# Overview of Case Studies
<!--
The following articles provide a selection of current research topics from PhD students who participate in the *Uncertainty Quantification* project. Hence, the content is quite different and sheds light on the sources and impacts of UQ from various perspectives. Furthermore, field-specific methods for dealing with UQ are presented and will link to the corresponding articles of interest.
-->
The PhD students who participate in the *Uncertainty Quantification* project write articles about their current research topics. Due to the wide range of topics and relations with UQ, we have assembled these articles into case studies. Each such case study sheds light on sources and impacts of UQ on the particular field, presents field-specific methods for dealing with UQ and provides link to further readings. The following list consists of a brief description of every case study and the link to its main article:


<!--
- [Tackling the numerous uncertainties regarding Covid-19](mixture_of_finite_polya_trees_model.md) -->
<!--
- Seismic tomography is a geophysical technique to illuminate the Earth's structure and understand its subsurface properties. However, the inherent uncertainty which arises from ill-posed nature of the geophysical inverse problem may potentially make ambiguous inferences about the Earth's structure. In this case study, we present how do we deal with [uncertainty in seismic tomography](UQinSI.md).
-->
- [Uncertainty in seismic tomography](UQinSI.md) is often a result of ill-posed inverse problems, which oppose reliable inference about the Earth's structure.
<!--
- We envision the [energy system of the future](energy_systems_intro.md) to be sustainable, reliable, and affordable. However, sustainable energy systems with large shares of renewables are subject to major uncertainties in renewable energy generation.
-->
- The vision of sustainable, reliable, and affordable [energy system of the future](energy_systems_intro.md) is subject to major uncertainties with respect to renewable energy generation.
<!--
- Due to large complexity of modern climate models it is important to perform uncertainty quantification in an efficient manner. The exponentially growing costs of the ensemble approach can be reduced by [efficient Monte Carlo methods for the global climate models](uq_in_ESM.md) with a focus on Ozone holes.
-->

- [Efficient Monte Carlo methods](uq_in_ESM.md) are a promising deal to solve the exponential costs of uncertainty quantification in global climate models.
<!--
- Marine biogeochemical (BGC) models are highly uncertain in their parameterization. The value of the BGC parameters are poorly known and lead to large uncertainties in the model outputs. This project focuses on the [uncertainty quantification for ocean biogeochemical models](uq_obgc_models.md) applying data assimilation. Data assimilation is a method of combining observations and numerical model outputs to perform better analysis of underlying phenomena.
-->
- Data assimilation may help do grasp the underlying phenomena behind [parameter uncertainty in biogeochemical (BGC) models](uq_obgc_models.md).

<!--
- The biocompatibility and biodegradability of magnesium alloys make them highly attractive as temporary implant materials. But the development process of magnesium (Mg) based biodegradable implants requires labor-intensive and costly studies. The establishment of reliable computational models can assist in enabling predictability, however, the complex multiphysics nature of the existing models and their high computational costs make estimating and calibrating different model parameters one of the main challenges in the model development process. [Quantifying uncertainties in degradation models](uq_implants_materials.md) can be accomplished by identifying various sources of uncertainty within the model and characterized based on their inputs.
-->
- [Studies in degradation models](uq_implants_materials.md) are monetary and labor-wise costly, which underpins the value of computational feasible methods for uncertainty quanitification.

<!--
- Human activities are causing drastic changes in biodiversity (the identities and abundances of species in a community). Biological communities experience high natural variability and are difficult to sample, leading to large uncertainties in the nature and magnitude of biodiversity change. This project seeks to quantify and reduce the various sources of [uncertainty affecting measurements of biodiversity change](uq_in_biodiversity.md). 
-->
- Biological communities experience high natural variability and are difficult to sample, leading to large uncertainties (affecting, e.g. measurements) in the [nature and magnitude of biodiversity change](uq_in_biodiversity.md).
<!--
- Changes on the level of gene expressions can help to understand the underlying microbiological mechanisms, the progression of a disease itself and finally to deduce appropriate treatments. However, one cannot observe and count these molecules directly, but need to account for the multitude of [uncertainties in RNA biology](uq_in_scRNA.md).
-->
- Our ability to study even single biological cells seems promising to understand disease progressions and find appropriate treatments if we can account for the [multitude of uncertainties and complexity of RNA data](uq_in_scRNA.md).
<!--
- The mapping of characteristics visible at the Earth’s surface in the field by skilled human experts partly relying on their sense of sight for sampling is a routine geoscientific method. Such mapping approaches are at the beginning of the production process of many geoscientific map products. While the information signal sensed by a human expert is objective, its cognitive perception is subjective. The degree of subjectivity cannot be quantified by the human perceiver making it impossible to quantify the uncertainty of the information sampled by a human expert using his sense of sight. to address this challenge we used [information fusion of multiple technically sampled maps and a partially subjective map](uncertainty_quantification_Subjectivity_in_imaging.md) to estimate the quantified uncertainties for each datum in the partially subjective map.
-->
- Subjective cognitive perception in geoscientific methods introduces uncertainty to the sampled information which can be addressed by [information fusion of technically sampled and partially subjective maps](uq_in_earth_science_data.md).
<!--
..
-->

- UQ in weather prediction involves addressing the inherent uncertainties in atmospheric models, data assimilation processes, and complex interactions, enhancing the accuracy and reliability of weather forecasts.The main sources of uncertainty are discussed in the article [UQ in Weather Prediction](uq_weather_prediction.md).



## Authors
Jonas Bauer