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Simultaneous Confidence Bands for Monte Carlo Simulations.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Simultaneous Confidence Bands for Monte Carlo Simulations./
作者:	Yang, Jinhui.
出版者:	Ann Arbor : ProQuest Dissertations & Theses, : 2021,
面頁冊數:	126 p.
附註:	Source: Dissertations Abstracts International, Volume: 83-02, Section: B.
Contained By:	Dissertations Abstracts International83-02B.
標題:	Statistics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=28495683
ISBN:	9798534695045

Simultaneous Confidence Bands for Monte Carlo Simulations.
Yang, Jinhui.

Simultaneous Confidence Bands for Monte Carlo Simulations. - Ann Arbor : ProQuest Dissertations & Theses, 2021 - 126 p.

Source: Dissertations Abstracts International, Volume: 83-02, Section: B.

Thesis (Ph.D.)--University of California, Riverside, 2021.

This item must not be sold to any third party vendors.

Markov Chain Monte Carlo (MCMC) methods are widely used and preferred when the sampling distribution is intractable. In estimation problems with Monte Carlo samples, it is critical to quantify uncertainty of estimators on some intervals since the true function could not be obtained in most cases. Traditional pointwise confidence intervals could provide certain coverage probability in a single point but fail to provide simultaneous coverage for the whole function without a multiplicity correction. The Bonferroni method corrects for multiplicity, but these conservative intervals do not achieve the desired nominal level. This dissertation focuses on providing and quantifying the uncertainty of estimators in the form of a confidence band (CB) to increase the reliability of the resulting inferences.We begin with MCMC basics and point estimation methods. Then we provide estimators for densities and general functions separately. We discuss the covariance matrix and Central Limit Theorem as preliminary settings. Afterwards, we review pointwise and Bonferroni methods to construct CBs. We propose three methods in calculating simultaneous CBs with theories and algorithms which are followed by examples to compare the coverage probabilities and the band widths. To provide more intuitive results, we compared the bands with three simulation examples: AR(1) model, mixed normal distribution, and a general function case. Then we used four real data examples: Michigan survey example, Telescope data example, time varying model, and a Bayesian reliability model to explain our proposed simultaneous bands.

ISBN: 9798534695045Subjects--Topical Terms:

517247
Statistics.
Subjects--Index Terms:

Confidence band

Simultaneous Confidence Bands for Monte Carlo Simulations.
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100 1 $a Yang, Jinhui. $3 3688949
245 1 0 $a Simultaneous Confidence Bands for Monte Carlo Simulations.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2021
300 $a 126 p.
500 $a Source: Dissertations Abstracts International, Volume: 83-02, Section: B.
500 $a Advisor: Flegal, James.
502 $a Thesis (Ph.D.)--University of California, Riverside, 2021.
506 $a This item must not be sold to any third party vendors.
520 $a Markov Chain Monte Carlo (MCMC) methods are widely used and preferred when the sampling distribution is intractable. In estimation problems with Monte Carlo samples, it is critical to quantify uncertainty of estimators on some intervals since the true function could not be obtained in most cases. Traditional pointwise confidence intervals could provide certain coverage probability in a single point but fail to provide simultaneous coverage for the whole function without a multiplicity correction. The Bonferroni method corrects for multiplicity, but these conservative intervals do not achieve the desired nominal level. This dissertation focuses on providing and quantifying the uncertainty of estimators in the form of a confidence band (CB) to increase the reliability of the resulting inferences.We begin with MCMC basics and point estimation methods. Then we provide estimators for densities and general functions separately. We discuss the covariance matrix and Central Limit Theorem as preliminary settings. Afterwards, we review pointwise and Bonferroni methods to construct CBs. We propose three methods in calculating simultaneous CBs with theories and algorithms which are followed by examples to compare the coverage probabilities and the band widths. To provide more intuitive results, we compared the bands with three simulation examples: AR(1) model, mixed normal distribution, and a general function case. Then we used four real data examples: Michigan survey example, Telescope data example, time varying model, and a Bayesian reliability model to explain our proposed simultaneous bands.
590 $a School code: 0032.
650 4 $a Statistics. $3 517247
650 4 $a Telescopes. $3 539024
650 4 $a Simulation. $3 644748
650 4 $a Regression analysis. $3 529831
650 4 $a Random variables. $3 646291
650 4 $a Normal distribution. $3 3561025
650 4 $a Independent sample. $3 3681910
650 4 $a Probability. $3 518898
650 4 $a Methods. $3 3560391
650 4 $a Time series. $3 3561811
650 4 $a Confidence intervals. $3 566017
650 4 $a Markov analysis. $3 3562906
650 4 $a Bias. $2 gtt $3 1374837
653 $a Confidence band
653 $a Confidence interval
653 $a Density estimation
653 $a Function estimation
653 $a Markov chain
653 $a Monte carlo
690 $a 0463
710 2 $a University of California, Riverside. $b Applied Statistics. $3 1676131
773 0 $t Dissertations Abstracts International $g 83-02B.
790 $a 0032
791 $a Ph.D.
792 $a 2021
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=28495683