Statistický návrh experimentu pro regresní modely

Abstract

In this bachelor thesis, we study the design of an experiment for linear regression models using Bayesian methods. Our goal is to find an input regression vector such that the parameter estimation error is minimized. In Bayesian methods, we view the parameters as random variables, which gives us an advantage over classical methods where we are able to obtain reasonable statements from a small amount of data. Furthermore, we are able to incorporate prior experience into our model, which gives us an advantage over classical methods. The text includes a brief introduction to Bayesian statistics and then the derivation of some selected models together with a parametric linear regression model from which the decision problem is then derived. Everything, except the search for the resulting input regression vector, is derived analytically. An example is then given in the text showing the correctness of the solution, i.e. that indeed the algorithm chooses the input vectors to minimize the parameter error. The possible behaviour of the algorithm in the case of, inappropriately chosen basis functions is then pointed out, where the chosen experiments achieve a smaller error at the beginning, but for larger amounts of data, random experiments may be more efficient, as a consequence of the incorrect a priori information represented by the chosen basis functions.

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