Bayesian source detection and parameter estimation of a plume model based on sensor network measurements' by C. Huang et al.: Discussion 3
The underlying problem addressed by this paper is the interpretation of data from a sensor network, which in this specific case is a sensor network intended to detect and track one or more plumes of hazardous material released by an explosion or accident. A data analyst with a background in data mining or machine learning would likely prefer to treat this as a problem of building a predictive model from training data. In other words, if data were available from sample plume releases, then the analyst would try to extract features from the data and use it to build a model that could predict the origin of the plume and its evolution over time. This would be a strictly data-driven approach that uses little if any of the underlying physical knowledge of how plumes of material disperse throughout the surrounding region. (However, such models might well apply techniques that take into account the spatio-temporal nature of the domain.) Given enough training data, there are significant advantages to such an approach in that the actual physics of a situation is often hard to model and thus simulation or analytical models of such phenomena are often difficult to construct and are only approximate.
In contrast, the approach taken by this paper is to adopt a physics-based analytical model for the diffusion of one or more plumes. Given an estimate of the model parameters, which must be derived from the data, the model is then capable of predicting the intensity of the plume at any location and time. The accuracy of this prediction will of course depend both on the accuracy of the model, which is known to be valid to some level, and the accuracy with which the parameters can be estimated. The parameters are estimated by using a Bayesian inference approach that chooses the parameters that maximize the likelihood function of the parameters given the data and an initial prior. More informally, the parameter estimates that are chosen are those that give the best statistical fit of the data to the model. This is accomplished by using a technique commonly employed for this purpose, namely the Markov Chain, Monte Carlo method. In contrast to a data mining or machine learning approach, knowledge of the physics of the situation must be incorporated, but no training data are needed. (It could however be helpful for determining prior probabilities.)
This approach can also be compared with a simulation approach. Such an approach is based on knowing the initial parameters of the plumes and then conducting a simulation where the evolution of the plumes is determined by using the current condition and the applicable physical laws to determine the conditions (concentration of the chemical, etc.) at the next time point. Such an approach can embody more detailed physical modeling since there is no necessity to obtain an analytical model whose parameters can be estimated from the data. However, these types of approaches are also approximations to some extent and are not guaranteed to produce more accurate results than simpler models. In addition, there is the challenge of initializing the simulation model from observed data.
From the above, it seems that each of the three approaches, data-driven data mining/machine learning, statistical estimation of the parameters of simple physical models, and physics-based Copyright q 2010 John Wiley & Sons, Ltd.