Contents
Is lasso Bayesian?
The Lasso estimate for linear regression parameters can be interpreted as a Bayesian posterior mode estimate when the regression parameters have independent Laplace (i.e., double-exponential) priors.
What is BF inclusion?
The inclusion Bayes factor “BFInclusion” is the change from prior to posterior inclusion odds. The remaining columns of the effects output are based on including and excluding specific effects, in a way that is similar to backward and forward regression.
How is a Bayesian model compared to a Bayes model?
Bayesian Model Comparison Will Penny Bayes rule for models Bayes factors Nonlinear Models Variational Laplace Free Energy Complexity Decompositions AIC and BIC Linear Models fMRI example DCM for fMRI Priors Decomposition Group Inference Fixed Effects Random Effects Gibbs Sampling References Likelihood
How to use the Penny Bayes model comparison?
This is implemented using Bayes rule p(mjy) = p(yj m) p(y) where p(yjm) is referred to as the evidence for model m and the denominator is given by p(y) = X m0 p(yjm0)p(m0) Bayesian Model Comparison Will Penny Bayes rule for models Bayes factors Nonlinear Models Variational Laplace Free Energy Complexity Decompositions AIC and BIC Linear Models
The posterior model probability is a sigmoidal function of the log Bayes factor p(m = ijy) = ˙(logBij) Bayesian Model Comparison Will Penny Bayes rule for models Bayes factors Nonlinear Models Variational Laplace Free Energy Complexity Decompositions AIC and BIC Linear Models fMRI example DCM for fMRI Priors Decomposition Group Inference
How to calculate Bayesian estimation of nonlinear models?
We consider the same frameworks as in lecture 4, ie Bayesian estimation of nonlinear models of the form y = g(w)+e where g(w) is some nonlinear function, and e is zero mean additive Gaussian noise with covariance Cy.