Discussion of paper by Mira and Baddeley Richard

This very impressive paper brings together an enormous number of ideas from seemingly disconnected fields. There are frequentist ideas associated with estimating equations for general stochastic processes, and approaches to optimality associated with the names of Godambe and Heyde; connections with the method of maximum likelihood and the method of moments, also pseudo-likelihood, general Bayes estimators and a new concept called the pseudo-posterior; connections with admissibility theory; connections with ideas of ordering Markov chains in terms of their rates of convergence in different metrics; and there is even a passing reference to the Stein (or Stein-Chen) method of probability approximation, which is usually regarded as a means of obtaining explicit upper bounds in rate-of-convergence problems. With so many ideas interacting, it is difficult to identify any one specific theme to concentrate on for a discussion. In my discussion, I would like to give my own perspective on what is going on. I hope that by so doing, I can persuade other to read the paper and form their own perspective of what are the most important themes.