Binary operations on commutative Jordan algebras are used to carry out the ANOVA of a two layer model. The treatments in the first layer nests those in the second layer, that being a sub-model for each treatment in the first layer. We present an application with data retried from agricultural experiments.
Given a base design with quantitative factors and a primary linear regression to each of the treatments, we may adjust secondary regressions of linear combinations of the adjusted coefficients on the primary regressions on the factor levels, thus obtaining a biregressional model. A biregressional design was established for a set of treatments, defined from quantitative factors and a linear regression in the same variables. Afterwards the action of the regression coefficients...
A nonstandard approach to change point estimation is presented in this paper. Three models with random coefficients and Bayesian approach are used for modelling the year average temperatures measured in Prague Klementinum. The posterior distribution of the change point and other parameters are estimated from the random samples generated by the combination of the Metropolis-Hastings algorithm and the Gibbs sampler.