Statistical methods | Bayesian statistics
Bayesian model reduction is a method for computing the evidence and posterior over the parameters of Bayesian models that differ in their priors. A full model is fitted to data using standard approaches. Hypotheses are then tested by defining one or more 'reduced' models with alternative (and usually more restrictive) priors, which usually – in the limit – switch off certain parameters. The evidence and parameters of the reduced models can then be computed from the evidence and estimated (posterior) parameters of the full model using Bayesian model reduction. If the priors and posteriors are normally distributed, then there is an analytic solution which can be computed rapidly. This has multiple scientific and engineering applications: these include scoring the evidence for large numbers of models very quickly and facilitating the estimation of hierarchical models (Parametric Empirical Bayes). (Wikipedia).
(ML 13.6) Graphical model for Bayesian linear regression
As an example, we write down the graphical model for Bayesian linear regression. We introduce the "plate notation", and the convention of shading random variables which are being conditioned on.
From playlist Machine Learning
(ML 12.4) Bayesian model selection
Approaches to model selection from a Bayesian perspective: Bayesian model averaging (BMA), "Type II MAP", and Type II Maximum Likelihood (a.k.a. ML-II, a.k.a. the evidence approximation, a.k.a. empirical Bayes).
From playlist Machine Learning
(ML 7.1) Bayesian inference - A simple example
Illustration of the main idea of Bayesian inference, in the simple case of a univariate Gaussian with a Gaussian prior on the mean (and known variances).
From playlist Machine Learning
Kerrie Mengersen: Bayesian Modelling
Abstract: This tutorial will be a beginner’s introduction to Bayesian statistical modelling and analysis. Simple models and computational tools will be described, followed by a discussion about implementing these approaches in practice. A range of case studies will be presented and possibl
From playlist Probability and Statistics
Bayesian Linear Regression : Data Science Concepts
The crazy link between Bayes Theorem, Linear Regression, LASSO, and Ridge! LASSO Video : https://www.youtube.com/watch?v=jbwSCwoT51M Ridge Video : https://www.youtube.com/watch?v=5asL5Eq2x0A Intro to Bayesian Stats Video : https://www.youtube.com/watch?v=-1dYY43DRMA My Patreon : https:
From playlist Bayesian Statistics
(ML 12.8) Other approaches to model selection
Brief mention of a few other approaches to model selection: AIC (Akaike Information Criterion), BIC (Bayesian Information Criterion), MDL (Minimum Description Length), and VC dimension.
From playlist Machine Learning
11f Machine Learning: Bayesian Regression Example
Review of a Bayesian linear regression model with posterior distributions for model parameters and the prediction model. Follow along with the demonstration workflow: https://github.com/GeostatsGuy/PythonNumericalDemos/blob/master/SubsurfaceDataAnalytics_BayesianRegression.ipynb
From playlist Machine Learning
11d Machine Learning: Bayesian Linear Regression
Lecture on Bayesian linear regression. By adopting the Bayesian approach (instead of the frequentist approach of ordinary least squares linear regression) we can account for prior information and directly model the distributions of the model parameters by updating with training data. Foll
From playlist Machine Learning
Bayesian Evidential Learning a protocol for uncertainty quantification in Earth systems
Webinar for CSDMS, Oct 14, 2019
From playlist Bayesian Evidential Learning
Short introduction to Bayesian Evidential Learning: a protocol for uncertainty quantification
From playlist Bayesian Evidential Learning
The virtue of Bayesian analysis in food risk assessment, Jukka Ranta - Bayes@Lund 2018
Find more info about Bayes@Lund, including slides, here: https://bayesat.github.io/lund2018/bayes_at_lund_2018.html
From playlist Bayes@Lund 2018
Locally Differentially Private Bayesian Inference
A Google TechTalk, presented by Antti Honkela, University of Helsinki / FCAI, at the 2021 Google Federated Learning and Analytics Workshop, Nov. 8-10, 2021. For more information about the workshop: https://events.withgoogle.com/2021-workshop-on-federated-learning-and-analytics/#content
From playlist 2021 Google Workshop on Federated Learning and Analytics
Quantifying Uncertainty in Subsurface Systems
Presentation based on the book published by Wiley Scheidt, C., Li, L & Caers, J, 2018. "Quantifying Uncertainty in Subsurface Systems.
From playlist Uncertainty Quantification
Noel Cressie: Inference for spatio-temporal changes of arctic sea ice
Abstract: Arctic sea-ice extent has been of considerable interest to scientists in recent years, mainly due to its decreasing trend over the past 20 years. In this talk, I propose a hierarchical spatio-temporal generalized linear model (GLM) for binary Arctic-sea-ice data, where data depen
From playlist Probability and Statistics
Catherine Calder - Spatial Confounding and Restricted Spatial Regression Methods
Professor Catherine Calder (University of Texas at Austin) presents “Spatial Confounding and Restricted Spatial Regression Methods”, 18 June 2021.
From playlist Statistics Across Campuses
Kerrie Mengersen - Bayesian modelling of complex trajectories: a case study of COVID-19
Professor Kerrie Mengersen (QUT) presents "Bayesian modelling of complex trajectories: a case study of COVID-19", 12 June 2020.
From playlist Statistics Across Campuses
AI Weekly Update - May 11th, 2020 (#20)
Thank you for watching! Please Subscribe! Machine Learning Street Talk: https://www.youtube.com/channel/UCMLtBahI5DMrt0NPvDSoIRQ Paper Links: Deep Learning with Graph-Structured Representations: https://dare.uva.nl/search?identifier=1b63b965-24c4-4bcd-aabb-b849056fa76d Yoshua Bengio ICLR
From playlist AI Research Weekly Updates
(ML 8.6) Bayesian Naive Bayes (part 4)
When all the features are categorical, a naïve Bayes classifier can be made fully Bayesian by putting Dirichlet priors on the parameters and (exactly) integrating them out.
From playlist Machine Learning
Bio As a practical statistician and machine learner, Franz is interested in creating a data analytics workflow which is empirically solid, quantitative, and useful in the real world, with a focus on predictive modelling. He is working on what he considers to be two of the most pressing c
From playlist Short Talks
An introduction to the use of Bayes' rule in statistics. If you are interested in seeing more of the material, arranged into a playlist, please visit: https://www.youtube.com/playlist?list=PLFDbGp5YzjqXQ4oE4w9GVWdiokWB9gEpm Unfortunately, Ox Educ is no more. Don't fret however as a whol
From playlist Bayesian statistics: a comprehensive course