Independent Study, Chaotic Modeling PDF
During my final semester at Rutgers-New Brunswick, I was able to continue my independent study with Dr. Michael LuValle in modeling chaotic systems, in particular weather. While the first semester was spent rewriting the code and with that, figuring out what the model was doing, the second semester was spent building upon that new tools to continue research on this approach. My paper (attached above, below) focuses on the capabilities of the work I did, but I do want to raise some issues with the thought of the work in the first place.
First, residuals are added to the regression predictions to give the predictive densities a more forgiving shape. This helps boost variance to cover any actual results that may be outside the original density. It looks nice, but makes the predictive density somewhat more useless. The “most significant” variables are most significant after some residual values are added, making the predictions somewhat more murky. Because this is an even addition across all variables, it shouldn't affect the results too much, but it feels like it is cheating to make the predictive density cover more ground for outlier events.
Second, it isn’t more accurate than anything before it. Yes, it predicts most possible outputs of many combinations of variables that may or may not be significant, but there is no parsing of the signal from the noise. My addition to this project was trying to pinpoint what is causing the signal for each respective season, and I have at least succeeded in producing an output that brings us closer to distilling these variables; but, why do all this when we could throw our data into an ANOVA model and see which variables are most significant. It would be interesting to compare the results. This brings me to suggestions for research continuing my own, and correct me if it has already been studied at length, but deciphering the sequence of variables that express themselves as significant from year to year seems worthwhile in understanding which is signal and noise.
These are two mere thoughts of my own, but important to put in writing for the next time I, or someone else, picks this up.