Science-Based Probability Approach

Science-Based Probability Modeling and Life Cycle Engineering 

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A general method has been developed for the estimation of model parameters from experimental observations when the model relating the parameters and input variables to the output responses is a Monte Carlo simulation. The method provides point estimates as well as joint probability regions of the parameters. In comparison to methods based on analytical models, this approach can prove to be more flexible and gives the investigator a more quantitative insight into the effects of parameter values on the model. The parameter estimation technique has been applied to three examples in polymer science, all of which concern sequence distributions in polymer chains. The first is the estimation of binary reactivity ratios for the terminal or Mayo-Lewis copolymerization model from both composition and sequence distribution data. Next a procedure for discriminating between the penultimate and the terminal copolymerization models on the basis of sequence distribution data is described. Finally, the estimation of a parameter required to model the epimerization of isotactic polystyrene is discussed. 

In fact, the chemical industry often favors heterogeneous catalysis, which is also more than a century old (Sabatier was probably one of its real fathers), despite its so-far empirical nature. The development of better catalysts in heterogeneous catalysis has always relied on empirical improvement since it has been difficult to characterize active sites on the surfaces, as the so-called active sites are usually small in number(s). Presently, the number of accepted elementary steps (as defined above) is stiU Hmited to a few examples, mostly demonstrated by means of surface science [1-3] and the predictive approach, based on molecular concepts. 

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