We consider the identification of large-scale linear and stable dynamic systems whose outputs may be the result of many correlated inputs. Hence, severe ill-conditioning may affect the estimation problem. This is a scenario often arising when modeling complex physical systems given by the interconnection of many sub-units where feedback and algebraic loops can be encountered. We develop a strategy based on Bayesian regularization where any impulse response is modeled as the realization of a zero-mean Gaussian process. The stable spline covariance is used to include information on smooth exponential decay of the impulse responses. We then design a new Markov chain Monte Carlo scheme that deals with collinearity and is able to efficiently reconstruct the posterior of the impulse responses. It is based on a variation of Gibbs sampling which updates possibly overlapping blocks of the parameter space on the basis of the level of collinearity affecting the different inputs. Numerical experiments are included to test the goodness of the approach where hundreds of impulse responses form the system and inputs correlation may be very high.

翻译：我们考虑确定大规模线性和稳定的动态系统,其产出可能是许多相关投入的结果。因此,严重的调节可能影响到估算问题。这是在建模由许多子单位的相互连接而导致的复杂物理系统时经常出现的一种情景,在这种系统中,可以遇到反馈和代数环路;我们根据巴伊西亚的正规化制定战略,在这种正规化的基础上,将任何脉冲反应作为实现零平均值高斯过程的模型;稳定的样条共性被用来包括脉冲反应平稳指数衰减的信息。然后我们设计一个新的Markov连锁蒙特卡洛计划,处理对脉冲反应的相继性,并能有效地重建脉冲反应的后部,其基础是Gibs抽样的变异性,根据影响不同投入的相近性水平更新参数空间的重叠区块;包括数字实验,以测试方法的优劣性,在这种情况下,数百个脉冲反应形成系统和投入的关联性可能非常高。