# Applications of Bayesian Sensitivity and Uncertainty Analysis to the Statistical Analysis of Computer Simulators for Carbon Dynamics

Uncertainties about the dynamics of carbon in forest ecosystems have a major impact on defining and verifying policies, as is evident from the difficulties in ratifying the Kyoto protocol. Quantifying and reducing this uncertainty requires the combination of mathematical models for ecological processes, and earth observation data, within a unifying statistical framework. The Centre for Terrestrial Carbon Dynamics (CTCD) is developing several computer codes to simulate the relevant processes at different spatial and temporal scales. Inputs to theses codes at a given site describe the characteristics of the vegetation grown there. Soil and climate data are also used to drive the model. My talk will illustrate the use of efficient Bayesian tools both in the development of these codes and in their use for prediction and uncertainty reduction. The first step is to build an emulator of the computer code. The emulator is a statistical representation of the code output based on a Gaussian process prior model. From this we can derive inferences about a range of sensitivity and uncertainty measures: Sensitivity analysis is performed to find out the level of influence each input or group of inputs have on the output. This can lead to efficiency gains by revealing inactive inputs. Examination of the expected response curve of the output as a function of individual inputs has also uncovered a number of coding errors. Uncertainty analysis is employed to assess the uncertainty in the prediction resulting from the various uncertain input conditions. It also tells us where to concentrate research effort in reducing uncertainties in inputs if we want to reduce the total uncertainty in the output. Conventional approaches to sensitivity analysis and uncertainty analysis involve Monte Carlo sampling of code outputs. This is highly inefficient and is not feasible for complex models. Bayesian methods can reduce the required number of simulator runs by several orders of magnitude. I will also mention some extensions to the methodology that are being developed to handle the dynamic and multivariate nature of the CTCD vegetation models.

*Author: Marc Kennedy, University Of Sheffield*