NDLI: A discrepancy bound for deterministic acceptance-rejection samplers beyond $$N^{-1/2}$$ in dimension 1

Content Provider	Springer Nature Link
Author	Zhu, Houying Dick, Josef
Copyright Year	2016
Abstract	In this paper we consider an acceptance-rejection (AR) sampler based on deterministic driver sequences. We prove that the discrepancy of an N element sample set generated in this way is bounded by $$\mathcal {O} (N^{-2/3}\log N)$$ , provided that the target density is twice continuously differentiable with non-vanishing curvature and the AR sampler uses the driver sequence $$\mathcal {K}_M= \{( j \alpha , j \beta ) ~~ mod~~1 \mid j = 1,\ldots ,M\},$$ where $$\alpha ,\beta $$ are real algebraic numbers such that $$1,\alpha ,\beta $$ is a basis of a number field over $$\mathbb {Q}$$ of degree 3. For the driver sequence $$\mathcal {F}_k= \{ ({j}/{F_k}, \{{jF_{k-1}}/{F_k}\} ) \mid j=1,\ldots , F_k\},$$ where $$F_k$$ is the k-th Fibonacci number and $$\{x\}=x-\lfloor x \rfloor $$ is the fractional part of a non-negative real number x, we can remove the $$\log $$ factor to improve the convergence rate to $$\mathcal {O}(N^{-2/3})$$ , where again N is the number of samples we accepted. We also introduce a criterion for measuring the goodness of driver sequences. The proposed approach is numerically tested by calculating the star-discrepancy of samples generated for some target densities using $$\mathcal {K}_M$$ and $$\mathcal {F}_k$$ as driver sequences. These results confirm that achieving a convergence rate beyond $$N^{-1/2}$$ is possible in practice using $$\mathcal {K}_M$$ and $$\mathcal {F}_k$$ as driver sequences in the acceptance-rejection sampler.
Starting Page	901
Ending Page	911
Page Count	11
File Format	PDF
ISSN	09603174
Journal	Statistics and Computing
Volume Number	27
Issue Number	4
e-ISSN	15731375
Language	English
Publisher	Springer US
Publisher Date	2016-05-18
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Acceptance-rejection sampler Discrepancy Fibonacci lattice points Integration error Statistics and Computing/Statistics Programs Artificial Intelligence (incl. Robotics) Statistical Theory and Methods Probability and Statistics in Computer Science
Content Type	Text
Resource Type	Article
Subject	Statistics and Probability Theoretical Computer Science Computational Theory and Mathematics Statistics, Probability and Uncertainty

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

A Discrepancy Bound for Deterministic Acceptance-Rejection Samplers Beyond $N^{-1/2}$ in Dimension 1

A Discrepancy Bound for a Deterministic Acceptance-Rejection Sampler

Discrepancy Bounds for Deterministic Acceptance-Rejection Samplers∗

Transformed density rejection with inflection points

Adaptive independence samplers

Deterministic versus stochastic seasonal fractional integration and structural breaks

On sequential Monte Carlo, partial rejection control and approximate Bayesian computation

A generalization of the adaptive rejection sampling algorithm

A regularized bridge sampler for sparsely sampled diffusions

A discrepancy bound for deterministic acceptance-rejection samplers beyond $$N^{-1/2}$$ in dimension 1

Similar Documents

A Discrepancy Bound for Deterministic Acceptance-Rejection Samplers Beyond $N^{-1/2}$ in Dimension 1

A Discrepancy Bound for a Deterministic Acceptance-Rejection Sampler

Discrepancy Bounds for Deterministic Acceptance-Rejection Samplers∗

Transformed density rejection with inflection points

Adaptive independence samplers

Deterministic versus stochastic seasonal fractional integration and structural breaks

On sequential Monte Carlo, partial rejection control and approximate Bayesian computation

A generalization of the adaptive rejection sampling algorithm

A regularized bridge sampler for sparsely sampled diffusions

A discrepancy bound for deterministic acceptance-rejection samplers beyond $$N^{-1/2}$$ in dimension 1