Blog #2: Model Interpretation

In the last week, I have read about the foundations of Schelling-like models. I have read literature that reformulates the classic schelling agent-based model as a graph coloring model. I have also read about the classic Schelling segregation problem as a graph coloring model combined with Markov Chain Monte Carlo (MCMC) techniques. I must say that this is really interesting, especially because it changes focus from individual agent movement to global configuration updates over a finite graph G = (V, E). Each vertex represents an agent that is assigned one of q labels/color. All these different versions of Schelling’s 1971 original have one goal in mind: that is, to minimize a global unhappiness function H(f) based on agent demographics.

While reading about the metropolis-hastings function, I learned that it actually underlies MCMC simulation in this model. Metropolis-Hastings was actually created between 1950-1970. This is especially important for sampling from complex probability distributions by suggesting candidate configurations that actually accept them in a manner that is favorable for low-energy states (i.e., those with low unhappiness or H(f)).

This reformulation also improves computational efficiency because it is equivalent to relabeling nodes instead of moving agents. It is also a connection between sociology and mathematics. From a sociological perspective, it offers a theoretical understanding of emergent segregation in complex systems such as demographics or social networks. From a mathematical perspective, it utilizes tools from graph theory and probability theory. It also offers error bounds on the effects of perturbing the transition matrices. Some of the nuances include issues related to the structure of the graphs, such as grids versus random graphs. It also has implications for policy interventions in cities.

I am currently in the process of implementing this in code. I will begin by implementing it on simple graphs. Some of the edge cases I will consider include balanced versus imbalanced demographics.