A theory of statistical models for Monte Carlo integration

By Augustine Kong, Peter McCullagh, Xiao-Li Meng, Dan L. Nicolae, Zhiqiang Tan. 2003

112 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/7bf81da532358ff96072d71b070d7f949644abe5

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

In Statistics and Probability

Citations in the corpus

A Bayesian information criterion for singular models (2013, methodology): “The integral in equation (2.3) may thus be approximated by the product of P.Yn|π̂i, Mi/ and a Gaussian integral, in which the inverse covariance matrix equals n times the Fisher information. This di-dimensional Gaussian integral depends on n via the multiplicative factor n−di=2, and taking logarithm”
Statistical paradises and paradoxes in big data (I): Law of large populations, big data paradox, and the 2016 US presidential election (2018, unknown): “[See Kong et al. (2003) and Kong et al. (2007) for a general likelihood theory about reformulating Monte Carlo integrations as an estimation of measure ν.] Consequently, μ̂ − μ = ∫ g(x)(ν̂ − ν)(dx) = 〈g, ν̂ − ν〉‖g‖ × ‖ν̂ − ν‖ × ‖ν̂ − ν‖ × ‖g‖ (5.5) ≡ CNF(g, ν̂ − ν) × DSC(ν̂ − ν) × VAR(g), where…”
Two‐component mixtures of normal, gamma, and Gumbel distributions for hydrological applications (2011, background): “…‘‘patch’’ originates from a failure in the MCMC techniques applied for exploring the posterior distribution, Lee et al. [2008] argue that it also has the property to stabilize Chib’s estimator and thus to reduce its variance, by exploiting the symmetry in the dominating measure [Kong et al., 2003].”
Control variates for quasi-Monte Carlo (2005, methodology): “Similarly, Kong et al. (2003) have shown that the optimal bridge sampling estimator given in Meng and Wong (1996) is the same as the MLE when we have {Xij , i = 1, . . . , nj ; j = 1,2} as our data.”
Calibration estimation using empirical likelihood in survey sampling (2009, background): “See, for example, Vardi (1985), Qin (1993) and Kong et al. (2003). When the unequal probability sampling design is well approximated by a Poisson sampling, the empirical likelihood function (2.”
Multiensemble Markov models of molecular thermodynamics and kinetics (2016, methodology): “A widely used estimator is the binless WHAM method, (50, 51), also called MBAR (49), which provides an optimal estimate of μ ð x Þ under the assumption that at each ensemble k , the samples x are drawn independently from their global equilibrium distribution μ k ð x Þ .”
Efficient Sequential Monte Carlo With Multiple Proposals and Control Variates (2016, background): “Another estimator combining multiple proposals and control variates is proposed by Tan (2004) based on the perspective of Kong et al. (2003).”
On a Likelihood Approach for Monte Carlo Integration (2004, methodology): “For two different situations where independent observations are simulated from multiple distributions, we show that the likelihood approach of Kong et al. (2003) achieves the lowest asymptotic variance possible by using estimating equations for Monte Carlo integration.”
Importance Nested Sampling and the MultiNest Algorithm (2013, background): “As described in Cameron and Pettitt (2013) the initial idea for INS arose from the study of recursive marginal likelihood estimators, as characterised by Reverse Logistic Regression (RLR; Geyer 1994; Chen and Shao 1997; Kong et al. 2003) and the Density of States (DoS; Habeck 2012; Tan et al. 2012).”