Session 8

Group Discussion

Practicals

INLA

The integrated nested Laplace approximation (INLA) is a method for approximate Bayesian inference. It is a faster alternative to Markov chain Monte Carlo, available via the R-INLA package.

Communication

Key things to report in a paper

  1. The data
    • methods, key observational uncertainties
  2. The model
    • \(f\) function(s), \(x\) variables, \(\theta\) parameters
  3. Priors
    • All parameters or a subset? What joint probability distribution did you assign? What information did you use to quantify it: literature, personal judgment, expert elicitation?
  4. Likelihood function
    • what likelihood function did you assign? How did you account for stochastic, systematic and representativeness errors?
  5. MCMC
    • Which algorithm did you use? How many chains and iterations? How did you assess convergence?
  6. Posterior distribution for the parameters
    • What were posterior modes, means, variances and major correlations? How different was the posterior from the prior?
  7. Posterior predictions
    • when using the posterior probability distribution for the parameters, how well did the model(a) reproduce data used in the calibration, (b) predict data not used in the calibration?

See Chapter 11 in Oijen, M. van. (2020). Bayesian Compendium. Springer International Publishing.

Isotopes

SIBER: Stable Isotope Bayesian Ellipses in R

BACON: Radiocarbon Isotope Age-Depth Modelling using Bayesian Statistics

Bayesian Software Decision Tree

BayesianSoftware_DecisionTree

Example papers reporting Bayesian methods

Levy, P., Drewer, J., Jammet, M., Leeson, S., Friborg, T., Skiba, U., & Oijen, M. van. (2020). Inference of spatial heterogeneity in surface fluxes from eddy covariance data: A case study from a subarctic mire ecosystem. Agricultural and Forest Meteorology, 280, 107783. https://doi.org/10.1016/j.agrformet.2019.107783

Levy, P. E., Cowan, N., van Oijen, M., Famulari, D., Drewer, J., & Skiba, U. (2017). Estimation of cumulative fluxes of nitrous oxide: Uncertainty in temporal upscaling and emission factors. European Journal of Soil Science, 68(4), 400–411. https://doi.org/10.1111/ejss.12432

Levy, P. E., & the COSMOS-UK team. (2024). Mapping soil moisture across the UK: Assimilating cosmic-ray neutron sensors, remotely sensed indices, rainfall radar and catchment water balance data in a Bayesian hierarchical model. Hydrology and Earth System Sciences, 28(21), 4819–4836. https://doi.org/10.5194/hess-28-4819-2024

Levy, P., van Oijen, M., Buys, G., & Tomlinson, S. (2018). Estimation of gross land-use change and its uncertainty using a Bayesian data assimilation approach. Biogeosciences, 15(5), 1497–1513. https://doi.org/10.5194/bg-15-1497-2018

Ramsden, A. E., Ganesan, A. L., Western, L. M., Rigby, M., Manning, A. J., Foulds, A., France, J. L., Barker, P., Levy, P., Say, D., Wisher, A., Arnold, T., Rennick, C., Stanley, K. M., Young, D., & O’Doherty, S. (2021). Quantifying fossil fuel methane emissions using observations of atmospheric ethane and an uncertain emission ratio. Atmospheric Chemistry and Physics Discussions, 1–28. https://doi.org/10.5194/acp-2021-734

Van Oijen, M., & Thomson, A. (2010). Toward Bayesian uncertainty quantification for forestry models used in the United Kingdom Greenhouse Gas Inventory for land use, land use change, and forestry. Climatic Change, 103(1–2), 55–67. https://doi.org/10.1007/s10584-010-9917-3

Wang, Y.-S., Chu, C.-J., Zhu, K., & Shen, Z.-H. (2011). Effects of inter-specific variability on biomass allocation: A hierarchical Bayesian approach. Ecological Informatics, 6(6), 341–344. https://doi.org/10.1016/j.ecoinf.2011.08.003



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