In proto4426/PissoortThesis: Thesis in Extreme Value Theory

knitr::opts_chunk$set(echo = TRUE)

R code

The application is hosted at the following URL (to update !).
The global repository for the thesis which contains the R package can be found here
The specific code for this app can be found in this folder.

The following package are needed to run the application :

install.packages(c("shiny", "htmltools", "shinythemes","tidyverse","DT", "foreach", "doParallel", "doSNOW", "pander", "GEVcdn", "gridExtra","grid","mvtnorm","plotly","HDInterval","ggjoy","scales","heatmaply"))
## And of course the package for this thesis ...
devtools::install_github("proto4426/PissoortThesis", build_vignettes=T)

Tools developped for the App'

You can ook at R console to follow bootstrap parallel computation's progress.
The computations are made in parralel using all your cores-1 by default.
But, computations with much bootstrap resamples could still take time.
For the bootstrap resampling methods, the values are 2 times the displayed values : e.g. the maximum value is actually 1000.

Model and hyperparameters

The Hyperbolic tangent activation function, i.e. $$tanh(x)= \frac{\exp(x)-\exp(x)}{\exp(x) + \exp(x)}$$ is not implemented in GEVcdn and hence, we have problems to locally implement this function in the GEVcdn framework.

Prior distributions

By default, we do not regularize the weights, i.e. we do not control for the overfitting in this way as we put a very large variance prior (near-flat) on the prior distribution of these weigths. It is interesting to see how controlling this value can indeed regularize ("smooth") the model. Try for example a nonstationary model with a nonlinear activation function (e.g. logistic sigmoid) and with a large number of hidden layers (e.g. 5). Then, you will see the effect of decreasing to very small values the variance of this prior.
Two other prior values are needed, but here it is to control the shape parameter. The values set by default are the values given by the authors Martins and Stedinger [2000] of the Generalized Maximum Likelihood method.