Data interpretation probability density function

The knowledge required to implement Bayes formula is daunting in that a priori as well as class conditional probabilities must be known. Some reduction in requirements can be accomplished by using joint probability distributions in place of the a priori and class conditional probabilities. Even with this simplification, few interpretation problems are so well posed that the information needed is available. It is possible to employ the Bayesian approach by estimating the unknown probabilities and probability density functions from exemplar patterns that are believed to be representative of the problem under investigation. This approach, however, implies supervised learning where the correct class label for each exemplar is known. The ability to perform data interpretation is determined by the quality of the estimates of the underlying probability distributions. 

The probability of these processes is a function of the density of states in the conductivity and valence band respectively at the potentials corresponding to the redox potential of the adsorbed species. In the electronic theory of catalysis in the later fifties only general thermodynamic rules were considered, but the conditions of the electron transfer were never applied to analyze the behaviour of different oxide catalysts in the oxidation of hydrocarbons. No quantitative data are available to make such analysis, although recently an attempt was made to interpret the changes of the rate of ethanol oxidation in terms of the density of states (36). The relative positions of the energy bands in the solid and the redox potential of the reacting molecule may be adjusted by a) formation of one or more oxide/oxide interfaces with such values of the contact potentials that the conductivity band will... 

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