Efficient Interpolation of Computationally Expensive Posterior Densities With Variable Parameter Costs | PERPUSTAKAAN UNIVERSITAS KATOLIK PARAHYANGAN

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Efficient Interpolation of Computationally Expensive Posterior Densities With Variable Parameter Costs

Bliznyuk, Nikolay - Nama Orang; Ruppert, David - Nama Orang; Shoemaker, Christine A - Nama Orang;

Markov chain Monte Carlo (MCMC) is nowadays a standard approach to numerical computation of integrals of the posterior density π of the parameter vector η. Unfortunately, Bayesian inference using MCMC is computationally intractable when the posterior density π is expensive to evaluate. In many such problems, it is possible to identify a minimal subvector β of η responsible for the expensive computation in the evaluation of π. We propose two approaches, DOSKA and INDA, that approximate π by interpolation in ways that exploit this computational structure to mitigate the curse of dimensionality. DOSKA interpolates π directly while INDA interpolates π indirectly by interpolating functions, for example, a regression function, upon which π depends. Our primary contribution is derivation of a Gaussian processes interpolant that provably improves over some of the existing approaches by reducing the effective dimension of the interpolation problem from dim(η) to dim(β). This allows a dramatic reduction of the number of expensive evaluations necessary to construct an accurate approximation of π when dim(η) is high but dim(β) is low.

We illustrate the proposed approaches in a case study for a spatio-temporal linear model for air pollution data in the greater Boston area.

Supplemental materials include proofs, details, and software implementation of the proposed procedures.

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Barcode		Tipe Koleksi	Nomor Panggil	Lokasi	Status
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Informasi Detail

Judul Seri: JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS; Vol.20 No.3 September 2011
No. Panggil: -
Penerbit: : .,
Deskripsi Fisik: p. 636-655
Bahasa: English
ISBN/ISSN: -
Klasifikasi: -
Tipe Isi: -
Tipe Media: -
Tipe Pembawa: -
Edisi: -
Subjek: GAUSSIAN PROCESSES
MARKOV CHAIN MONTE CARLO
INVERSE PROBLEMS
COMPUTER EXPERIMENTS
RADIAL BASIS FUNCTIONS
SPATIO-TEMPORAL MODELING
Info Detail Spesifik: https://doi.org/10.1198/jcgs.2011.09212
Pernyataan Tanggungjawab: Nikolay Bliznyuk, David Ruppert, Christine A. Shoemaker

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