DRclass - Consider Ambiguity in Probabilistic Descriptions Using Density Ratio Classes

Consider ambiguity in probabilistic descriptions by replacing a parametric probabilistic description of uncertainty by a non-parametric set of probability distributions in the form of a Density Ratio Class. This is of particular interest in Bayesian inference. The Density Ratio Class is particularly suited for this purpose as it is invariant under Bayesian inference, marginalization, and propagation through a deterministic model. Here, invariant means that the result of the operation applied to a Density Ratio Class is again a Density Ratio Class. In particular the invariance under Bayesian inference thus enables iterative learning within the same framework of Density Ratio Classes. The use of imprecise probabilities in general, and Density Ratio Classes in particular, lead to intervals of characteristics of probability distributions, such as cumulative distribution functions, quantiles, and means. The package is based on a sample of the distribution proportional to the upper bound of the class. Typically this will be a sample from the posterior in Bayesian inference. Based on such a sample, the package provides functions to calculate lower and upper class boundaries and lower and upper bounds of cumulative distribution functions, and quantiles. Rinderknecht, S.L., Albert, C., Borsuk, M.E., Schuwirth, N., Kuensch, H.R. and Reichert, P. (2014) "The effect of ambiguous prior knowledge on Bayesian model parameter inference and prediction." Environmental Modelling & Software. 62, 300-315, 2014. <doi:10.1016/j.envsoft.2014.08.020>. Sriwastava, A. and Reichert, P. "Robust Bayesian Estimation of Value Function Parameters using Imprecise Priors." Submitted. <https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4973574>.

Last updated 3 days ago

1.00 score

timedeppar - Infer Constant and Stochastic, Time-Dependent Model Parameters

Infer constant and stochastic, time-dependent parameters to consider intrinsic stochasticity of a dynamic model and/or to analyze model structure modifications that could reduce model deficits. The concept is based on inferring time-dependent parameters as stochastic processes in the form of Ornstein-Uhlenbeck processes jointly with inferring constant model parameters and parameters of the Ornstein-Uhlenbeck processes. The package also contains functions to sample from and calculate densities of Ornstein-Uhlenbeck processes. References: Tomassini, L., Reichert, P., Kuensch, H.-R. Buser, C., Knutti, R. and Borsuk, M.E. (2009), A smoothing algorithm for estimating stochastic, continuous-time model parameters and its application to a simple climate model, Journal of the Royal Statistical Society: Series C (Applied Statistics) 58, 679-704, <doi:10.1111/j.1467-9876.2009.00678.x> Reichert, P., and Mieleitner, J. (2009), Analyzing input and structural uncertainty of nonlinear dynamic models with stochastic, time-dependent parameters. Water Resources Research, 45, W10402, <doi:10.1029/2009WR007814> Reichert, P., Ammann, L. and Fenicia, F. (2021), Potential and challenges of investigating intrinsic uncertainty of hydrological models with time-dependent, stochastic parameters. Water Resources Research 57(8), e2020WR028311, <doi:10.1029/2020WR028311> Reichert, P. (2022), timedeppar: An R package for inferring stochastic, time-dependent model parameters, in preparation.

Last updated 2 years ago

1.00 score 3 scripts 228 downloads