Bayesian methods for parameter estimation in effective field theories

Bayesian Methods of Parameter Estimation

The frequentest approach is the classical approach to parameter estimation. It assumes that there is an unknown but objectively fixed parameter θ [3]. It chooses the value of θ which maximizes the likelihood of observed data [4], in other words, making the available data as likely as possible. A common example is the maximum likelihood estimator (MLE). The frequentest approach is statistically ...

Bayesian parameter estimation via variational methods

We consider a logistic regression model with a Gaussian prior distribution over the parameters. We show that an accurate variational transformation can be used to obtain a closed form approximation to the posterior distribution of the parameters thereby yielding an approximate posterior predictive model. This approach is readily extended to binary graphical model with complete observations. For...

Bayesian parameter estimation through variational methods

We consider a logistic regression model with a Gaussian prior distribution over the parameters. We show that accurate variational techniques can be used to obtain a closed form posterior distribution over the parameters given the data thereby yielding a posterior predictive model. The results are readily extended to binary belief networks. For belief networks we also derive closed form posterio...

Effective Field Theories for Inflation

Effective Field Theories

Three lectures in which I give an introduction to effective field theories in particle physics.