L3: Hierarchical Modeling (State of Bayes Lecture Series)

State of Bayes is a series of webinars about advances in practical methods and modeling intuition. The major focus of the webinar series will be on understanding concepts of advanced statistical models and introducing prior knowledge into the loop. This free course will be interesting for Bayesian practitioners who want to deepen their understanding about Bayesian modeling. #HierarchicalModeling #ModelingStructure #NestedModels #MultiLevelModeling #HierarchicalApproach #SystemHierarchy #DesignFramework #StructuredModeling #HierarchyAnalysis a) Sign up on Meetup for the live events: https://www.meetup.com/pymc-labs-online-meetup/ b) State of Bayes Lecture Series playlist: https://www.youtube.com/playlist?list=PL1iMFW7frOOsh5KOcfvKWM12bjh8zs9BQ Slides: https://drive.google.com/file/d/1pMovrAEIT4_p2UxC8GjhGK50qTzG3Z86/view The full course will include: 1: Introduction 2: Bayesian Thinking 3: Hierarchical modelling 4: Interpretable Linear Regressions 5: Bayesian AB testing 6: Gaussian Processes 7: Gaussian Processes for Time Series ## About the speaker Maxim Kochurov Maxim is a core developer of PyMC, a probabilistic programming language. Since the foundation of PyMC Labs he helps to improve complex statistical models and create a reusable solution. Besides strong expertise in Bayesian modeling his background includes economics, software engineering, and large-scale computer vision. LinkedIn: https://www.linkedin.com/in/ferrine Twitter: https://twitter.com/ferrine96 GitHub: https://github.com/ferrine Website: https://ferrine.github.io ## Connecting with PyMC Labs - LinkedIn: https://www.linkedin.com/company/pymc... - Twitter: https://twitter.com/pymc_labs ## Lecture 3 timestamps 00:00 Introduction & welcome 00:17 Today's discussion 00:44 Agenda 01:38 Sampling from a distribution 03:28 Hamiltonian Monte-Carlo Intuition 04:41 HMC Distribution 05:27 HMC Differential equation 07:34 HMC Divergences 08:49 HMC Reading materials 09:27 Example 10:03 Toy example - Cobb-Douglas 11:22 Toy example - Carpet Knitters 12:57 The Simpson paradox 14:22 One group model 15:57 Starting with a simple model 16:39 Writing a model 18:18 Prior Beta 20:06 Visualize your prior 21:14 Setting a prior 21:52 The model so far 22:17 Prior for Epsilon 24:30 The model so far 24:49 Visual Model 25:30 Prior Predictive 28:12 Random prior 29:16 Analysing the prior predictive 30:10 Good prior predictive 31:05 What is good prior predictive? 32:20 Q/A Is prior predictive a probabilistic distribution? 35:55 HMC in action 37:24 Hierarchies 38:06 What is Hierarchy? 40:24 Treating Hierarchy 43:08 Bayesian Hierarchy 44:07 More on priors 47:41 Degeneracy 49:47 Why Funnel is created? 50:46 Inverted Funnel degeneracy 52:37 Setting a Hierarchical Prior 54:03 The Cobb-Douglas Case 57:35 Discussion Time 58:44 Q/A How would you set correlations between parameters? 1:00:18 Q/A What is the number of max hierarchies we can work with? 1:03:44 Q/A With the hierarchical model of similar countries where mainly scale is different, would you recommend using a pooled model? 1:06:24 Q/A Violation of assumptions of independence 1:08:50 Q/A Do you recommend some resources where we can get intuition on what probability distribution is more appropriate to use? 1:11:44 Q/A Is it possible to estimate parameters in group A and use them in group B, if we have high confidence in group A? #bayes #statistics #probabilistic