Bayesian calibration, process modeling and uncertainty quantification in biotechnology
Fig 4
Uncertainty about the independent variable.
An intuition for inferring the independent variable from an observed dependent variable is to cut (condition) the green probability distribution model at the observed value (blue slices) and normalize its area to 1. The resulting (blue) slice is a potentially asymmetric probability distribution that describes the likelihood of the observation, given the independent variable. Its maximum (the maximum likelihood estimate) is the value of the independent variable that best describes the observation. For multiple observations, the probability density function for the independent variable corresponds to the product of the PDFs of the observations. The red shoulders mark the regions outside of the 90% equal-tailed interval.