Bayesian inference when the physics is not quite right

Bayesian inference requires a physical and structural model for the portion of the environment being assessed. The model is characterized by a finite number of parameters, and these are assumed to each be a random variable. The forward problem can be solved given a knowldege of these parameters and the governing equations. Bayesian inference begins (prior probability) with some initial broad assumptions about the probability distributions. An intricate (Bayesian) process involving data and solutions to the forward problem leads to a refinement of these probability distributions. The range of possibilities becomes narrower, and one identifies most probable values of the parameters. The present paper raises the question as to what results when the parameterization is capriciously in conflict with what is known about the actual environment. An example from underwater acoustics is the choice of parameters to describe the frequency dependence of attenuation on a sediment layer. What is sometimes done is to assume the attenuation is directly proportional to frequency (just one parameter) or that the attenuation obeys a power law with a constant exponent (two parameters). The intrinsic shear modulus of the sediment is ignored in the numerical solutions of the forward problem, so the physics is incomplete. Some idealized examples are used to explore the consequences of such simplifying assumptions. Improved parameterizations are suggested that will yield more realistic frequency dependences of attenuation.Bayesian inference requires a physical and structural model for the portion of the environment being assessed. The model is characterized by a finite number of parameters, and these are assumed to each be a random variable. The forward problem can be solved given a knowldege of these parameters and the governing equations. Bayesian inference begins (prior probability) with some initial broad assumptions about the probability distributions. An intricate (Bayesian) process involving data and solutions to the forward problem leads to a refinement of these probability distributions. The range of possibilities becomes narrower, and one identifies most probable values of the parameters. The present paper raises the question as to what results when the parameterization is capriciously in conflict with what is known about the actual environment. An example from underwater acoustics is the choice of parameters to describe the frequency dependence of attenuation on a sediment layer. What is sometimes done is to ass...