In his paper “To Criticize the Critics” (1991), Peter Phillips discusses Bayesian methodology for time series models. The main point that Uhlig and I set out to make, however, was that careful consideration of the implications of the likelihood principle suggests that much of the recent work under the “unit root” label in the econometrics literature is being incorrectly interpreted in practice. We pointed out that time series models with possible unit roots are one of the few domains within which the implications of a likelihood principle approach to inference are diﬀerence, even in the large samples, from those of a classical hypothesis testing approach. Phillips addresses this part of our paper only indirectly.
Sims, Christopher A., "Comment on ‘To Criticize the Critics’, by Peter C.B. Phillips" (1991). Cowles Foundation Discussion Papers. 1228.