TY  - JOUR
A1  - Molkenthin, Christian
A1  - Donner, Christian
A1  - Reich, Sebastian
A1  - Zöller, Gert
A1  - Hainzl, Sebastian
A1  - Holschneider, Matthias
A1  - Opper, Manfred
T1  - GP-ETAS: semiparametric Bayesian inference for the spatio-temporal epidemic type aftershock sequence model
JF  - Statistics and Computing
N2  - The spatio-temporal epidemic type aftershock sequence (ETAS) model is widely used to describe the self-exciting nature of earthquake occurrences. While traditional inference methods provide only point estimates of the model parameters, we aim at a fully Bayesian treatment of model inference, allowing naturally to incorporate prior knowledge and uncertainty quantification of the resulting estimates. Therefore, we introduce a highly flexible, non-parametric representation for the spatially varying ETAS background intensity through a Gaussian process (GP) prior. Combined with classical triggering functions this results in a new model formulation, namely the GP-ETAS model. We enable tractable and efficient Gibbs sampling by deriving an augmented form of the GP-ETAS inference problem. This novel sampling approach allows us to assess the posterior model variables conditioned on observed earthquake catalogues, i.e., the spatial background intensity and the parameters of the triggering function. Empirical results on two synthetic data sets indicate that GP-ETAS outperforms standard models and thus demonstrate the predictive power for observed earthquake catalogues including uncertainty quantification for the estimated parameters. Finally, a case study for the l'Aquila region, Italy, with the devastating event on 6 April 2009, is presented.
KW  - Self-exciting point process
KW  - Hawkes process
KW  - Spatio-temporal ETAS model
KW  - Bayesian inference
KW  - Sampling
KW  - Earthquake modeling
KW  - Gaussian process
KW  - Data augmentation
Y1  - 2022
U6  - https://doi.org/10.1007/s11222-022-10085-3
SN  - 0960-3174
SN  - 1573-1375
VL  - 32
IS  - 2
PB  - Springer
CY  - Dordrecht
ER  - 
TY  - JOUR
A1  - Hempel, Sabrina
A1  - Adolphs, Julian
A1  - Landwehr, Niels
A1  - Janke, David
A1  - Amon, Thomas
T1  - How the selection of training data and modeling approach affects the estimation of ammonia emissions from a naturally ventilated dairy barn—classical statistics versus machine learning
JF  - Sustainability
N2  - Environmental protection efforts can only be effective in the long term with a reliable quantification of pollutant gas emissions as a first step to mitigation. Measurement and analysis strategies must permit the accurate extrapolation of emission values. We systematically analyzed the added value of applying modern machine learning methods in the process of monitoring emissions from naturally ventilated livestock buildings to the atmosphere. We considered almost 40 weeks of hourly emission values from a naturally ventilated dairy cattle barn in Northern Germany. We compared model predictions using 27 different scenarios of temporal sampling, multiple measures of model accuracy, and eight different regression approaches. The error of the predicted emission values with the tested measurement protocols was, on average, well below 20%. The sensitivity of the prediction to the selected training dataset was worse for the ordinary multilinear regression. Gradient boosting and random forests provided the most accurate and robust emission value predictions, accompanied by the second-smallest model errors. Most of the highly ranked scenarios involved six measurement periods, while the scenario with the best overall performance was: One measurement period in summer and three in the transition periods, each lasting for 14 days.
KW  - livestock
KW  - air pollutant
KW  - emission modeling
KW  - emission inventory
KW  - regression
KW  - artificial neural network
KW  - random forest
KW  - gradient boosting
KW  - Gaussian process
KW  - training sample
Y1  - 2020
U6  - https://doi.org/10.3390/su12031030
SN  - 2071-1050
VL  - 12
IS  - 3
PB  - MDPI
CY  - Basel
ER  - 
TY  - JOUR
A1  - Malem-Shinitski, Noa
A1  - Ojeda, Cesar
A1  - Opper, Manfred
T1  - Variational bayesian inference for nonlinear hawkes process with gaussian process self-effects
JF  - Entropy
N2  - Traditionally, Hawkes processes are used to model time-continuous point processes with history dependence. Here, we propose an extended model where the self-effects are of both excitatory and inhibitory types and follow a Gaussian Process. Whereas previous work either relies on a less flexible parameterization of the model, or requires a large amount of data, our formulation allows for both a flexible model and learning when data are scarce. We continue the line of work of Bayesian inference for Hawkes processes, and derive an inference algorithm by performing inference on an aggregated sum of Gaussian Processes. Approximate Bayesian inference is achieved via data augmentation, and we describe a mean-field variational inference approach to learn the model parameters. To demonstrate the flexibility of the model we apply our methodology on data from different domains and compare it to previously reported results.
KW  - Bayesian inference
KW  - point process
KW  - Gaussian process
Y1  - 2022
U6  - https://doi.org/10.3390/e24030356
SN  - 1099-4300
VL  - 24
IS  - 3
PB  - MDPI
CY  - Basel
ER  -