orecasting with Maximum Entropy. The interface between physics, biology, economics and information theory

Description

PRELIMS.pdf Preface Acknowledgements Author biography Hugo Fort References CH001.pdf Chapter 1 Entropy as missing information: from Shannon’s information theory to Jaynes’ maximum entropy principle 1.1 Information and its processing in biology, economics and physics 1.2 Uncertainty in communication systems: Shannon entropy 1.2.1 First attempts to quantify information content 1.2.2 Shannon’s information entropy 1.3 Entropy as missing information 1.4 Working with incomplete information: the principle of maximum entropy to find minimally prejudiced distributions 1.4.1 Frequentist or physical probability versus subjective or Bayesian probability 1.4.2 MaxEnt as a method of making predictions from limited data by assuming maximal ignorance References CH002.pdf Chapter 2 The synthesis of information theory and thermodynamics: Shannon entropy and Boltzmann entropy are the same thing 2.1 Basics of statistical physics 2.1.1 The program of statistical physics: from microphysics to macrophysics 2.1.2 Entropy and the Second Law of Thermodynamics: from the efficiency of heat engines and refrigerators to entropy as disorder 2.1.3 Boltzmann and the statistical character of the Second Law of Thermodynamics 2.1.4 Boltzmann–Gibbs maximum entropy approach to statistical mechanics 2.1.5 All is in the partition function 2.2 MaxEnt derivation of statistical mechanics 2.2.1 The equivalence between Boltzmann’s and Shannon’s entropy 2.2.2 Inferring the canonical probability distribution by the MaxEnt recipe 2.3 Converting information into energy: from Maxwell’s demon to Landauer’s eraser33The title as well as part of the content this section is based on the article by Lutz and Ciliberto (2015). 2.4 Conclusion References CH003.pdf Chapter 3 Elements of physical biology: the Lotka–Volterra equations 3.1 The kinetic formulation of population dynamics 3.1.1 One isolated species 3.1.2 Many interacting species 3.2 The Lotka–Volterra linear model for single-trophic communities 3.2.1 Obtaining the model parameters from monoculture and biculture experiments 3.2.2 Quantifying the accuracy of the linear model for predicting species yields in single-trophic communities33This section is based on Fort (2018). 3.3 The statistical mechanics of populations 3.3.1 Rationale and first attempts 3.3.2 MaxEnt formulations 3.3.3 Uses of statistical mechanics-inspired lattice models I: overgrazing of semi-arid lands 3.3.4 Uses of statistical mechanics-inspired lattice models II: modelling the dynamics of biodiversity of communities of trees in tropical forests 3.4 Conclusion Appendix A: Equilibrium stability in population ecology A.1 Local and global stability A.2 Stability for two-dimensional systems A.3 Some general theorems77This section is mainly based on chapters 1, 3 and 5 of the thorough study on stability by Goh (1980) and chapter 2 of May (1974). References CH004.pdf Chapter 4 Economics as physics, economics as biology 4.1 Economics as social physics, physics as Nature’s economics11The title of this section is borrowed from Philip Mirowski’s (1989) book, this volume inspired the content of this section. 4.2 Neoclassical economics 4.2.1 The homo economicus of rational choice theory 4.2.2 The marginalist revolution and the general equilibrium theory 4.3 Economics as biology, or evolutionary economics 4.3.1 The irrationality of rational decision theory 4.3.2 Evolutionary economics 4.4 Selection dynamics 4.4.1 The simplest selection model 4.4.2 Frequency dependent selection: the replicator dynamics equation 4.5 Linking selection dynamics with ecology and physics 4.5.1 The equivalence of the replicator dynamics with the generalized Lotka–Volterra equations 4.5.2 The selection equations regarded as master equations 4.6 Innovation through mutations 4.6.1 Evolution as a two-step mutation–selection process 4.6.2 Mutation–selection equations: from the Crow–Kimura equation to the replicator–mutator equation 4.7 Implementing evolution in economics 4.8 The ‘Marshall problem’ or a transdisciplinary synthetic perspective of economics References CH005.pdf Chapter 5 Inferring effective interaction matrices through MaxEnt 5.1 Working with imperfect information 5.2 The Lotka–Volterra maximum entropy interaction matrix 5.2.1 Choosing the right constraints 5.2.2 The MaxEnt interaction matrix and its properties 5.2.3 A non-symmetrical MaxEnt interaction matrix 5.3 How good is the pairwise approximation? References CH006.pdf Chapter 6 Early warning indications of species crashes from effective intraspecific interactions in tropical forests 6.1 Background: diversity loss and early warning signals 6.1.1 On fluctuations of biodiversity and what drives these changes 6.1.2 Early warning signals 6.2 Goal 6.3 Data 6.4 Estimating the interaction matrix through MaxEnt 6.5 Intraspecific competition interactions are enough to predict the trajectories of tree species 6.6 A new early warning signal 6.7 Conclusion, caveats and future developments References CH007.pdf Chapter 7 Modelling markets as ecosystems with the help of maximum entropy 7.1 Background: a short history of market modelling 7.1.1 Of pollen motion, drunks and bond prices 7.1.2 The efficient market hypothesis and the crypto-trading hamster Mr Goxx 7.1.3 Criticism to the efficient market hypothesis 7.1.4 Combining efficient market hypothesis with behavioral finance: the adaptive market hypothesis 7.1.5 Competition (and cooperation) in financial markets 7.2 Goal 7.3 Data 7.4 Modelling: replicator dynamics combined with pairwise maximum entropy or RDPME model 7.4.1 Frequency dependent evolutionary model 7.4.2 Parameter estimation 7.5 Model validation 7.5.1 Beat the market 7.5.2 Quantitative predictions for individual companies 7.5.3 Global accuracy of the RDPME method 7.6 Conclusion: balance, caveats, extensions and improvements Appendix A: A metric to measure the pace of change of the payoff matrix References