dcnick3 / statistics-assignment Goto Github PK

The first task included a lot of computations & equation solving, so I decided to use Mathematica language to do it. It's a functional language with focus on symbolic computation, which is useful for solving equations.

Then it somehow snowballed into implementing the second task in Mathematica too.

The repository (https://github.com/DCNick3/statistics-assignment) contains task*.nb, which are the Mathematica notebooks I used to solve the tasks. They are also rendered as PDF files so that one could look at the code without having Mathematica installed.

Task 1: Bayesian Statistics

The notebook contains all relevant info

Task 2: Simulated Annealing

I've tried doing the annealing with three temperature decay coefficients: 0.9, 0.95 and 0.99

The lengths of the resulting paths were as follows:

Here's also the plot of distances over time:

The 0.95 (called middle) seemed to have some trouble settling at the beginning, probably due to bad luck, and came to worse solution.

For visualization I used built-in mathematica GIS support, so it already came with a reasonable projection and graph visualization capabilities.

Here's a visualization for temperature decay coefficient 0.99.

Looking at the final solution that was found with the 0.99 decay coefficient seems pretty reasonable to me.