‘Bayesian source detection and parameter estimation of a plume model based on sensor network measurements’ by C. Huang et al.: Discussion 2

Abstract

Bayesian source detection and parameter estimation of a plume model based on sensor network measurements' by C. Huang et al.: Discussion 2The problem of source detection and parameter estimation for plume models based on sensor network measurements is timely and important. The authors are to be congratulated for going beyond the product-form model to a model motivated by an advection-diffusion PDE model. From a historical perspective, plumes have often been modeled using analytic solutions to various diffusion PDEs, leading to such formulations as the so-called Gaussian plume model (see Ermak [1], Lushi and Stokie [2], and the references therein). Relatively few efforts (by comparison) have been made to 'fit' these models from a rigorous statistical perspective and to perform statistical inference. Therefore, we believe that the authors' contribution is also rooted in raising the awareness of the statistics community to the problem of rigorously modeling plumes in the presence of uncertainty.In spite of the authors' careful and detailed coverage of the problem, there are a few places we believe that more extensive treatment/exposition might be illuminating. First, a more comprehensive simulation study would be informative. In this direction, there would be several avenues for extending the simulation (e.g. varying the spatial covariance, the design, and examining model mis-specification, among others). In the absence of a real data example, the simulations become critically important. In this case, it is unclear how effective the model will perform when applied to real sensor network data. In future research (by the authors and/or other researchers) we look forward to seeing the authors' model applied in practice.The authors suggest using an approximate (quasi-) likelihood, instead of the true likelihood, that may prove to be useful in extremely high dimensions. Although the simulation example presented does not necessitate such an approximation, real-world applications might require such approximations for real-time implementation. The approach, taken by the authors, assumes independent measurement errors and, as a result, produces an MCMC algorithm in which samples do not come from the 'target' distribution. Instead, samples are taken from a, potentially biased, approximation to the target distribution. Although this technique may be preferable from a purely computational efficiency perspective, it is philosophically appealing (and potentially more accurate) to use the exact likelihood. One possible alternative, that can be viewed as a compromise between the authors' approach and using the exact likelihood, would be to use a Whittle formulation [3]. In this context one would also avoid determinant calculations and matrix inversions.While the authors demonstrate the 'robustness' for their approximate approach, the simulation study is limited. The one MCMC simulation with 50 samples examines the independent measurement error case. Thus, in the future, it will be of interest to further investigate the accuracy of...