Scaling
This exercise covers content related to the lecture on Scaling. The goal of the exercise is to implement the "ball falling down a stairway" model for Sample Space Reducing proccesses, and answer some questions regarding the final distributions.
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SSR Proccess
The jupyter notebook "Scaling_exercise.ipynb" contains the template for implementing this model. The main task is to create a function that obtains samples for visiting a new state, including prior parameters for visiting each state (q), and a driving rate continuing the descent or restarting from the top of the stairs.

A basic implementation that simulates the process can be found in "run_ssrp". After verifying that the basic case holds (all prior probabilities equal and driving rate equal to 1), answer the quesitons:
What is the effect of the driving rate on the distribution? *
The power law has been found to be a robust attractor for a wide number of prior distributions, q, meaning that lower states end up being proportionally much likely to occur. Can we break this conditions if we make the prior distributions for larger states much larger?
Is the power law behaviour consistent with polynomial prioirs of degree three? (So that state i has a prior probability proporional to i^3) Why?
Is the power law behaviour consistent with polynomial prioirs of degree 3 (so that state i has a prior probability proportional to i^3)? Why do you think this happens?
Is the power law behaviour consistent with exponential priors (you visit i with probab. proportional to exp(i))? Why do you think that happens?
If we are following links in a network, what could this imply for the visiting distribution? (this is, of course, a very open question)
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