Using Copula Functions in Bayesian Analysis: A Comparison of the Lognormal Conjugate

Abstract

Bayesian techniques have been applied to analyze sequential investment decisions in the capital budgeting literature. This article introduces copula-based Bayesian analysis as an alternative to the traditional approach where conjugate relationships do not exist. Using a numerical example, we illustrate the steps involved in the copula-based Bayesian approach. Graphical techniques for selecting an appropriate copula are also discussed. The unique ability of copulas to model nonlinear dependence rationalizes the use of copula functions as an alternative technique.

Acknowledgments

The authors thank the participants at the Engineering Economic Section of Industrial Engineering Research Conference (2012 and 2008) for their input on an earlier version of this article and an anonymous reviewer for valuable suggestions. The usual disclaimers apply.

Notes

The fitted distributions are the ones with lowest squared errors.

Additional information

Funding

Hemantha S. B. Herath acknowledges research funding from the Social Sciences and Humanities Research Council (SSHRC) of Canada (Grant No. 410-2009-1398).

Notes on contributors

Hemantha S. B. Herath

Hemantha S. B. Herath is a professor of managerial accounting at the Goodman School of Business, Brock University, Canada. Previously, he worked in the Oil and Gas Division of the World Bank, Washington, D.C. He is a recipient of a Fulbright Scholarship. He has published articles in a variety of journals, including Abacus, Journal of Accounting and Public Policy, Journal of Management Information Systems, Decision Support Systems, Advances in Management Accounting, and The Engineering Economist. His research interests include real option analysis, economics of information security, and managerial accounting. He is a two-time recipient (2008, 2001) of the Eugene L. Grant Best Paper Award from the American Society of Engineering Education. He serves on the Editorial Boards of The Engineering Economist and Journal of Financial Economic Policy. He is a member of Sigma Xi research honor society. His work has been funded by SSHRC Canada and other grants.

Pranesh Kumar

Pranesh Kumar, PhD, is the Professor of Statistics in the Department of Mathematics and Statistics, University of Northern British Columbia, Canada. Previously, he held faculty positions at several institutions namely the Memorial University of Newfoundland (Canada), University of Transkei (South Africa), Bilkent University (Turkey), University of Dar-es-Salaam (Tanzania), University of Roma-La Sapienza (Italy), and Indian Agricultural Statistics Research Institute (New Delhi). After earning his M.Sc. and Ph.D. from the Indian Agricultural Research Institute, Dr. Kumar's main professional interests were teaching and training in applied statistics and survey methodology and conducting research in sample survey methodology. He has authored or co-authored a large number of journal articles (128 research publications, 83 in peer-reviewed journals), technical reports, and reviews. He has been the recipient of research grants. Dr. Kumar is a regular reviewer for Mathematical Reviews and has refereed for a number of statistics, mathematics, and computer science journals. Dr. Kumar provided statistical consulting as well on the statistical designs, and statistical analysis of research studies and sample surveys to universities, international organizations (UN, WB, FAO, FINNIDA, SIDA), and industries. He is a member of several professional societies, including the International Statistical Institute and Statistical Society of Canada. He also serves as an associate editor and referee of many professional journals.