  This paper develops new insights into quantitative methods for the validation
of computational model prediction. Four types of methods are investigated,
namely classical and Bayesian hypothesis testing, a reliability-based method,
and an area metric-based method. Traditional Bayesian hypothesis testing is
extended based on interval hypotheses on distribution parameters and equality
hypotheses on probability distributions, in order to validate models with
deterministic/stochastic output for given inputs. Two types of validation
experiments are considered - fully characterized (all the model/experimental
inputs are measured and reported as point values) and partially characterized
(some of the model/experimental inputs are not measured or are reported as
intervals). Bayesian hypothesis testing can minimize the risk in model
selection by properly choosing the model acceptance threshold, and its results
can be used in model averaging to avoid Type I/II errors. It is shown that
Bayesian interval hypothesis testing, the reliability-based method, and the
area metric-based method can account for the existence of directional bias,
where the mean predictions of a numerical model may be consistently below or
above the corresponding experimental observations. It is also found that under
some specific conditions, the Bayes factor metric in Bayesian equality
hypothesis testing and the reliability-based metric can both be mathematically
related to the p-value metric in classical hypothesis testing. Numerical
studies are conducted to apply the above validation methods to gas damping
prediction for radio frequency (RF) microelectromechanical system (MEMS)
switches. The model of interest is a general polynomial chaos (gPC) surrogate
model constructed based on expensive runs of a physics-based simulation model,
and validation data are collected from fully characterized experiments.
