In genome-enabled prediction, parametric, semi-parametric, and non-parametric regression models have been used. This study assessed the predictive ability of linear and non-linear models using dense molecular markers. The linear models were linear on marker effects and included the Bayesian LASSO, Bayesian ridge regression, Bayes A, and Bayes B. The non-linear models (this refers to non-lineari...

This material is compiled for the course Empirical Modelling. Sections marked with a star (∗) are not central in the courses. The main source of inspiration when writing this text has been Chapter 4 in the book ”System Identification” by Söderström and Stoica (Prentice Hall, 1989) which also may be consulted for a more thorough treatment of the material presented here. The book is available for...

We have previously described how to model shape variability by means of point distribution models (TDMs,) in which there is a linear relationship between a set of shape parameters and the positions of points on the shape. This linear formulation can fail for shapes which articulate or bend.' we show examples of such failure for both real and synthetic classes of shape. A new, more general formu...

For a certain class of martingales, the convergence to mixture normal distribution is established under the convergence in distribution for the conditional variance. This is less restrictive in comparison with the classical martingale limit theorem where one generally requires the convergence in probability. The extension removes a main barrier in the applications of the classical martingale li...

Linear regression is probably the most popular model for predicting a RV Y ∈ R based on multiple RVs X1, . . . , Xd ∈ R. It predicts a numeric variable using a linear combination of variables ∑ θiXi where the combination coefficients θi are determined by minimizing the sum of squared prediction error on the training set. We use below the convention that the first variable is always one i.e., X1...

Probablistic Model: We start with the assumption that prior to starting a sequence of experiments we have a family of random variables with means that vary linearly with respect to some deterministic independent variable. That is, there exist an intercept β0 and a slope β1 such that for each value of the independent variable x, we have a random variable Y with mean β0 + β1x. We are then given p...

Dalam kertas ini, prestasi ralat piawai bootstrap bagi anggaran berpemberat MM (WMM) dibandingkan dengan ralat piawai Monte Carlo dan ralat piawai Berasimptot. Sifat-sifat selang keyakinan bootstrap bagi anggaran berpemberat WMM seperti 'Percentile' (PB), 'Bias-corrected Percentile' (BCP), 'Bias and Accelerated' (BC.), 'Studentzed Percentile' (SPB) dan 'Symmetric' (SB) te1ah diperiksa dan diban...

We consider linear models where d potential causes X1, . . . , Xd are correlated with one target quantity Y and propose a method to infer whether the association is causal or whether it is an artifact caused by overfitting or hidden common causes. We employ the idea that in the former case the vector of regression coefficients has ‘generic’ orientation relative to the covariance matrix ΣXX of X...

Indian summer monsoon rainfall (ISMR) is an important metric to quantify the Asian monsoon system. Artificial Neural Networks, ANNs, are being increasingly used for nonlinear regression and classification problems in meteorology. The issues raised for this study can be summarized as the problem of simulation of the ISMR time series with the ANN model to get away with the need of external parame...

In this chapter recent research in the area of multi-objective optimisation of regression models is presented and combined. Evolutionary multi-objective optimisation techniques are described for training a population of regression models to optimise the recently defined Regression Error Characteristic Curves (REC). A method which meaningfully compares across regressors and against benchmark mod...