Monte Carlo Statistical Methods (Springer Texts in Statistics)

By Christian P. Robert, George Casella. 2005

1,287 citations recorded by the source corpus.

Subfields: Statistics and Probability, Probabilistic & Bayesian Methods

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Citations in the corpus

Kernel Mean Embedding of Distributions: A Review and Beyonds (2016, methodology): “More detailed accounts on this topic can be found, in Schölkopf and Smola (2002), Berlinet and Thomas-Agnan (2004), and Hofmann et al.”
Variational Inference: A Review for Statisticians (2016, background): “The inference problem is to compute the conditional density of the latent variables given the observations, p ( z | x ) .”
On the Equivalence between Kernel Quadrature Rules and Random Feature Expansions (2015, background): “…of high-dimensional integrals is one of the core computational tasks in many areas of machine learning, signal processing and more generally applied mathematics, in particular in the context of Bayesian inference (Gelman, 2004), or the study of complex systems (Robert and Casella, 2005).”
A Distributional Approach to Controlled Text Generation (2020, methodology): “3One possible sampling approach here would be to employ MCMC techniques, such as Metropolis- Hastings (Robert & Casella, 2005).”
Fast and Scalable Bayesian Deep Learning by Weight-Perturbation in Adam (2018, neutral): “5.2 in Robert & Casella (2005).”
Variational inference for Dirichlet process mixtures (2006, background): “Writing the gamma distribution in its canonical form we have: p(α | s1, s2) = (1/α) exp{−s2α + s1 log α − a(s1, s2)}, where s1 is the shape parameter and s2 is the inverse scale parameter.”
Bayesian Inference from Composite Likelihoods, with an Application to Spatial Extremes (2009, methodology): “1 Magnitude adjustment The magnitude adjustment to the composite log likelihood is inspired by Rotnitzky and Jewell [1990], who, in the context of hypothesis testing in longitudinal studies, estimate λ1, .”
The nested chinese restaurant process and bayesian nonparametric inference of topic hierarchies (2007, methodology): “proximate the posterior for hLDA. In MCMC, one samples from a target distribution on a set of variables by constructing a Markov chain that has the target distribution as its stationary distribution (Robert and Casella, 2004). One then samples from the chain for sufﬁciently long that it approaches t”
Pseudo-Marginal Bayesian Inference for Gaussian Processes (2013, background): “From the theory of importance sampling [38], the variance of the estimator is zero when q(f |y, θ) is proportional to p(y|f)p(f |θ), which is proportional to the posterior distribution over f that we do not know how to sample from in the first place.”