In this work we consider Bayesian inference problems with intractable likelihood functions. We present a method to compute an approximate of the posterior with a limited number of model simulations. The method features an inverse Gaussian Process regression (IGPR), i.e., one from the output of a simulation model to the input of it. Within the method, we provide an adaptive algorithm with a tempering procedure to construct the approximations of the marginal posterior distributions. With examples we demonstrate that IGPR has a competitive performance compared to some commonly used algorithms, especially in terms of statistical stability and computational efficiency, while the price to pay is that it can only compute a weighted Gaussian approximation of the marginal posteriors.

翻译：在这项工作中,我们考虑贝叶斯的推论问题和难以解决的可能性函数。我们提出了一个计算近似后方算法,其模型模拟数量有限。该方法的特点是逆高斯进程回归(IGPR),即从模拟模型的输出到输入。在这个方法中,我们提供了一种适应性算法,并有一个调和程序来构建边缘后方分布的近似值。我们举例说明了IGPR与一些常用算法相比具有竞争性的性能,特别是在统计稳定性和计算效率方面,而要付出的代价是它只能计算边缘后方的加权高斯近似值。