Optimization and Statistical Analysis
acslX Optimization Module
The optimization capabilities in acslX include robust parameter estimation, min/max optimization, sensitivity analysis, and Monte Carlo analysis. Wizards and a graphical interface provide guided input to make setup and execution of these functions quick and easy.
Enhancing Modeling and Simulation
These include robust parameter estimation, min/max optimization, sensitivity analysis, and Monte Carlo analysis. Wizards and a graphical interface provide guided input to make setup and execution of these functions quick and easy.
Parameter Estimation
Parameter estimation in acslXtreme OptStat is the mechanism by which model outputs are fitted to user-supplied experimental data by adjusting one or more model parameters. In OptStat, this is accomplished by maximizing a log likelihood function using one of the supported OptStat min/max algorithms. acslX supports an adjustable likelihood function error model: heteroscedasticity parameters for each target variable may be either explicitly specified by the user, or varied by the solver to determine the best fit.
Min/Max Optimization
Min/Max analysis simply refers to the minimization or maximization of some functional value (sometimes called the objective function) with respect to variations in the inputs to the function (the parameters). In the OptStat module, the objective function is a model output variable and the parameters are model constants. In many cases, multiple input variables will be varied simultaneously in an attempt to seek a minimum or maximum value of the output variable. Such scenarios can be computationally demanding, as iterative algorithms are usually necessary and each iteration typically requires one or more runs of the simulation.
Sensitivity Analysis
Sensitivity analysis is the calculation of the partial derivatives of model responses with respect to model parameters. Another name for these partial derivatives is sensitivity coefficients.
Monte Carlo Analysis
Monte Carlo analysis is used to determine statistical dependencies between simulation inputs and outputs; i.e., given a prescribed uncertainty (probability distribution) of values of one or more inputs, Monte Carlo analysis seeks to determine what the corresponding uncertainty will be in a set of outputs.
The method by which this analysis is performed is straightforward: for each of the inputs, sample a value from the corresponding distribution for that input, set the inputs to the sampled values, then run the simulation and collect the desired outputs. Repeat this process, collecting appropriate statistical information on the outputs until the desired accuracy has been reached.
The routines used to generate random values for the model inputs are of particular importance to Monte Carlo calculations. acslXtreme provides a variety of high-quality random number generators for use with Monte Carlo analysis applications.
Bayesian Analysis Utilities and Demos
A number of new M functions and example are included which support analyses using Markov Chain Monte Carle (MCMC) techniques via the acslX Analysis Language. In particular, a variety of new functions for computing probability distribution values corresponding to the random number generators now available in Optimum will be provided, along with functions for setting up model-specific sampling using the Metropolis-Hastings sampling algorithm.
An Eye to the Future
acslXtreme incorporates a very flexible and open architecture that was designed from the beginning with the future in mind. This approach will pay dividends by enabling continued evolution of the acslXtreme product to support the rapidly changing modeling and simulation environment.
acslXtreme incorporates the .NET distributed component framework that will provide maximum flexibility and extensibility downstream. By selecting this architecture, we have paved the way to many future enhancements such as distributed processing, interchangeable components for basic services like plotting/animation, and platform and operating system independence through the .NET virtual machine interface.