Mathematics of Uncertainty for Coping with World Challenges


Book Description

This book ranks countries with respect to their achievement of the Sustainable Development Goals and their vulnerability to climate change. Human livelihoods, stable economies, health, and high quality of life all depend on a stable climate and earth system, and a diversity of species and ecosystems. Climate change significantly impacts human trafficking, modern slavery, and global hunger. This book examines these global problems using techniques from mathematics of uncertainty. Since accurate data concerning human trafficking and modern slavery is impossible to obtain, mathematics of uncertainty is an ideal discipline to study these problems. The book also considers the interconnection between climate change, world hunger, human trafficking, modern slavery, and the coronavirus. Connectivity properties of fuzzy graphs are used to examine trafficking flow between regions in the world. The book is an excellent reference source for advanced undergraduate and graduate students in mathematics and the social sciences as well as for researchers and teachers.




Do Dice Play God?


Book Description

A celebrated mathematician explores how math helps us make sense of the unpredictable We would like to believe we can know things for certain. We want to be able to figure out who will win an election, if the stock market will crash, or if a suspect definitely committed a crime. But the odds are not in our favor. Life is full of uncertainty --- indeed, scientific advances indicate that the universe might be fundamentally inexact --- and humans are terrible at guessing. When asked to predict the outcome of a chance event, we are almost always wrong. Thankfully, there is hope. As award-winning mathematician Ian Stewart reveals, over the course of history, mathematics has given us some of the tools we need to better manage the uncertainty that pervades our lives. From forecasting, to medical research, to figuring out how to win Let's Make a Deal, Do Dice Play God? is a surprising and satisfying tour of what we can know, and what we never will.




Coping with Uncertainty


Book Description

Ongoing global changes pose fundamentally new scientific problems requiring new concepts and tools. A key issue concerns a vast variety of practically irreducible uncertainties, which challenge traditional models and require new concepts and analytical tools. Uncertainty can dominate, as in the climate change debates. Increasing the resolution of models does not always yield sufficient certainty. This book presents much-needed new tools for modeling and management of uncertainty.




Mathematics of Uncertainty


Book Description







Dealing with Uncertainties


Book Description

Dealing with Uncertainties proposes and explains a new approach for the analysis of uncertainties. Firstly, it is shown that uncertainties are the consequence of modern science rather than of measurements. Secondly, it stresses the importance of the deductive approach to uncertainties. This perspective has the potential of dealing with the uncertainty of a single data point and of data of a set having differing weights. Both cases cannot be dealt with the inductive approach, which is usually taken. This innovative monograph also fully covers both uncorrelated and correlated uncertainties. The weakness of using statistical weights in regression analysis is discussed. Abundant examples are given for correlation in and between data sets and for the feedback of uncertainties on experiment design.







Computational Uncertainty Quantification for Inverse Problems


Book Description

This book is an introduction to both computational inverse problems and uncertainty quantification (UQ) for inverse problems. The book also presents more advanced material on Bayesian methods and UQ, including Markov chain Monte Carlo sampling methods for UQ in inverse problems. Each chapter contains MATLAB® code that implements the algorithms and generates the figures, as well as a large number of exercises accessible to both graduate students and researchers. Computational Uncertainty Quantification for Inverse Problems is intended for graduate students, researchers, and applied scientists. It is appropriate for courses on computational inverse problems, Bayesian methods for inverse problems, and UQ methods for inverse problems.




Modeling and Inverse Problems in the Presence of Uncertainty


Book Description

Modeling and Inverse Problems in the Presence of Uncertainty collects recent research-including the authors' own substantial projects-on uncertainty propagation and quantification. It covers two sources of uncertainty: where uncertainty is present primarily due to measurement errors and where uncertainty is present due to the modeling formulation i




Coping with Uncertainty


Book Description

Ongoing global changes pose fundamentally new scientific problems requiring new concepts and tools. A key issue concerns a vast variety of practically irreducible uncertainties, which challenge traditional models and require new concepts and analytical tools. Uncertainty can dominate, as in the climate change debates. Increasing the resolution of models does not always yield sufficient certainty. This book presents much-needed new tools for modeling and management of uncertainty.