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Introduction to Bayesian Inference

Introduction to Bayesian Inference

Course Level: Foundation

The capturing and quantification of uncertainty is a very important aspect of model-fitting and parameter inference. Bayesian inference represents a fully-probabilistic approach to parameter inference, allowing a practitioner to quantify their uncertainties through probability densities. However, fitting models in a Bayesian framework can be an involved and complicated affair, often necessitating the use of Markov chain Monte Carlo (MCMC) algorithms and their programmatic implementation.

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Course Details

  • Course Outline
  • Learning Outcomes
  • Materials
  • Prior Knowledge

Course Outline

  • Bayesian inference: Motivation of the Bayesian philosophy and an introduction to Bayes’ Theorem.
  • Markov chain Monte Carlo (MCMC) methods: An overview of MCMC methods and the problems they seek to overcome.
  • Posterior predictive simulation: Capturing uncertainty about the predictions of a model.

Learning Outcomes

By the end of this course participants will…

  • Understand the merits of the Bayesian workflow and the importance of uncertainty quantification.
  • Have developed an intuitive understanding of prior beliefs, the likelihood function, and the posterior distribution.
  • Be able to articulate the difficulties of fitting models in a Bayesian framework.
  • Understand how MCMC algorithms work and how they can be used to alleviate difficulties in model-fitting.

Materials

  • Page 1 of example course material for Introduction to Bayesian Inference
  • Page 2 of example course material for Introduction to Bayesian Inference
  • Page 3 of example course material for Introduction to Bayesian Inference
  • Page 4 of example course material for Introduction to Bayesian Inference
  • Page 5 of example course material for Introduction to Bayesian Inference

Prior Knowledge

Prior to attending this course, participants should be familiar with basic concepts of probability and statistics, including common probability distributions and regression methods.

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