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            	{"first" : "Hoshin V.",	"last" : "Gupta"},
            	{"first" : "Uwe",	"last" : "Ehret"},
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         "volume": "26","number": "5","abstract": "Using information-theoretic quantities in practical applications with continuous data is often hindered by the fact that probability density functions need to be estimated in higher dimensions, which can become unreliable or even computationally unfeasible. To make these useful quantities more accessible, alternative approaches such as binned frequencies using histograms and k-nearest neighbors (k-NN) have been proposed. However, a systematic comparison of the applicability of these methods has been lacking. We wish to fill this gap by comparing kernel-density-based estimation (KDE) with these two alternatives in carefully designed synthetic test cases. Specifically, we wish to estimate the information-theoretic quantities: entropy, Kullback\u2013Leibler divergence, and mutual information, from sample data. As a reference, the results are compared to closed-form solutions or numerical integrals. We generate samples from distributions of various shapes in dimensions ranging from one to ten. We evaluate the estimators\u2019 performance as a function of sample size, distribution characteristics, and chosen hyperparameters. We further compare the required computation time and specific implementation challenges. Notably, k-NN estimation tends to outperform other methods, considering algorithmic implementation, computational efficiency, and estimation accuracy, especially with sufficient data. This study provides valuable insights into the strengths and limitations of the different estimation methods for information-theoretic quantities. It also highlights the significance of considering the characteristics of the data, as well as the targeted information-theoretic quantity when selecting an appropriate estimation technique. These findings will assist scientists and practitioners in choosing the most suitable method, considering their specific application and available data. We have collected the compared estimation methods in a ready-to-use open-source Python 3 toolbox and, thereby, hope to promote the use of information-theoretic quantities by researchers and practitioners to evaluate the information in data and models in various disciplines.",
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         "description" : "The comprehensive differential split-sample test: A stress-test for hydrological model robustness under climate variability - ScienceDirect",
         "date" : "2024-01-23 17:02:29",
         "changeDate" : "2024-01-23 17:02:29",
         "count" : 4,
         "pub-type": "article",
         "journal": "Journal of Hydrology",
         "year": "2019", 
         "url": "https://www.sciencedirect.com/science/article/pii/S0022169419302835", 
         
         "author": [ 
            "D.F. Motavita","R. Chow","A. Guthke","W. Nowak"
         ],
         "authors": [
         	
            	{"first" : "D.F.",	"last" : "Motavita"},
            	{"first" : "R.",	"last" : "Chow"},
            	{"first" : "A.",	"last" : "Guthke"},
            	{"first" : "W.",	"last" : "Nowak"}
         ],
         "volume": "573","pages": "501-515","abstract": "The choice of data periods for calibrating and evaluating conceptual hydrological models often seems ad-hoc, with no objective guidance on choosing calibration periods that produce the most reliable predictions. We therefore propose to systematically investigate the effects of calibration and validation data choices on parameter identification and predictive performance. We demonstrate our analysis on the Deggendorf/Kollbach catchment in Bavaria, Germany, for its long series of continuous hydrological and meteorological records. After classifying these data into three hydrological conditions (wet, dry and mixed) and combining them into periods of varied data length (2, 4, 8, 15, 20 and 25\u202Fyears), we repeatedly calibrate a conceptual rainfall runoff hydrological model \u2013 Hydrologiska Byråns Vattenbalansavdelning (HBV) to these distinct data sets via Bayesian updating in a Monte Carlo setting. Then, we analyze predictive performance and posterior parameter statistics in various validation periods of distinct hydrological condition and time-series length. We call this the Comprehensive Differential Split-Sample Test (CDSST). Our results suggest that hydrological conditions in calibration tend to have a stronger impact than time-series length, and that calibrating on dry conditions might be a robust choice when aiming at predicting arbitrary future conditions (wet, dry or mixed). Furthermore, we found that posterior parameter estimates converged to a common optimum range with increasing data size under all investigated calibration scenarios, indicating that compensation of model structural errors by parameter fitting is independent of the chosen calibration condition. However, calibrating on time-series 8\u202Fyears or longer led to overconfident predictions that failed to reliably envelope future data. While these findings are specific to our case study, we recommend using the CDSST to stress-test conceptual hydrological models to identify robust model parameters and/or deficiencies in the model structure. In general, we expect our proposed approach to be a valuable basis for model error diagnosis in any type of dynamic environmental system model, because it answers the following three questions: (1) what is the importance of physical processes not explicitly covered by the model? (2) How much overconfidence is present in the model? And (3), what are case-specific recommendations for appropriate calibration and validation setups?",
         "issn" : "0022-1694",
         
         "doi" : "https://doi.org/10.1016/j.jhydrol.2019.03.054",
         
         "bibtexKey": "motavita2019comprehensive"

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         "journal": "Water Resources Research",
         "year": "2012", 
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         "author": [ 
            "Anneli Schöniger","W. Nowak","H. J. Hendricks Franssen"
         ],
         "authors": [
         	
            	{"first" : "Anneli",	"last" : "Schöniger"},
            	{"first" : "W.",	"last" : "Nowak"},
            	{"first" : "H. J. Hendricks",	"last" : "Franssen"}
         ],
         "volume": "48","number": "W04502",
         "doi" : "10.1029/2011WR010462 (was the top cited 2012 WRR article in 2013)",
         
         "bibtexKey": "Schoeniger_al_2011WRR_tEnKF"

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         "label" : "Model selection on solid ground: rigorous comparison of nine ways to evaluate Bayesian evidence",
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         "journal": "Water Resources Research",
         "year": "2014", 
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         "author": [ 
            "A. Schöniger","T. Wöhling","L. Samaniego","W. Nowak"
         ],
         "authors": [
         	
            	{"first" : "A.",	"last" : "Schöniger"},
            	{"first" : "T.",	"last" : "Wöhling"},
            	{"first" : "L.",	"last" : "Samaniego"},
            	{"first" : "W.",	"last" : "Nowak"}
         ],
         "volume": "50","number": "12","pages": "9484-9513",
         "doi" : "10.1002/2014WR016062",
         
         "bibtexKey": "Schoeniger_al_2014_rigorous_BME"

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         "label" : "Bayesian model averaging to explore the worth of data for soil-plant model selection and prediction",
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         "journal": "Water Resources Research","publisher":"Wiley",
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            "Thomas Wöhling","Anneli Schöniger","Sebastian Gayler","Wolfgang Nowak"
         ],
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            	{"first" : "Anneli",	"last" : "Schöniger"},
            	{"first" : "Sebastian",	"last" : "Gayler"},
            	{"first" : "Wolfgang",	"last" : "Nowak"}
         ],
         "volume": "51","number": "4","pages": "2825-2846",
         "research-areas" : "Environmental Sciences & Ecology; Marine & Freshwater Biology; Water Resources",
         
         "language" : "eng",
         
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         "affiliation" : "Wohling, T (Reprint Author), Univ Tubingen, Inst Geosci, Water & Earth Syst Sci WESS Competence Cluster, Tubingen, Germany.\r\n   Woehling, Thomas; Gayler, Sebastian, Univ Tubingen, Inst Geosci, Water & Earth Syst Sci WESS Competence Cluster, Tubingen, Germany.\r\n   Woehling, Thomas, Lincoln Agritech Ltd, Ruakura Res Ctr, Hamilton, New Zealand.\r\n   Schoeniger, Anneli, Univ Tubingen, Ctr Appl Geosci, Tubingen, Germany.\r\n   Nowak, Wolfgang, Univ Stuttgart, Inst Modelling Hydraul & Environm Syst LH3 SimTec, D-70174 Stuttgart, Germany.",
         
         "unique-id" : "ISI:000354733500054",
         
         "doi" : "10.1002/2014WR016292",
         
         "bibtexKey": "wohling2015bayesian"

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         ],
         "volume": "51","number": "9","pages": "7524-7546",
         "research-areas" : "Environmental Sciences & Ecology; Marine & Freshwater Biology; Water\r\n   Resources",
         
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         "affiliation" : "Schoniger, A (Reprint Author), Univ Tubingen, Ctr Appl Geosci, Tubingen, Germany.\r\n   Schoeniger, Anneli, Univ Tubingen, Ctr Appl Geosci, Tubingen, Germany.\r\n   Woehling, Thomas, Univ Tubingen, WESS Competence Cluster, Tubingen, Germany.\r\n   Woehling, Thomas, Lincoln Agritech Ltd, Lincoln Environm Res, Hamilton, New Zealand.\r\n   Nowak, Wolfgang, Univ Stuttgart, Inst Modelling Hydraul & Environm Syst LS3, SimTech, D-70174 Stuttgart, Germany.",
         
         "unique-id" : "ISI:000363391300034",
         
         "doi" : "10.1002/2015WR016918",
         
         "bibtexKey": "schoniger2015statistical"

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         "label" : "Finding the Right Balance Between Groundwater Model Complexity and Experimental Effort via Bayesian Model Selection",
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         "date" : "2024-01-23 16:52:13",
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         "pub-type": "article",
         "journal": "Journal of Hydrology",
         "year": "2015", 
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         "author": [ 
            "Anneli Schöniger","W. Illman","T. Wöhling","W. Nowak"
         ],
         "authors": [
         	
            	{"first" : "Anneli",	"last" : "Schöniger"},
            	{"first" : "W.",	"last" : "Illman"},
            	{"first" : "T.",	"last" : "Wöhling"},
            	{"first" : "W.",	"last" : "Nowak"}
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         "volume": "531","number": "1","pages": "96-110",
         "doi" : "10.1016/j.jhydrol.2015.07.047",
         
         "bibtexKey": "Schoeniger2015"

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         "label" : "Bayesian Model Selection Helps To Choose Objectively between Thermodynamic Models: A Demonstration of Selecting a Viscosity Model Based on Entropy Scaling",
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         "pub-type": "article",
         "journal": "Industrial & engineering chemistry research","publisher":"American Chemical Society",
         "year": "2016", 
         "url": "", 
         
         "author": [ 
            "Oliver Lötgering-Lin","Anneli Schöniger","Wolfgang Nowak","Joachim Groß"
         ],
         "authors": [
         	
            	{"first" : "Oliver",	"last" : "Lötgering-Lin"},
            	{"first" : "Anneli",	"last" : "Schöniger"},
            	{"first" : "Wolfgang",	"last" : "Nowak"},
            	{"first" : "Joachim",	"last" : "Groß"}
         ],
         "volume": "55","number": "38","pages": "10191-10207",
         "research-areas" : "Engineering",
         
         "language" : "eng",
         
         "researcherid-numbers" : "Gross, Joachim/B-9633-2017",
         
         "issn" : "0888-5885",
         
         "affiliation" : "Gross, J (Reprint Author), Univ Stuttgart, Inst Thermodynam & Thermal Proc Engn, Pfaffenwaldring 9, D-70569 Stuttgart, Germany.\r\n   Loetgering-Lin, Oliver; Gross, Joachim, Univ Stuttgart, Inst Thermodynam & Thermal Proc Engn, Pfaffenwaldring 9, D-70569 Stuttgart, Germany.\r\n   Schoeniger, Anneli, Univ Tubingen, Ctr Appl Geosci, Holderlinstr 12, D-72074 Tubingen, Germany.\r\n   Nowak, Wolfgang, Univ Stuttgart, Inst Modelling Hydraul & Environm Syst SimTech LS, Pfaffenwaldring 5a, D-70569 Stuttgart, Germany.",
         
         "orcid-numbers" : "Gross, Joachim/0000-0001-8632-357X\r\n   Guthke (geb. Schoniger), Anneli/0000-0003-2901-1603",
         
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   ]
}
