Sequential importance sampling for nonparametric Bayes models: The next generation

By S. MacEachern, Merlise A. Clyde, Jun S. Liu. 1999

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Kernel Bayes' Rule (2010, methodology): “ nonparametric Bayesian inference ([26] and references therein), in which the prior is typically givenin the form of a processwithout a density form. In this case, sampling methods are often applied ([21, 22, 41] among others). Alternatively, the posterior may be approximated using variational metho”
Monte Carlo Smoothing for Nonlinear Time Series (2004, methodology): “…importance sampling ﬁlter (Doucet et al. 2000; Gordon et al. 1993; Liu and Chen 1998), the auxiliary particle ﬁlter (APF) (Pitt and Shephard 1999a), and schemes that incorporate local MCMC moves to improve the ﬁltering approximation (MacEachern, Clyde, and Liu 1999; Gilks and Berzuini 2000).”
Generalized weighted Chinese restaurant processes for species sampling mixture models (2003, methodology): “This class includes the Dirichlet process, the two parameter extension of the Dirichlet process, the two-parameter Poisson-Dirichlet process (Pitman and Yor (1997)), which we refer to as the Pitman-Yor process, and the class of finite dimensional Dirichlet priors discussed in detail in Ishwaran and ”
Mixture Modeling for Marked Poisson Processes (2010, background): “hese are easy to work with or intuitive to specify. There are substantial beneﬁts (refer to Section 4) to be gained from the Rao-Blackwellization of posterior inference for mixture models (see, e.g., MacEachern et al., 1999, for empirical demonstration of the improvement in estimators) that is only ”
Sequential Monte Carlo samplers (2002, methodology): “In the case where the dimension of the target distributions increases over time, it was used in Gilks and Berzuini (2001) and MacEachern et al. (1999).”
Toward a general, scaleable framework for Bayesian teaching with applications to topic models (2016, methodology): “A better approach is to use the collapsed Gibbs sampler in Equation 2 to implement a sequential importance sampler [SIS; 16] from which proposals are drawn by incrementally generating z .”
Sequential Monte Carlo Methods in Practice (2001, methodology): “qt(~t let-I) = 7rt(~t let-I) for sequential sampling, then the marginalised SIS performs better than the original one (MacEachern et al. 1999).”
Kernel Bayes' rule: Bayesian inference with positive definite kernels (2013, methodology): “In this case, sampling methods are often applied (MacEachern, 1994; West et al., 1994; MacEachern et al., 1999, among others).”
Estimating Ratios of Normalizing Constants Using Linked Importance Sampling (2005, background): “This is the situation for the ‘sequential importance sampler’ of MacEachern, Clyde, and Liu (1999), which can be seen as an instance of AIS (Neal 2001).”
Marginal Likelihood and Bayes Factors for Dirichlet Process Mixture Models (2003, methodology): “…and Chan (1996), Ishwaran and James (2001b), Ishwaran et al. (2001), and Ishwaran and Takahara (2002) in the general context of weighted Chinese restaurant processes and by Quintana (1998), MacEachern, Clyde, and Liu (1999), and Quintana and Newton (2000) in the setting of categorical DPM models.”