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.
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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.
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Baysean
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.
For
more information on acslX Optimum, please contact us at AEgis
Technologies.
View
our acslX
Optimum Product Brochure.
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