NDLI: Computing Bayesian Means Using Simulation

Content Provider	ACM Digital Library
Author	Andradóttir, Sigrún Glynn, Peter W.
Copyright Year	2016
Abstract	This article is concerned with the estimation of α = $\textit{E}{\textit{r}(\textit{Z})},$ where $\textit{Z}$ is a random vector and the function values $\textit{r}(\textit{z})$ must be evaluated using simulation. Estimation problems of this form arise in the field of Bayesian simulation, where $\textit{Z}$ represents the uncertain (input) parameters of a system and $\textit{r}(\textit{z})$ is the expected performance of the system when $\textit{Z}$ = $\textit{z}.$ Our approach involves obtaining (possibly biased) simulation estimates of the function values $\textit{r}(\textit{z})$ for a number of different values of $\textit{z},$ and then using a (possibly weighted) average of these estimates to estimate α. We start by considering the case where the chosen values of $\textit{z}$ are independent and identically distributed observations of the random vector $\textit{Z}$ (independent sampling). We analyze the resulting estimator as the total computational effort $\textit{c}$ grows and provide numerical results. Then we show that improved convergence rates can be obtained through the use of techniques other than independent sampling. Specifically, our results indicate that the use of quasi-random sequences yields a better convergence rate than independent sampling, and that in the presence of a suitable special structure, it may be possible to use other numerical integration techniques (such as Simpson’s rule) to achieve the best possible rate $\textit{c}™$ 1/2 as $\textit{c}$ → ∞. Finally, we present and analyze a general framework of estimators for α that encompasses independent sampling, quasi-random sequences, and Simpson’s rule as special cases.
Starting Page	1
Ending Page	26
Page Count	26
File Format	PDF
ISSN	10493301
e-ISSN	15581195
DOI	10.1145/2735631
Volume Number	26
Issue Number	2
Journal	ACM Transactions on Modeling and Computer Simulation (TOMACS)
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2016-01-13
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Bayesian simulation Simpson’s rule Bias Consistency Convergence rate Independent sampling Nested simulation Numerical integration Quasi-random numbers
Content Type	Text
Resource Type	Article
Subject	Computer Science Applications Modeling and Simulation

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

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