Bayes is the New Black: Agent-Based Modeling and Bayesian Inference in Species Foraging

Transcript

1. Bayes is the New Black Agent-Based Modeling and Bayesian Inference in Species Foraging Trin Turner Department of Philosophy Western Michigan University trinity.s.turner@wmich.edu Tom Schenk Jr. Department of Economics Iowa State University tschenk@iastate.edu
2. Key Questions & Objective • Causal Model Theorists – Agent-Based and Bayesian Models simulations are sufficient for causally explanatory and predictive claims • We will argue… – Neither of these suffice as wholly explanatory models… – but, do well for prediction… – And are replicatively and predicatively valid
3. Common Bayesian Model • Animal forages in an area with a well- defined distribution of food – Establishes knowledge of food location • Food is moved to new areas – Animal no longer sure of qualiy of food patch • Bayesian model is supposed to predict behavior of animals – Prior information → Future Expectations
4. Theorist’s Position: • Bayesian model is meant to represent the causal mechanisms of the system being simulated • In generating the regularity, the simulation uncovers the causal relationships that produced the regularity
5. Bayesian Model Results • Retrodicted data from 11 previous studies • Novel predictions confirmed by further empirical studies
6. Agent-Based Modeling • Computer based: programmed with object-oriented languages (e.g., Java, C++) • Model a network of individual agents interacting with each other • Individual attributes produce group-level behavior, emphasis on heterogeneity • Variety of algorithms can be employed for each ―agent‖ (animal, person, etc.)
7. Agent-Based Model Overview Agents interact with each other in the scope of the environment over time. environment Agents Agents may be heterogeneous and may parish if certain conditions are not met.
8. EPICURE Model & IFD • Predominent (i.e., only) ABM is EPICURE • Tests Ideal Free Distribution (IFD) model Hypothesis: Given a distribution of food, animals should distribute themselves proportionally to the location of food (Fretwell & Lucas, 1970) Reality: Animals tend to undermatch—less than proportional amount of animals end up in food-rich areas (Godin & Keenleyside, 1984; Gillis & Kramer, 1984; Baum & Kraft, 1998)
9. Building EPICURE • Food is dropped randomly on a grid, with some areas having a higher concentration • Agents are also randomly distributed on the same grid • Agents move according to previous successes at the location
10. EPICURE Model Results • Reproduced undermatching (see fig.) • Derived potential causes for undermatching • Produced potentially confirmed predictions
11. Our Claims 1. Causal Explanatory Models must be structurally valid 2. Agent-Based and Bayesian Models are not structurally valid 3. Thus, they cannot be causally explanatory 4. However, they are predictive
12. Model Validity • Replicative validity –model matches data already acquired by a real system • Predictive validity –model matches data not yet known • Structural validity –model matches known data and reflects the actual way a system operates (Grune-Yanoff, forthcoming)
13. Validity of Bayesian Approach • Certainly Replicatively Valid – Replicates data from previous studies • Certainly Predictively Valid – Makes novel predictions • Not Structurally Valid – Does not purport to model an underlying physiological (causal) process
14. Validity of ABM Approach • Certainly Replicatively Valid – Replicates data from previous studies • Potentially Predictively Valid – Makes novel predictions, but has not yet been formally tested in non-ABM setting • Not Structurally Valid – Does not purport to model an underlying physiological (causal) process
15. Structural Validation (SV) • Necessary to overcome the critique of underdetermination – SV imposes strict constraints on the casual relationships programmed in the model by adherence to theoretical laws which limit the structure of the model. – The limitation imposed requires that the organizational structure of the model accurately represent the organizational structure of the system its modeling
16. Neither Models are SV • Theoretical law-like regularities (may) are not be present in biology • SV models sometimes still don’t produce law- like regularities on grounds that: – Entities are not governed by a single regularity; – Entities are too complex to adequately model using a handful of (sometimes competing) independent behavioral rules, and; – Given the complexity of the real system, the models are incapable to imitating behavior
17. Implications • Hence, models cannot reflect the full range of causal relationships contained within the system • Without causal relationships built into models, we cannot expect knowledge of causal relationships from the results
18. Links, etc. http://tschenk.public.iastate.edu/bnb Bayes: Are Animals Capable of Bayesian Updating? An Empirical View. Thomas Valone, Oikos (2006). Bayesian Foraging with Only Two Patch Types. Ola Olsson, Oikos (2006). Bayes’ Theorem and its Applications in Animal Behavior. John M. McNamera, Richard F. Green, and Ola Olsson, Oikos (2006). EPICURE: EPICURE: Spatial and Knowledge Limitations in Group Foraging. Michael E. Roberts and Robert L. Goldstone, Adaptive Behavior (2006).