Basic Monte Carlo formulations

For a batch process modeled in SuperPro Designer, Monte Carlo simulation can be performed by combining Monte Carlo formulation tools, such as Oracle Crystal Ball from Oracle Corporation (Redwood Shores, CA) and Risk from Palisade Corporation (Ithaca, NY) with SuperPro. Both Oracle Crystal Ball and Risk are Microsoft Excel add-in applications that enable users to assign probability distributions to input parameters, manage the Monte Carlo simulation calculations, record the values of output variables, and analyze them statistically. The communication between Oracle Crystal Ball or Risk and SuperPro is accomplished using Visual Basic for Applications (VBA) scripts written in Excel. A detailed Monte Carlo simulation example based on a variation of this process that utilizes Oracle Crystal Ball and SuperPro Designer is available in the literature [144]. 

In the next subsection, I describe how the basic elements of Bayesian analysis are formulated mathematically. I also describe the methods for deriving posterior distributions from the model, either in terms of conjugate prior likelihood forms or in terms of simulation using Markov chain Monte Carlo (MCMC) methods. The utility of Bayesian methods has expanded greatly in recent years because of the development of MCMC methods and fast computers. I also describe the basics of hierarchical and mixture models. 

---