Diagnostics: A Comparative Review

Citations in the corpus

• Optimally-Weighted Herding is Bayesian Quadrature (2012, methodology): “MCMC methods can be applied to almost any problem but convergence of the estimate depends on several factors and is hard to estimate (Cowles & Carlin, 1996).”
• Inductive biases for deep learning of higher-level cognition (2020, background): “Standard graphical models only represent the declarative knowledge and typically require expensive but generic iterative computations (such as Monte-Carlo Markov chains) to perform approximate inference (Cowles and Carlin, 1996; Gilks et al., 1995).”
• Small Sample Size Solutions (2020, methodology): “Though there is no way of definitively knowing that a chain has converged to the posterior distribution, there are several techniques one can use to find evidence of convergence (Cowles & Carlin, 1996).”
• Bayesian Methods for Hidden Markov Models (2002, background): “Cowles and Carlin (1996) and Mengersen, Robert, and Guihenneuc-Jouyaux (1999) have reviewed the large body of work on MCMC convergence diagnostics.”
• Flexible Imputation of Missing Data (2012, background): “Several expository reviews are available that assess convergence diagnostics for MCMC methods (Cowles and Carlin, 1996; Brooks and Gelman, 1998; El Adlouni et al., 2006).”
• Revisiting the Gelman–Rubin Diagnostic (2018, background): “In the early 1990s, research in Markov chain Monte Carlo (MCMC) diagnostics surged producing convergence diagnostics such as Geweke (1992), Gelman and Rubin (1992), and Raftery and Lewis (1992); a detailed discussion can be found in Cowles and Carlin (1996).”
• Sufficient burn-in for Gibbs samplers for a hierarchical random effects model (2004, background): “Our results are useful from a practical standpoint because they obviate troublesome, ad hoc convergence diagnostics [Cowles and Carlin (1996) and Received January 2002; revised December 2002.”
• Bayesian interpolation of unequally spaced time series (2015, methodology): “Convergence of the chain was assessed by comparing the ergodic means plots of model parameters for multiple chains, which justified that the number of iterations was adequate (Cowles and Carlin 1996).”
• Bayesian Poisson log-bilinear mortality projections (2005, background): “More formal diagnostics are developed in Cowles & Carlin (1996) and Brooks & Roberts (1998).”
• Markov chain Monte Carlo Estimation of Classical and Dynamic Switching and Mixture Models (2001, methodology): “Step 1 is a standard step that occurs in mixture and switching models, and can be carried out as discussed by Diebolt and Robert (1994) for an exchangeable prior on I , by Chib (1996) for Markov mixture models with s = 1, by Hamilton (1989) for models with s > 1, and by Carter and Kohn (1994) for sw”
• Robust linear mixed models with skew-normal independent distributions from a Bayesian perspective (2009, unknown): “To monitor the convergence of the Gibbs samples we used the methods recommended by Cowles and Carlin (1996).”
• Near-Optimal Algorithms for Differentially-Private Principal Components (2012, background): “ain is suciently close to its stationary distribution. Statisticians employ a range of diagnostic methods and statistical tests to empirically determine if the Markov chain is close to stationarity [Cowles and Carlin, 1996, Brooks and Roberts, 1998, Brooks and Gelman, 1998, El Adlouni et al., 2006].”
• A Practical Sequential Stopping Rule for High-Dimensional Markov Chain Monte Carlo (2016, background): “Further, convergence diagnostics (see, e.g., Cowles and Carlin 1996) were designed for problems of at most moderate dimension and can be essentially impossible to implement in high-dimensions.”
• Discrete Choice Methods with Simulation by Kenneth E. Train (2003, background): “Cowles and Carlin (1996) provide a description of the various tests and diagnostics that have been proposed.”