Bayesian inversion using nested trans-dimensional Gaussian processes

SUMMARY To understand earth processes, geoscientists infer subsurface properties such as electromagnetic resistivity or seismic velocity from surface observations of data. These are used to populate an model vector, and the spatial variation across this vector sheds light on underlying structure physical phenomenon interest, groundwater aquifers plate tectonics. However, these characteristics need be known in advance. Typically, assumptions made about length scales properties, which encoded a priori Bayesian probabilistic setting. In optimization setting, appeals promote simplicity together with constraints keep models close preferred model. All approaches valid, though they can lead unintended features resulting inferred geophysical owing inappropriate prior assumptions, even nature solution basis functions. work it will shown that order make accurate inferences first very general basis. From mathematical point view, conveniently thought ‘properties’ properties. Thus, same machinery their scales. This ‘infer infer’ paradigm analogous ‘learning learn’ is now commonplace machine learning literature. must noted (geophysical) inference not (machine) learning, there many common elements allow for cross-pollination useful ideas one field other, here. A non-stationary trans-dimensional Gaussian Process (TDGP) parametrize multichannel stationary TDGP associated property question. Using kernels, kernels spatially variable scales, sharp discontinuities represented within framework. As GPs multidimensional interpolators, theory computer code solve problems 1-D, 2-D 3-D. demonstrated through combination 1-D non-linear regression examples controlled source example. The key difference between previous using generalized nested marginalization better posterior characterization.