Agnar Höskuldsson 
HMethods in Applied Sciences 
New horizon in  
A personal website 
Superior methods for multivariate data analysis 
industrial mathematics  

A new framework for mathematical modelling within applied sciences is presented on this website. It is characteristic for data from ‘nature and industry’ that they have reduced rank for inference. It means that full rank solutions normally do not give satisfactory solutions. The basic idea of Hmethods is to build up the mathematical model in steps by using weighing schemes. Each weighing scheme produces a score and/or a loading vector that that are expected to perform a certain task. Optimisation procedures are used to obtain ‘the best’ solution at each step. At each step the optimisation is concerned with finding a balance between the estimation task and the prediction task. The name Hmethods has been chosen because of close analogy with the Heisenberg uncertainty inequality. A similar situation is present in modelling data. The mathematical modelling stops, when the prediction aspect of the model can not be improved. Hmethods have been applied to wide range of fields within applied sciences. In each case the Hmethods provide with superior solutions compared to the traditional ones. Examples of application areas: Advanced Linear Regression, nonlinear models, Advanced Path and Multiblock modelling, Advanced Chemometrics, Advanced Classification Procedures.

A review of ideas and philosophy of the Hmethods  
Graphic procedures for latent structures in multivariate models  
Maximum Likelihood methods have low prediction ability  
Presentation of results from methods in simple terms  
Important to test the solution of methods  
Confidence intervals of parameters based on observed data  
Basic issues in modelling data  