“…The key components of these models involve the specification of a distribution over a smooth random function (surface) with its mean surface representing the unknown HRTFs or HRIRs over a mesh of incident angles for a given anatomy configuration. In approaching the design of such a model, one must consider the spatial and temporal dependence features of the response: it is in this respect that we differ from the standard approach to such a problem, which involves separating the spatial and temporal dependences through a product space formulation, which is often common in machine learning and various applications of GP modeling, e.g., motion tracking modeling [14], modeling gas distribution [15], environmental surveillance [16], modeling MRI brain images [17], transcriptional landscape estimation [18], clustering gene expression [19], inter atomic potential models [20], and modeling of wire-cut electrical discharge machining(WEDM) [21] as discussed in [22,23]. In this paper, we consider the temporal and spatial features (co-variates) jointly in the covariance and mean functions.…”