Introduction to Modern Goodness of Fit Methods

Assessment of Goodness of Fit Methods in Determining the Best Regional Probability Distribution of Rainfall Data

One of the most important problems in time series analysis of stream flow and rainfall data in an area is selecting the best probability distribution. Since the rainfall stations are associated and correlated with each other, so statistical analysis of the station data seamlessly are very important. Therefore, the first step in data analysis, is selecting the prevailing probability distribution...

Goodness of Fit

Nonparametric Goodness-of-fit

This paper develops an approach to testing the adequacy of both classical and Bayesian models given sample data. An important feature of the approach is that we are able to test the practical scientiic hypothesis of whether the true underlying model is close to some hypothesized model. The notion of closeness is based on measurement precision and requires the introduction of a metric for which ...

Goodness-of-fit methods for generalized linear mixed models.

We develop graphical and numerical methods for checking the adequacy of generalized linear mixed models (GLMMs). These methods are based on the cumulative sums of residuals over covariates or predicted values of the response variable. Under the assumed model, the asymptotic distributions of these stochastic processes can be approximated by certain zero-mean Gaussian processes, whose realization...

A brief introduction to modern amplitude methods

I provide a basic introduction to modern helicity amplitude methods, including color organization, the spinor helicity formalism, and factorization properties. I also describe the BCFW (on-shell) recursion relation at tree level, and explain how similar ideas — unitarity and on-shell methods — work at the loop level. These notes are based on lectures delivered at the 2012 CERN Summer School and...