Bayesian hierarchical modelling is a statistical model written in multiple levels (hierarchical form) that estimates the parameters of the posterior distribution using the Bayesian method. The sub-models combine to form the hierarchical model, and Bayes' theorem is used to integrate them with the observed data and account for all the uncertainty that is present. The result of this integration is the posterior distribution, also known as the updated probability estimate, as additional evidence on the prior distribution is acquired. Frequentist statistics may yield conclusions seemingly incompatible with those offered by Bayesian statistics due to the Bayesian treatment of the parameters as random variables and its use of subjective information in establishing assumptions on these parameters. As the approaches answer different questions the formal results aren't technically contradictory but the two approaches disagree over which answer is relevant to particular applications. Bayesians argue that relevant information regarding decision-making and updating beliefs cannot be ignored and that hierarchical modeling has the potential to overrule classical methods in applications where respondents give multiple observational data. Moreover, the model has proven to be robust, with the posterior distribution less sensitive to the more flexible hierarchical priors. Hierarchical modeling is used when information is available on several different levels of observational units. For example, in epidemiological modeling to describe infection trajectories for multiple countries, observational units are countries, and each country has its own temporal profile of daily infected cases. In decline curve analysis to describe oil or gas production decline curve for multiple wells, observational units are oil or gas wells in a reservoir region, and each well has each own temporal profile of oil or gas production rates (usually, barrels per month). Data structure for the hierarchical modeling retains nested data structure. The hierarchical form of analysis and organization helps in the understanding of multiparameter problems and also plays an important role in developing computational strategies. (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 13.7) Graphical model for Bayesian Naive Bayes
As an example, we write down the graphical model for Bayesian naïve Bayes.
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
(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
(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
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 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
Clusterfck A Practical Guide to Bayesian Hierarchical Modeling in PyMC3 || Hanna van der Vlis
At Apollo Agriculture, a Kenya based agro-tech startup, one of the challenging problems we face is to predict yields of Kenyan maize farmers. Like almost all data-sets, this data-set has a hierarchical structure: farmers within the same region aren’t independent. By ignoring this fact, a m
From playlist Machine Learning
(ML 8.3) Bayesian Naive Bayes (part 1)
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
Ruslan Salakhutdinov: "Advanced Hierarchical Models"
Graduate Summer School 2012: Deep Learning, Feature Learning "Advanced Hierarchical Models" Ruslan Salakhutdinov Institute for Pure and Applied Mathematics, UCLA July 24, 2012 For more information: https://www.ipam.ucla.edu/programs/summer-schools/graduate-summer-school-deep-learning-fe
From playlist GSS2012: Deep Learning, Feature Learning
Hierarchical modelling of weak lensing and photometric (...) - Heavens - Workshop 2 - CEB T3 2018
Heavens (Imperial College) / 22.10.2018 Hierarchical modelling of weak lensing and photometric redshifts ---------------------------------- Vous pouvez nous rejoindre sur les réseaux sociaux pour suivre nos actualités. Facebook : https://www.facebook.com/InstitutHenriPoincare/ Twitter
From playlist 2018 - T3 - Analytics, Inference, and Computation in Cosmology
A description of the syllabus that will be covered in this course on Bayesian 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 m
From playlist Bayesian statistics: a comprehensive course
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
Matthew Schofield - Genetic maps from genotype-by-sequencing data
Matthew Schofield (University of Otago) presents "Genetic maps from genotype-by-sequencing data", 5 June 2020.
From playlist Statistics Across Campuses
William Wen: "Bayesian Statistics and its Application to Integrative Statistical Genomics"
Computational Genomics Summer Institute 2016 "Bayesian Statistics and its Application to Integrative Statistical Genomics" Xiaoquan (William) Wen, University of Michigan Institute for Pure and Applied Mathematics, UCLA July 18, 2016 For more information: http://computationalgenomics.bio
From playlist Computational Genomics Summer Institute 2016
Daniel Yekutieli: Hierarchical Bayes Modeling for Large-Scale Inference
CIRM VIRTUAL EVENT Recorded during the meeting "Mathematical Methods of Modern Statistics 2" the June 03, 2020 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians
From playlist Virtual Conference
Poisson random fields for dynamic feature models: Valerio Perrone, Oxford-Warwick Stats Programme
This talk is based on the article: http://jmlr.org/papers/volume18/16-541/16-541.pdf In a feature allocation model, each data point depends on a collection of unobserved latent features. For example, we might classify a corpus of texts by describing each document via a set of topics; the
From playlist Turing Seminars
Sudipto Banerjee: High-dimensional Bayesian geostatistics
Abstract: With the growing capabilities of Geographic Information Systems (GIS) and user-friendly software, statisticians today routinely encounter geographically referenced data containing observations from a large number of spatial locations and time points. Over the last decade, hierarc
From playlist Probability and Statistics
(ML 8.4) Bayesian Naive Bayes (part 2)
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