PhD

My PhD Project

Regression modelling using priors with Fisher information covariance kernels (I-priors).

Regression modelling using priors depending on Fisher information covariance kernels (I-priors)

Regression analysis is undoubtedly an important tool to understand the relationship between one or more explanatory and independent variables of interest. In this thesis, we explore a novel methodology for fitting a wide range of parametric and …

R/iprobit

Binary and multinomial probit regression using I-priors in `R`.

Binary and Multinomial Regression using Fisher Information Covariance Kernels (I-priors)

In a regression setting, we define an I-prior as a Gaussian process prior on the regression function with covariance kernel equal to its Fisher information. We present some methodology and computational work on estimating regression functions by …

Binary probit regression with I-priors

An extension of the I-prior methodology to binary response data is explored. Starting from a latent variable approach, it is assumed that there exists continuous, auxiliary random variables which decide the outcome of the binary responses. Fitting a …

R/ipriorBVS

Bayesian Variable Selection for Linear Models using I-priors in `R`.

R/iprior

An `R` package for I-prior regression.

Two-stage Bayesian variable selection for linear models using I-priors

In a previous work, I showed that the use of I-priors in various linear models can be considered as a solution to the over-fitting problem. In that work, estimation was still done using maximum likelihood, so in a sense it was a kind of …

Regression Modelling using I-Priors

The I-prior methodology is a new modelling technique which aims to improve on maximum likelihood estimation of linear models when the dimensionality is large relative to the sample size. By putting a prior which is informed by the dataset (as opposed …