  For multiple reasons -- such as avoiding overtraining from one data set or
because of having received numerical estimates for some parameters in a model
from an alternative source -- it is sometimes useful to divide a model's
parameters into one group of primary parameters and one group of nuisance
parameters. However, uncertainty in the values of nuisance parameters is an
inevitable factor that impacts the model's reliability. This paper examines the
issue of uncertainty calculation for primary parameters of interest in the
presence of nuisance parameters. We illustrate a general procedure on two
distinct model forms: 1) the GARCH time series model with univariate nuisance
parameter and 2) multiple hidden layer feed-forward neural network models with
multivariate nuisance parameters. Leveraging an existing theoretical framework
for nuisance parameter uncertainty, we show how to modify the confidence
regions for the primary parameters while considering the inherent uncertainty
introduced by nuisance parameters. Furthermore, our study validates the
practical effectiveness of adjusted confidence regions that properly account
for uncertainty in nuisance parameters. Such an adjustment helps data
scientists produce results that more honestly reflect the overall uncertainty.
