Decision Entropy: A New Theory for Representing Uncertainty in Managing Natural Hazard Risks

本研究的目标是建立一个新的理论基础，以合理和防御性地管理罕见的自然灾害造成的重大后果的风险。 如果成功，这项研究将通过优化公共和私人资源如何投资于减轻或接受自然灾害的风险来造福社会。 此外，它有潜力改善从医学到经济学到公共政策等广泛领域的决策。 它将提高对不确定性和危险的认识，并倾向于认为我们知道的比我们真正做的决策，它将提高小学生的批判性思维和决策技能，并促进对工程机会的兴奋。 决策熵理论是由主要研究者开发的一种新理论，旨在为决策背景下的概率评估建立一个客观（非信息）的起点。 这个起点是通过最大化决策的熵来获得的，熵是关于可能的决策结果来定义的。 将解决以下目标：1。完成理论的公理化描述。 这些数学公理通过贝叶斯定理建立了用于基于任何和所有可用信息（客观和主观）评估概率的起点（样本空间）。为一组简化的风险管理问题生成解析或无量纲数值解。3.发展数值方法，将理论应用于更复杂、更现实的风险管理问题.将决策熵理论集成到自然灾害工程研究基础设施（NHERI）网络基础设施DesignSafe-ci.org中，以支持数据分析、关键数据需求的评估和风险管理决策。将该理论应用于现实世界的案例历史，以展示其在自然灾害风险管理中的应用和理解。创建简单的游戏和练习来说明和传播的理论向公众。对小学进行外展活动，教育学生批判性思维、风险和决策。该项目将是德克萨斯大学奥斯汀分校工程系、挪威岩土研究所和NHERI的合作项目。 这项研究是一项高风险、高回报的奋进。 几个世纪以来，包括伯努利、凯恩斯、杰恩斯和莱法在内的许多杰出的理论家都试图解决这个问题，但都没有成功。 这项研究有可能在不确定性下的知识和决策方面取得变革性进展。 首先，它表明，评估概率的起点取决于使用这些概率的决定，这意味着概率不是一个绝对的概念，而是一个相对的概念。 采用这种相对性的观点，可以提供一些见解，让我们能够代表不确定性和管理风险，这些见解发人深省，但并不总是直观的，在某些情况下令人欣慰，但在另一些情况下却令人不安。 其次，本研究将产生简化的风险管理决策问题的分析或无量纲数值解。 这些解决方案将为应用该理论提供一般见解和实际手段。第三，本研究将推进创新的数值方法，以最大限度地提高“决策熵”在现实中，多维决策问题。 最后，这项研究将被纳入NHERI网络基础设施DesignSafe-ci.org门户网站，以便用户能够将其与真实的数据一起应用于管理自然灾害风险的实际问题。

The goal of this research is to develop a new theoretical basis to rationally and defensibly manage risks from rare natural hazards that cause large consequences. If successful, this research will benefit society by optimizing how public and private resources are invested in mitigating or accepting risks from natural hazards. In addition, it has the potential to improve decision making in a wide variety of fields from medicine to economics to public policy. It will increase awareness about uncertainty and the dangers and tendencies to think we know more than we really do in making decisions, it will improve critical thinking and decision skills in primary school students and foster excitement about opportunities in engineering This research will develop a theoretical basis, Decision Entropy Theory, to rationally and defensibly manage risks from rare natural hazards that cause large consequences. Decision Entropy Theory is a new theory developed by the Principal Investigators to establish an objective (non-informative) starting point for assessing probabilities in the context of making decisions. This starting point is obtained by maximizing the entropy of the decision, which is defined concerning the possible decision outcomes. The following objectives will be addressed:1. Finalize axiomatic descriptions of the theory. These mathematical axioms establish the starting point (sample space) used to assess probabilities based on any and all available information (objective and subjective) through Bayes' Theorem.2. Produce analytical or non-dimensional numerical solutions for a set of simplified risk management problems.3. Develop numerical means to implement the theory on more complicated and realistic risk management problems.4. Integrate Decision Entropy Theory into the Natural Hazards Engineering Research Infrastructure (NHERI) Cyberinfrastructure DesignSafe-ci.org to support the analysis of data, the valuation of critical data needs and risk-management decision making.5. Apply the theory to real-world case histories to demonstrate its use and the understanding it provides in managing risks for natural hazards.6. Create simple games and exercises to illustrate and communicate the theory to the public.7. Conduct outreach to primary schools to educate students about critical thinking, risk and decision making.This project will be a collaborative effort comprising two departments in engineering at The University of Texas at Austin, the Norwegian Geotechnical Institute and NHERI. This research is a high risk, high reward endeavor. For centuries, a variety of extremely distinguished theoreticians, including Bernoulli, Keynes, Jaynes, and Raiffa, have unsuccessfully attempted to address this problem. This research has the potential to make a transformative advancement in knowledge and decision-making under uncertainty. First, it suggests that the starting point in assessing probabilities depends on the decision in which these probabilities will be used, meaning that probability is not an absolute but a relative concept. Adopting this perspective of relativity provides insights in representing uncertainty and managing risk that are thought-provoking, not always intuitive, and comforting in some cases but disconcerting in others. Second, this research will produce analytical or non-dimensional numerical solutions for simplified risk-management decision problems. These solutions will provide both general insights and practical means for applying the theory. Third, this research will advance innovative numerical methods to maximize "decision entropy" in realistic, multi-dimensional decision problems. Finally, this research will be integrated into the NHERI Cyberinfrastructure DesignSafe-ci.org web portal so that users will be able to apply it with real data to practical problems of managing risks from natural hazards.