Approximate Bayesian computation for censored data and its application to reliability assessment

ABSTRACT

Approximate Bayesian Computation (ABC) refers to a family of algorithms that perform Bayesian inference under intractable likelihoods. It is widely used to perform statistical inference on complex models. In this article, we propose using ABC for reliability analysis, and we extend the scope of ABC to encompass problems that involve censored data. We are motivated by the need to assess the reliability of nanoscale components in devices. This type of analysis is difficult to perform, due to the complex structure of nanodevices and limitations imposed by fabrication processes. A consequence is that failure data often include a high proportion of censored observations. We demonstrate that our proposed ABC algorithms perform well and produce accurate parameter estimates in this setting.

KEYWORDS:

• Approximate Bayesian computation
• censored data
• nanowire
• nanosensor
• summary statistic

Additional information

Notes on contributors

Kristin McCullough

Kristin McCullough is an assistant professor in the Division of Statistics at Northern Illinois University. She received her M.S. in applied mathematics and Ph.D. in statistics from Northern Illinois University. Her primary research interests are reliability theory, approximate Bayesian computations, and the applications of statistics to nanotechnology and nanoscience.

Nader Ebrahimi

Nader Ebrahimi is a professor of statistics in the Division of Statistics at Northern Illinois University. He received his M.S. from Shiraz University, Iran, and his Ph.D. from Iowa State University, Iowa. He works in the areas of reliability theory and survival analysis, information theoretic statistics and modeling and applications in hardware, nano and software engineering, and medical sciences.