How useful is my model? Barcelona, 24-26 May

Our colleagues from Barcelona are organising a two-day workshop on the challenges of relating formal models (not only ABMs but other types of simulation and computational models as well) to the archaeological data. See below for an extended summary. The deadline for abstract submission has been extended to 25th April. For more information, check out their website.

 

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Aim

The last decade saw a rapid growth of quantitative and computational methods apt to analyse long-term cultural and biological processes. In particular, the wide diffusion of agent-based simulation platforms and the enhanced accessibility of computer-intensive statistical analyses are offering the possibility to replace explanations based on natural language with formal models.

While these advances are providing powerful tools that are enabling us to tackle old and new research questions, their use is rarely coupled with appropriate epistemological discussions on how to ultimately relate the model to the data. Problems such as the choice of an appropriate statistic describing the empirical record, the balance between parsimony, complexity, and goodness-of-fit, the integration of taphonomic and sampling biases, or the inferential framework for selecting or rejecting alternative hypotheses rarely occupy the spotlight. In the case of simulation models, discussions are often limited to the model-building stage, and comparisons between prediction and observation are too often qualitative and not supported by sufficient statistical rigour. Yet this is the fundamental step that enables us to evaluate our models. In historical sciences, where the challenges imposed by the nature and the quality of our samples is at its greatest, this issue deserves more discussions and solutions. We believe that this is a critical issue that transcends the specific used in each discipline and cannot be dismissed as a challenge for statisticians.

We invite experts at different stage of this endeavour, sharing the same challenge of evaluating archaeological, historical, and anthropological model to the empirical evidence. We welcome the widest range of expertise (e.g. agent-based simulation, phylogenetics, network analysis, Bayesian inference, etc.) in order to promote the cross-fertilisation of techniques, as well as to engage into deeper theoretical and methodological discussions that transcends the specific of a given geographical and historical context. Participants will present examples showcasing problems (and solutions) on a variety of topics, including: uncertainty in the observed data, parameter search and estimation, model reusability and reproducibility, and more broadly applications of hypothesis testing and model-comparison frameworks in archaeology, anthropology, and history.

Call For Papers
Abstract Deadline: 25th April 2016 
Abstract Length : max 300 words
Please submit via email to the address simulpast@gmail.com with the subject: “WK-Empirical Challenge”

Image source: https://en.wikipedia.org/wiki/Palau_de_la_Música_Catalana#/media/File:Palau_-_Vitrall_platea.jpg

Guest Blog: Fuzzy Logic and Computational Modeling

We are delighted to have Luis R Izquierdo as a guest blogger today. Luis is a complex systems modeler with a strong background in economics, computer simulation and mathematics. His main area of expertise is game theory and the analysis of complex systems. Luis is currently lecturing Economics, Finance, Machine Learning, Complex Systems Modeling and Statistics at the University of Burgos (Spain).

Computational modeling is particularly useful to formalize models and hypotheses written in natural language. Indeed, computers can only deal with formal languages, so if we want to implement a computer model we must get rid of any imprecision, ambiguity, incompleteness and inconsistency in our description. This is one of the reasons why the mere effort of trying to translate a model expressed in natural language into computer code can be a very fruitful exercise in itself.

Models expressed in natural language often contain imprecise concepts (such as “wealthy” or “poor”) and fuzzy logic is a discipline that can assist us in formalizing them. Concepts such as “wealthy” are imprecise because we do not find it natural to assert that any given person is definitely either “wealthy” or “not wealthy”, i.e. we do not feel comfortable dividing the whole population into two sets such that everyone in one set is definitely wealthy whilst everyone in the other set is definitely not wealthy. Instead, we seem to be more comfortable conceding that propositions of the type “Person x is wealthy” may be true to some extent, i.e. they may have a truth value that lies somewhere in between the two absolute extremes true and false. Allowing for more than two truth values (besides the traditional true and false) takes us to the realm of many-valued logics, of which a particularly relevant instance for computer modeling is fuzzy logic.

In fuzzy logic, imprecise concepts are formalized using fuzzy sets. Fuzzy sets are an extension of classical sets in the sense that –besides full membership and full non-membership– fuzzy sets allow for partial membership. In this way, an element may belong to a certain fuzzy set, it may not belong…, or it may belong to some extent. The degree to which a particular element belongs to a fuzzy set ranges from 0 (full non-membership) to 1 (full membership). Thus, graded concepts such as “wealthy” can be naturally modelled as fuzzy sets, with individual people belonging to the set “wealthy” to a greater or a lesser degree (which can be interpreted as the truth value of the proposition “Person x is wealthy”).

Sometimes the degree of membership of an element in a fuzzy set depends only on a certain property of the element. For instance, it seems natural that the degree of membership of any person in the set “wealthy” (i.e. the extent to which the person is wealthy) depends only on the monetary value of the person’s possessions. A possible way of formalizing the concept “wealthy” as a fuzzy set is sketched below.

The membership function of the fuzzy set “wealthy” drawn above would assign a degree of membership 0.2 to every person whose possessions are worth $1000 and a degree of membership 0.85 to every person whose possessions are worth $200 000. Equivalently, this definition of “wealthy” would assign a truth value 0.2 to the proposition “A person whose possessions are worth $1000 is wealthy”. Naturally, this is just one possible way of formalizing the concept “wealthy” made up for this post (and I purposefully didn’t specify which dollar I am using), so please do not read anything else into it! 😀

The logical connectives AND and OR can be modeled in fuzzy logic with various functions, but the most commonly used are the minimum (min) and the maximum (max) respectively. As an example, let us compute the degree to which a certain person x is “Tall AND middle-aged”, assuming the assigned truth value to the proposition “x is Tall” is 0.8 and the assigned truth value to the proposition “x is Middle-aged” is 0.4.

TruthValue(x is Tall AND x is Middle-aged) =
= min(TruthValue(x is Tall), TruthValue(x is Middle-aged)) = min(0.8, 0.4) = 0.4

Similarly:

TruthValue(x is Tall OR x is Middle-aged) =
= max(TruthValue(x is Tall), TruthValue(x is Middle-aged)) = max(0.8, 0.4) = 0.8

 There are also methods to deal with fuzzy “IF-THEN” rules, i.e. rules whose antecedents and consequents may contain fuzzy concepts. A nice example is provided here, where the authors use fuzzy logic to compute a numeric tip given the following rules:

• IF service is poor or the food is rancid, THEN tip is cheap
• IF service is good, THEN tip is average
• IF service is excellent or food is delicious, THEN tip is generous

Recently we have released a well-documented library of functions that facilitates the use of fuzzy logic within NetLogo. Using these functions, it becomes simple to implement agent-based models where individual agents hold their own fuzzy sets (representing subjective imprecise concepts) and follow fuzzy rules which may affect the way agents behave and interact. As an example of a potentially useful application, our library makes it particularly easy to analyse the robustness of a certain theory expressed in natural language to different specifications of the imprecise concepts that the theory contains (which may be represented with different fuzzy sets). Also, it facilitates the exploration of the effect that heterogeneity in concept interpretations may have in a society (i.e. the significance of the fact that different people may have different interpretations of the same concept).

Obviously, neither fuzzy logic nor our library are strictly necessary to build models with agents holding different instances of imprecise concepts, but the work we have developed helps implement such models in a natural and transparent way. Thus, we hope that the NetLogo fuzzy logic library will make the endeavour of translating theories expressed in natural language into computer programs both easier and more rigorous at the same time.

Featured image:  Agents with heights drawn from a normal distribution, shaded light-to-dark based on membership in a logistic fuzzy set for “tall”.