On Estimating Non-standard Discrete Distributions Using Adaptive MCMC Methods

In this paper, we compare empirically the performance of some adaptive MCMC methods, that is, Adaptive Metropolis (AM) algorithm, Single Component Adaptive Metropolis (SCAM) algorithm and Delayed Rejection Adaptive Metropolis (DRAM) algorithm. The context is the simulation of non-standard discrete distributions. The performance criterion used is the precision of the frequency estimator. An application to a Bayesian hypothesis testing problem shows the superiority of the DRAM algorithm over the other considered sampling schemes.

Calibrating a wetland methane emission model with hierarchical modeling and adaptive MCMC

Methane (CH4) emission estimation for natural wetlands is complex and the estimates contain large uncertainties. The models used for the task are typically heavily parametrized and the parameter values are not well known. In this study we perform a Bayesian model calibration for a new wetland CH4 model to improve quality of the predictions and to understand the limitations of such models. The detailed process model that we analyze contains descriptions for CH4 production from anaerobic respiration, CH4 oxidation, and gas transportation by diffusion, ebullition, and the aerenchyma cells of vascular plants. The processes are controlled by several tunable parameters. We use a hierarchical statistical model to describe the parameters and obtain the posterior distributions of the parameters and uncertainties in the processes with adaptive MCMC techniques. For the estimation, the analysis utilizes measurement data from the Siikaneva flux measurement site in Southern Finland. The model parameters are calibrated using six different modeled peat column depths, and the hierarchical modeling allows us to assess the effect of the parameters on an annual basis. The results of the calibration and their cross validation suggest that the early spring net primary production and soil temperatures could be used to predict the annual methane emissions. The modeled peat column depth has an effect on how much the plant transport pathway dominates the gas transport, and the optimization moved most of the gas transport from the diffusive pathway to plant transport. This is in line with other research, highlighting the usefulness of algorithmic calibration of biogeochemical models. Modeling only 70 cm of the peat column gives the best flux estimates at the flux measurement site, while the estimates are worse for a column deeper than one meter or shallower than 50 cm. The posterior parameter distributions depend on the modeled peat depth. At the process level, the flux measurement data is able to constrain CH4 production and gas transport processes, but for CH4 oxidation, which is an important constituent of the total CH4 emission, the determining parameter is not identifiable.