Forecasting with Maximum Entropy: The Interface Between Physics, Biology, Economics and Information Theory

This book aims at providing a unifying framework, based on Information Entropy and its maximization, to connect the phenomenology of evolutionary biology, community ecology, financial economics, and statistical physics. This more comprehensive view, besides providing further insight into problems, enables problem-solving strategies by applying proven methods in one discipline to formally similar problems in other areas. The book also proposes a forecasting method for important practical problems in these disciplines and is directed to researchers, students and practitioners working on modelling the dynamics of complex systems.

The common thread is how the flux of information both controls and serves to predict the dynamics of complex systems. It is shown how maximizing the Shannon information entropy allows one to infer a central object controlling the dynamics of complex systems, such as ecosystems or markets. The resulting models, which are known as pairwise maximum-entropy models, can be used to infer interactions from data in a wide variety of systems. Here, two examples are analysed in detail. The first is an application to conservation ecology, namely the issue of providing early warning indicators of population crashes of species of trees in tropical forests. The second is about forecasting the market values of firms through evolutionary economics. An interesting lesson is that PME modelling often produces accurate predictions despite not incorporating explicit interaction mechanisms.

Key features

• Written to be suitable for a broad spectrum of readers and assumes little mathematical specialism.
• Includes pedagogical features: Worked examples, case studies and summaries.
• The interdisciplinary approach builds bridges between disciplines.
• Oriented to solve practical problems.
• Includes a combination of analytical derivations and numerical simulations with experiments

本書旨在提供一個統一的框架，基於信息熵及其最大化，以連接演化生物學、群落生態學、金融經濟學和統計物理學的現象學。這種更全面的觀點不僅能進一步洞察問題，還能通過將一個學科中的成熟方法應用於其他領域中形式相似的問題，從而實現問題解決策略。本書還提出了這些學科中重要實際問題的預測方法，並針對研究模擬複雜系統動態的研究人員、學生和從業人員。

共同的主題是信息流如何既控制又用於預測複雜系統的動態。本書展示了如何通過最大化香農信息熵來推斷控制複雜系統動態的中心對象，例如生態系統或市場。由此產生的模型被稱為成對最大熵模型，可以用於在各種系統中從數據中推斷相互作用。本書詳細分析了兩個例子。第一個是應用於保護生態學的應用，即提供熱帶森林樹種族群崩潰的預警指標問題。第二個是關於通過演化經濟學預測公司市值的問題。有趣的是，成對最大熵模型通常能夠產生準確的預測，儘管沒有納入明確的相互作用機制。

主要特點：
- 適合廣泛讀者，不需要太多數學專業知識。
- 包含教學特點：實例、案例研究和摘要。
- 跨學科的方法建立學科之間的橋樑。
- 以解決實際問題為導向。
- 結合分析推導、數值模擬和實驗。