TY  - JOUR
A1  - Rosenbaum, Benjamin
A1  - Raatz, Michael
A1  - Weithoff, Guntram
A1  - Fussmann, Gregor F.
A1  - Gaedke, Ursula
T1  - Estimating parameters from multiple time series of population dynamics using bayesian inference
JF  - Frontiers in ecology and evolution
N2  - Empirical time series of interacting entities, e.g., species abundances, are highly useful to study ecological mechanisms. Mathematical models are valuable tools to further elucidate those mechanisms and underlying processes. However, obtaining an agreement between model predictions and experimental observations remains a demanding task. As models always abstract from reality one parameter often summarizes several properties. Parameter measurements are performed in additional experiments independent of the ones delivering the time series. Transferring these parameter values to different settings may result in incorrect parametrizations. On top of that, the properties of organisms and thus the respective parameter values may vary considerably. These issues limit the use of a priori model parametrizations. In this study, we present a method suited for a direct estimation of model parameters and their variability from experimental time series data. We combine numerical simulations of a continuous-time dynamical population model with Bayesian inference, using a hierarchical framework that allows for variability of individual parameters. The method is applied to a comprehensive set of time series from a laboratory predator-prey system that features both steady states and cyclic population dynamics. Our model predictions are able to reproduce both steady states and cyclic dynamics of the data. Additionally to the direct estimates of the parameter values, the Bayesian approach also provides their uncertainties. We found that fitting cyclic population dynamics, which contain more information on the process rates than steady states, yields more precise parameter estimates. We detected significant variability among parameters of different time series and identified the variation in the maximum growth rate of the prey as a source for the transition from steady states to cyclic dynamics. By lending more flexibility to the model, our approach facilitates parametrizations and shows more easily which patterns in time series can be explained also by simple models. Applying Bayesian inference and dynamical population models in conjunction may help to quantify the profound variability in organismal properties in nature.
KW  - Bayesian inference
KW  - chemostat experiments
KW  - ordinary differential equation
KW  - parameter estimation
KW  - population dynamics
KW  - predator prey
KW  - time series analysis
KW  - trait variability
Y1  - 2019
U6  - https://doi.org/10.3389/fevo.2018.00234
SN  - 2296-701X
VL  - 6
PB  - Frontiers Research Foundation
CY  - Lausanne
ER  - 
TY  - JOUR
A1  - Savoy, Heather
A1  - Heße, Falk
T1  - Dimension reduction for integrating data series in Bayesian inversion of geostatistical models
JF  - Stochastic environmental research and risk assessment
N2  - This study explores methods with which multidimensional data, e.g. time series, can be effectively incorporated into a Bayesian framework for inferring geostatistical parameters. Such series are difficult to use directly in the likelihood estimation procedure due to their high dimensionality; thus, a dimension reduction approach is taken to utilize these measurements in the inference. Two synthetic scenarios from hydrology are explored in which pumping drawdown and concentration breakthrough curves are used to infer the global mean of a log-normally distributed hydraulic conductivity field. Both cases pursue the use of a parametric model to represent the shape of the observed time series with physically-interpretable parameters (e.g. the time and magnitude of a concentration peak), which is compared to subsets of the observations with similar dimensionality. The results from both scenarios highlight the effectiveness for the shape-matching models to reduce dimensionality from 100+ dimensions down to less than five. The models outperform the alternative subset method, especially when the observations are noisy. This approach to incorporating time series observations in the Bayesian framework for inferring geostatistical parameters allows for high-dimensional observations to be faithfully represented in lower-dimensional space for the non-parametric likelihood estimation procedure, which increases the applicability of the framework to more observation types. Although the scenarios are both from hydrogeology, the methodology is general in that no assumptions are made about the subject domain. Any application that requires the inference of geostatistical parameters using series in either time of space can use the approach described in this paper.
KW  - Geostatistics
KW  - Stochastic hydrogeology
KW  - Dimension reduction
KW  - Bayesian inference
Y1  - 2019
U6  - https://doi.org/10.1007/s00477-019-01697-9
SN  - 1436-3240
SN  - 1436-3259
VL  - 33
IS  - 7
SP  - 1327
EP  - 1344
PB  - Springer
CY  - New York
ER  -