  Two fundamental research tasks in science and engineering are forward
predictions and data inversion. This article introduces a recent R package
RobustCalibration for Bayesian data inversion and model calibration by
experiments and field observations. Mathematical models for forward predictions
are often written in computer code, and they can be computationally expensive
slow to run. To overcome the computational bottleneck from the simulator, we
implemented a statistical emulator from the RobustGaSP package for emulating
both scalar-valued or vector-valued computer model outputs. Both posterior
sampling and maximum likelihood approach are implemented in the
RobustCalibration package for parameter estimation. For imperfect computer
models, we implement Gaussian stochastic process and the scaled Gaussian
stochastic process for modeling the discrepancy function between the reality
and mathematical model. This package is applicable to various types of field
observations, such as repeated experiments and multiple sources of
measurements. We discuss numerical examples of calibrating mathematical models
that have closed-form expressions, and differential equations solved by
numerical methods.
