Statistical Analysis of Hit/Miss Data (Preprint)

Abstract

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Bayesian methods in probability of detection estimation and model-assisted probability of detection evaluation

“…Lastly, there is need to better leverage model form uncertainty evaluation approaches. Recent work has demonstrated the benefits of using Bayes methods [13,19] to identify the best models and minimize issues associated with model discrepancy. …”

“…In practice, the posterior distribution can be evaluated, providing a refinement to the original prior distribution through numerical methods such as Markov Chain Monte Carlo (MCMC) simulation [7][8][9]. In prior work on NDE reliability, Bayesian methods have been generally proposed [10][11] with several examples for the evaluation of statistical POD models for hit-miss data [12][13] and ahat-versus-a reliability studies [14][15]. In particular, Bayesian methods are dvantageous for more complex can be quite useful to evaluate address complex estimation problems and when prior information is available.…”

Efficient finite element modelling of eddy current probability of detection with transmitter–receiver sensors

“…New approaches using Bayesian statistics are demonstrated e.g. under the condition that the POD will hit a limit below 100 % detection probability [38]. However, the transmitter-receiver system addressed here must be assumed to also have a lower POD at larger defect sizes.…”

Contributions to the design and analysis of nondestructive evaluation experiments

“…Rules of thumb for choosing one model over another based on Bayes Factors are provided in Kass and Raftery (1995) and are summarized in Table 2.2 below. From the results in Table 2.3, we conclude that Model D (the model suggested by Knopp and Zeng (2013) for their hit-miss dataset) would be a reasonable model for our hit-miss data. We will use this model in subsequent analyses.…”