在非线性反向问题中,在特性错误和异质性的情况下,前收缩

Posterior contraction under misspecification and heteroscedasticity in non-linear inverse problems

In many practical and numerical inverse problems, the exact data log-likelihood is not fully accessible, motivating the use of surrogate models. We study heteroscedastic nonparametric nonlinear regression problems with Gaussian errors and establish contraction results for posterior distributions arising from a surrogate log-likelihood constructed from proxy error variances, an approximate forward map, and an appropriate Gaussian process prior. Under general assumptions on the approximation quali