Varying prior information in Bayesian inversion

Abstract

Bayes' rule is used to combine likelihood and prior probability distributions. The former represents knowledge derived from new data, the latter represents pre-existing knowledge; the Bayesian combination is the so-called posterior distribution, representing the resultant new state of knowledge. While varying the likelihood due to differing data observations is common, there are also situations where the prior distribution must be changed or replaced repeatedly. For example, in mixture density neural network (MDN) inversion, using current methods the neural network employed for inversion needs to be retrained every time prior information changes. We develop a method of prior replacement to vary the prior without re-training the network. Thus the efficiency of MDN inversions can be increased, typically by orders of magnitude when applied to geophysical problems. We demonstrate this for the inversion of seismic attributes in a synthetic subsurface geological reservoir model. We also present results which suggest that prior replacement can be used to control the statistical properties (such as variance) of the final estimate of the posterior in more general (e.g., Monte Carlo based) inverse problem solutions.