We discuss a formal mathematical framework for certain coupling constructions via minorisation conditions, which are often used to prove bounds on convergence to stationarity of stochastic processes and Markov chain Monte Carlo algorithms.

Heterogeneous data are common in social, educational, medical and behavioral sciences. Recently, finite mixture structural equation models (SEMs) and two-level SEMs have been respectively proposed to analyze different kinds of heterogeneous data. Due to the complexity of these two kinds of SEMs,...

Stochastic volatility models, aka SVOL, are more difficult to estimate than standard time-varying volatility models (ARCH). Advances in the literature now offer well tested estimators for a basic univariate SVOL model. However, the basic model is too restrictive for many economic and finance...

We would like to thank all the discussants for their stimulating comments. While our article to a large extent reviews current practice of Bayesian analysis of Dynamic Stochastic General Equilibrium (DSGE) models the discussants provide many ideas to improve upon the current practice, thereby...