ScholarBank@NUShttps://scholarbank.nus.edu.sgThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Fri, 12 Apr 2024 14:03:44 GMT2024-04-12T14:03:44Z5031- Importance sampling as a variational approximationhttps://scholarbank.nus.edu.sg/handle/10635/105175Title: Importance sampling as a variational approximation
Authors: Nott, D.J.; Li, J.; Fielding, M.
Abstract: There is a well-recognized need to develop Bayesian computational methodologies that scale well to large data sets. Recent attempts to develop such methodology have often focused on two approaches-variational approximation and advanced importance sampling methods. This note shows how importance sampling can be viewed as a variational approximation, achieving a pleasing conceptual unification of the two points of view. We consider a particle representation of a distribution as defining a certain parametric model and show how the optimal approximation (in the sense of minimization of a Kullback-Leibler divergence) leads to importance sampling type rules. This new way of looking at importance sampling has the potential to generate new algorithms by the consideration of deterministic choices of particles in particle representations of distributions. © 2011 Elsevier B.V.
Mon, 01 Aug 2011 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1051752011-08-01T00:00:00Z
- On a generalization of the Laplace approximationhttps://scholarbank.nus.edu.sg/handle/10635/105247Title: On a generalization of the Laplace approximation
Authors: Nott, D.J.; Fielding, M.; Leonte, D.
Abstract: Laplace approximation is one commonly used approach to the calculation of difficult integrals arising in Bayesian inference and the analysis of random effects models. Here we outline a procedure which is an extension of the Laplace approximation and which attempts to find changes of variable for which the integrand becomes approximately a product of one-dimensional functions. When the integrand is a product of one-dimensional functions, an approximation to the integral can be obtained using one-dimensional quadrature. The approximation is exact for a broader class of functions than the ordinary Laplace approximation and can be applied when the integrand is not smooth at the mode. As an illustration of this last point we consider calculation of marginal likelihoods for smoothing parameter selection in the lasso. © 2009 Elsevier B.V. All rights reserved.
Mon, 01 Jun 2009 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1052472009-06-01T00:00:00Z
- Efficient MCMC schemes for computationally expensive posterior distributionshttps://scholarbank.nus.edu.sg/handle/10635/115082Title: Efficient MCMC schemes for computationally expensive posterior distributions
Authors: Fielding, M.; Nott, D.J.; Liong, S.-Y.
Abstract: We consider Markov chain Monte Carlo (MCMC) computational schemes intended to minimize the number of evaluations of the posterior distribution in Bayesian inference when the posterior is computationally expensive to evaluate. Our motivation is Bayesian calibration of computationally expensive computer models. An algorithm suggested previously in the literature based on hybrid Monte Carlo and a Gaussian process approximation to the target distribution is extended in three ways. First, we consider combining the original method with tempering schemes in order to deal with multimodal posterior distributions. Second, we consider replacing the original target posterior distribution with the Gaussian process approximation, which requires less computation to evaluate. Third, we consider in the context of tempering schemes the replacement of the true target distribution with the approximation in the high temperature chains while retaining the true target in the lowest temperature chain. This retains the correct target distribution in the lowest temperature chain while avoiding the computational expense of running the computer model in moves involving the high temperatures. Application of our methodology is considered to calibration of a rainfall-runoff model where multimodality of the parameter posterior is observed. © 2011 American Statistical Association and the American Society for Quality.
Tue, 01 Feb 2011 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1150822011-02-01T00:00:00Z