Asymptotic properties of kernel density estimators when applying importance sampling

Nakayama,

doi:10.1109/wsc.2011.6147785

Cited by 8 publications

(12 citation statements)

References 16 publications

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“…For FD, we apply the approach of Chu and Nakayama [2012], in which the FD estimator (13) uses the IS CDF estimator (20). The column headed "Kernel" uses a plug-in kernel estimator of f (ξ p ) developed in Nakayama [2011a], with a Gaussian kernel and bandwidth h n = 2n −1/5 . As before, sectioning appears to provide better coverage than the other implementable methods for small n, especially as p approaches 1.…”

Section: Numerical Resultsmentioning

confidence: 99%

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Confidence Intervals for Quantiles Using Sectioning When Applying Variance-Reduction Techniques

Nakayama

2014

ACM Trans. Model. Comput. Simul.

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We develop confidence intervals (CIs) for quantiles when applying variance-reduction techniques (VRTs) and sectioning. Similar to batching, sectioning partitions the independent and identically distributed (i.i.d.) outputs into nonoverlapping batches and computes a quantile estimator from each batch. But rather than centering the CI at the average of the quantile estimators across the batches, as in batching, sectioning centers the CI at the overall quantile estimator based on all the outputs. A similar modification is made to the sample variance, which is used to determine the width of the CI. We establish the asymptotic validity of the sectioning CI for importance sampling and control variates, and the proofs rely on first showing that the corresponding quantile estimators satisfy a Bahadur representation, which we have done in prior work. Here, we present some numerical results. ACM Reference Format:Marvin K. Nakayama. 2014. Confidence intervals for quantiles using sectioning when applying variancereduction techniques. ACM Trans. Model. Comput.

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Section: Numerical Resultsmentioning

confidence: 99%

“…Coverages (with Average Half-Widths) and Relative Bias for IS The FD and Kernel columns contain results when applying the estimators fromChu and Nakayama [2012] andNakayama [2011a], respectively.…”

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confidence: 99%

Confidence Intervals for Quantiles Using Sectioning When Applying Variance-Reduction Techniques

Nakayama

2014

ACM Trans. Model. Comput. Simul.

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“…This is similar to importance sampling, with s(φ) acting as the proposal density. Nakayama (2011) notes importance sampling can be used to improve the mean square error (MSE) of a KDE in a specific local region, at the cost of an increase in global MSE. To ameliorate the decrease in global performance, we specify multiple regions in which we want accurate estimates for p(φ), and then combine the corresponding estimates of r(φ nu , φ de )…”

Section: Multiple Weighting Functionsmentioning

confidence: 99%

A numerically stable algorithm for integrating Bayesian models using Markov melding

Manderson,

Goudie

2020

Preprint

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When statistical analyses consider multiple data sources, Markov melding provides a method for combining the source-specific Bayesian models. Models often contain different quantities of information due to variation in the richness of model-specific data, or availability of model-specific prior information. We show that this can make the multi-stage Markov chain Monte Carlo sampler employed by Markov melding unstable and unreliable. We propose a robust multi-stage algorithm that estimates the required prior marginal self-density ratios using weighted samples, dramatically improving accuracy in the tails of the distribution, thus stabilising the algorithm and providing reliable inference. We demonstrate our approach using an evidence synthesis for inferring HIV prevalence, and an evidence synthesis of A/H1N1 influenza.

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“…While we have carried out some experiments testing such an estimator, the results are not presented here in favor of more generic methods. (Other estimators of are also possible; for example, Falk [35] develops a kernel estimator of for SRS, and Nakayama [36] considers another type of kernel estimator when using importance sampling. )…”

Section: 25mentioning

confidence: 99%

Advantages of variance reduction techniques in establishing confidence intervals for quantiles

Grabaskas

Nakayama

Denning

et al. 2016

Reliability Engineering & System Safety

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Over the past two decades, U.S. nuclear power plant regulation has increasingly depended on best-estimate plus uncertainty safety analyses. As a result of the shift to best-estimate analyses, the distribution of the output metric must be compared against a regulatory goal, rather than a single, conservative value. This comparison has historically been conducted using a 95% one-sided confidence interval for the 0.95-quantile of the output distribution, which is usually found following the technique of simple random sampling using order statistics (SRS-OS). While SRS-OS has certain statistical advantages, there are drawbacks related to the available sampling schemes and the accuracy and precision of the resulting value. Recent work has shown that it is possible to establish asymptotically valid confidence intervals for a quantile of the output of a model simulated using variance reduction techniques (VRTs). These VRTs can provide more informative results than SRS-OS. This work compares SRS-OS and the VRTs of antithetic variates and Latin hypercube sampling through several experiments, designed to replicate conditions found in nuclear safety analyses. This work is designed as an initial investigation into the use of VRTs as a tool to satisfy nuclear regulatory requirements, with hope of expanded analyses of VRTs in the future.

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Asymptotic properties of kernel density estimators when applying importance sampling

Cited by 8 publications

References 16 publications

Confidence Intervals for Quantiles Using Sectioning When Applying Variance-Reduction Techniques

Confidence Intervals for Quantiles Using Sectioning When Applying Variance-Reduction Techniques

A numerically stable algorithm for integrating Bayesian models using Markov melding

Advantages of variance reduction techniques in establishing confidence intervals for quantiles

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