  The objective of Bayesian inference is often to infer, from data, a
probability measure for a random variable that can be used as input for Monte
Carlo simulation. When datasets for Bayesian inference are small, a principle
challenge is that, as additional data are collected, the probability measure
inferred from Bayesian inference may change significantly. That is, the
original probability density inferred from Bayesian inference may differ
considerably from the updated probability density both in its model form and
parameters. In such cases, expensive Monte Carlo simulations may have already
been performed using the original distribution and it is infeasible to start
again and perform a new Monte Carlo analysis using the updated density due to
the large added computational cost. In this work, we discuss four strategies
for updating Mote Carlo simulations for such a change in probability measure:
1. Importance sampling reweighting; 2. A sample augmenting strategy; 3. A
sample filtering strategy; and 4. A mixed augmenting-filtering strategy. The
efficiency of each strategy is compared and the ultimate aim is to achieve the
change in distribution with a minimal number of added computational
simulations. The comparison results show that when the change in measure is
small importance sampling reweighting can be very effective. Otherwise, a
proposed novel mixed augmenting-filtering algorithm can robustly and
efficiently accommodate a measure change in Monte Carlo simulation that
minimizes the impact on the sample set and saves a large amount of additional
computational cost. The strategy is then applied for uncertainty quantification
in the buckling strength of a simple plate given ongoing data collection to
estimate uncertainty in the yield stress.
