Bayesian hierarchical Sample Clauses

Bayesian hierarchical spatial assessment of the bias in a multi-model ensemble This section describes the statistical model used in Arisido et al. (2017a). The reader is referred to Xxxxxxx et al. (2017a) and to PREFACE-MS34 for additional details about the rationale of the approach and for illustrative examples. Here, we only provide a few technical notes on the general approach. The model is aimed at obtaining a statistical representation of climate model biases in a multi-model ensemble to separate an overall common bias from the individual components. Climate model bias is determined by comparing output data against observations. We let Y(s) to represent the temperature observations and Xj(s) to denote the temperature simulated by the climate model j in an ensemble of Q models, at the spatial location s ∈ D for the domain D in R2. Empirical climate model biases are then calculated as Bj(s) =Y(s) - Xj(s); j = 1, ..., Q, where Bj(s) denotes the bias of climate model j relative to the observations at spatial location s. For n sites in D, we observe the biases, namely {Bj(si), ..., Bj(sn)}. The Bayesian hierarchical model is formulated based on three levels: data, process, and parameters (Xxxxxxxx et al., 2003, see also (1.1)). The data model captures the information given in the form of empirically measured biases, conditional on a hidden spatial bias process. The process level models the spatial structure and links the hidden spatial process to a set of parameters. In the parameter model, prior distributions are specified for the parameters. The three levels are specified in terms of probability distributions in a hierarchical structure shown in (a-c) of section 1.1 in this report.