H-Methods in Applied Sciences
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Superior methods for multivariate data analysis
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 H-methods 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 H-methods 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.
H-methods have been applied to wide range of fields within applied sciences. In each case the H-methods provide with superior solutions compared to the traditional ones.
|A review of ideas and philosophy of the H-methods|
|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|