Contents
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 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.
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 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
Which is the Bayes rule for posterior model?
The posterior model probability is a sigmoidal function of the log Bayes factor p(m = ijy) = ˙(logBij) From Raftery (1995). Bayesian Model Comparison Will Penny Bayes rule for models
How to use Bayesian inference in cognitive analysis?
In Section 6.3 of Chapter 6, we provided a Bayesian inference analysis for kid’s cognitive scores using multiple linear regression. We found that several credible intervals of the coefficients contain zero, suggesting that we could potentially simplify the model.