  This paper proposes a general optimization strategy, which combines results
from different optimization or parameter estimation methods to overcome
shortcomings of a single method. Shotgun optimization is developed as a
framework which employs different optimization strategies, criteria, or
conditional targets to enable wider likelihood exploration. The introduced
Shotgun optimization approach is embedded into an incremental mixture
importance sampling algorithm to produce improved posterior samples for
multimodal densities and creates robustness in cases where the likelihood and
prior are in disagreement. Despite using different optimization approaches, the
samples are combined into samples from a single target posterior. The diversity
of the framework is demonstrated on parameter estimation from differential
equation models employing diverse strategies including numerical solutions and
approximations thereof. Additionally the approach is demonstrated on mixtures
of discrete and continuous parameters and is shown to ease estimation from
synthetic likelihood models. R code of the implemented examples is stored in a
zipped archive (codeSubmit.zip).
