugate to normal likelihood - proof 2 04m
- Exercise: What is the result when a normal prior is conjugate to a normal likelihood when the variance is known?
- Video class: 33 - Normal prior conjugate to normal likelihood - intuition 07m
- Exercise: What concept is illustrated by the effect of decreasing sigma θ²?
- Video class: 34 - Normal prior and likelihood - prior predictive distribution 06m
- Exercise: What is the mean of the prior predictive distribution for the test score?
- Video class: 35 - Normal prior and likelihood - posterior predictive distribution 05m
- Exercise: What is the posterior predictive distribution with a normal prior and likelihood?
- Video class: 36 - Population mean test score - normal prior and likelihood 08m
- Exercise: What happens to the posterior distribution when more data is collected?
- Video class: 37 - The Poisson distribution - an introduction - 1 09m
- Exercise: What is necessary for events to be modeled by Poisson distribution?
- Video class: 38 - The Poisson distribution - an introduction - 2 10m
- Exercise: What is the mean of a Poisson distribution?
- Video class: 39 - The gamma distribution - an introduction 17m
- Exercise: What is the mean of a Gamma distribution with parameters α and β?
- Video class: 40 - Poisson model: crime count example introduction 05m
- Exercise: What is a key assumption for using the Poisson model in the described scenario?
- Video class: 41 - Proof: Gamma prior is conjugate to Poisson likelihood 08m
- Exercise: When is a Gamma prior conjugate to a Poisson likelihood?
- Video class: 42 - Prior predictive distribution for Gamma prior to Poisson likelihood 07m
- Exercise: What is the distribution derived from a gamma prior and Poisson likelihood?
- Video class: 43 - Prior predictive distribution (a negative binomial) for gamma prior to poisson likelihood 2 07m
- Exercise: What is the result of using a gamma prior with a Poisson likelihood in deriving the prior predictive distribution?
- Video class: 44 - Posterior predictive distribution a negative binomial for gamma prior to poisson likelihood 11m
- Exercise: What is the nature of the posterior predictive distribution given a Poisson likelihood and gamma prior?
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Learn aboutBayesian Statistics
Explore Bayesian Statistics with our free online course, designed to introduce you to fundamental concepts and practical applications. Enroll today and enhance your statistical skills!
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