In Monte Carlo Statistical Methods by Robert and Casella, I saw there is a reference to Understanding Monte Carlo Markov Chain (Springer Series in Statistics) by Gareth O. Roberts and Richard L. Tweedie published in 2004.
There is still reasonable hope that Gareth Roberts and Omiros Papaspiliopoulos complete a book inspired by this earlier project by Gareth Roberts and Richard Tweedie. A major part of the book is already written.
Check with a local university library. At my university there are two editions of this book. The first edition has a 1999 copyright date. And the second edition has a 2004 date. Both carry this title and author Monte Carlo statistical methods by Christian P. Robert, George Casella. Both were published by Springer.
With a check with Springer they show the 2004 title and the following by the same two authors
Introducing Monte Carlo Methods with R by Robert, Christian, Casella, George with a 2010 copyright date.