Rao–Blackwellisation in the Markov Chain Monte Carlo Era

Robert, Christian P.; Roberts, Gareth O.

doi:10.1111/insr.12463

Cited by 6 publications

(2 citation statements)

References 54 publications

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“…If the sufficient statistic t(X) is furthermore complete, to Rao-Blackwellize the unbiased estimator results in a uniformly minimal variance unbiased estimator (UMVUE; Lehmann & Scheffé (1950), implying that it cannot be further improved upon under squared loss. The Rao-Blackwell theorem has important implications in the design of Markov Chain Monte Carlo methods (Robert & Roberts, 2021, Kong et al, 2007, among many other appli-cations. It provides a guideline and inspires methods to construct estimators with reduced Monte Carlo variability (e.g.…”

Section: Conditioningmentioning

confidence: 99%

Six Statistical Senses

Craiu¹,

Gong²,

Meng³

2022

Preprint

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This article proposes a set of categories, each one representing a particular distillation of important statistical ideas. Each category is labeled a "sense" because we think of them as essential in helping every statistical mind connect in constructive and insightful ways with statistical theory, methodologies and computation. The illustration of each sense with statistical principles and methods provides a sensical (but not random) tour of the conceptual landscape of statistics, as a leading discipline in the data science ecosystem.

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Section: Conditioningmentioning

confidence: 99%

Six Statistical Senses

Craiu¹,

Gong²,

Meng³

2022

Preprint

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“…In computing the generalized Bayes estimator (posterior mean of β), we applied the Rao-Blackwellization technique for variance reduction (Robert and Roberts, 2021). Namely, we replaced step 2 of the above algorithm with β t = (1 − κ t−1 )y and took average of sampled β after burn-in.…”

Section: Algorithm For Posterior Samplingmentioning

confidence: 99%

Helical Pore Alignment on Cylindrical Carbon

Maruyama

Shinagawa

Watanabe

et al. 2019

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Interest in chiral substances has mainly focused on the substances themselves, but not on the accompanying space, especially regarding the pore alignment. As a method to form both the chiral substance and the accompanying space, cylindrical self‐assembly of uniform polystyrene nanoparticles with fructose is carried out in the presence of both carbon and sodium alginate, which is followed by heat treatment in an inert atmosphere. The carbonization generates fructose‐derived honeycomb‐like carbon walls with helically aligned nanopores left after the polystyrene decomposition. The diffuse reflectance circular dichroism measurements give peaks with opposite signs for the d‐ and l‐fructose‐derived cylindrical carbons. Circularly polarized light sensitivity in transient photoconductivity is confirmed apparently in the carbon‐based helical structures. This sensitivity as well as straightforward formation of composites with another component to give helicity shows potential applications of the helically aligned pores.

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Sampling-Like Dynamics of the Nonlinear Dynamical System Combined with Optimization

Yamashita

2023

Photonic Neural Networks With Spatiotemporal Dynamics

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When considering computation using physical phenomena beyond established digital circuits, the variability of the device must be addressed. In this chapter, we will focus on random sampling for its algorithmic solution. In particular, we discuss the nonlinear dynamical system that achieves the sampling behavior. The system, called herding, is proposed as an algorithm that can be used in the same manner as Monte Carlo integration. The algorithm combines optimization methods in the system and does not depend on random number generators. In this chapter, we review this algorithm using nonlinear dynamics and related studies, including the author’s previous results. Then we discuss the perspective of the application of herding in relation to the use of physical phenomena in computation.

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Rao–Blackwellisation in the Markov Chain Monte Carlo Era

Cited by 6 publications

References 54 publications

Six Statistical Senses

Six Statistical Senses

Helical Pore Alignment on Cylindrical Carbon

Sampling-Like Dynamics of the Nonlinear Dynamical System Combined with Optimization

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