Below you will find the discussion and relevant materials for the ES 105 final exam started on March 13th, 2009
For our final exam problem we had to devise an upgraded monitoring array under a limited budget of $20,000.
I decided to keep the status quo setup but improved it by: 1) upgrading the precision of the instruments at our original 12 locations @ 1/5 the instrument noise of the originals instruments (12 x $300 = $3,600), and 2) buying 8 new high precisions instruments to collect data at 8 new locations (8 x $1,000 + 8 x $1,000 = %16,000). This left us with about $400 dollars left to spare, which were used to boost up the morale of the research group with some good beers and a healthy barbecue.
The rationale for selecting the points I chose (see the Appendix Below as well as the PDF here) was that of trying to get rid of the "BOGUS" spot we encountered in the previous homeworks. As can be seen in the Appendinx and PDF I centered some new datapoint collection instruments symmetrically centered around our BOGUS. In addition I added another data point collection instrument to the lower far left of the plate where we had no data for tha location. In addition, I added a three more sources in area of "high magnitude". One at a (x= -0.3,y=0.6) where our previous inverse results shows an area of high negative magnitued and two to the mid-far right, where we have another area of nigh positive magnitude. By putting data collection instruments here I would be more faithful to encompassing more of the grid, still with a certain symmetry in acquisition, but taking into consideration our previous "sources" and BOGUS spot. Please see results below
We saw numerous results. Overall, adding more data collection sources at key places shows a more accurate map, matching more closely the TRUTH. Still, our model is not perfect and as such our inverse requires further tunning up. As for selection bias between the two COUNTRIES, we saw clearly how Bias was small on each country's side but high on its neighbor's side. This is expected as we have our data collection points only on one side so that is all our model has to work with. We saw also how the sources were decently found in each country's side but now by both on both. Overall, the model was improved by adding data points at key locations. Yet, it is important to note that the locations of the data collection instruments were key, as improper location of this points could lead to totally different results.
Inverse Truth, n=20, i.e., ALL DATAPOINTS
Difference Map: Truth vs Inverse Truth, n=20, i.e., ALL DATAPOINTS
Inverse Noise, n=20, i.e., ALL DATAPOINTS:
No instruments were placed in the upper part of the plate and as such we see high noise
Inverse Source, n=20, i.e., ALL DATAPOINTS
I successfully got rid of our bogus spot
Inverse Truth: NORTH Country
We see the assymetry in the map since we lack data on the SOUTH country side of the plate.
Difference Map: Truth vs Inverse Truth: NORTH Country
The error is small on the NORTH country side of things but at the SOUTH country side of things we see our error grew termendously
Inverse Noise: NORTH Country
Once again, given the assymetry of the data collection, we see low noise on the NORTH country side of things but high noise on the SOUTH country side and on the upper part of the Plate where we had no data collection instruments.
Inverse Sources: NORTH Country
Notice the assymetry and the BOGUS has reappeared!
Inverse Truth: SOUTH Country
We are lacking a lot of data and now our inverse solution is far far from our original truth
Difference Map: Truth vs Inverse Truth: SOUTH Country
This shows the difference even better, with large error on the NORTH country side and low to minimal on the SOUTH country.
Inverse Noise: SOUTH Country
Similar idea as for the NORTH country. On the SOUTH country noise is low, elsewhere high.
Inverse Sources: SOUTH Country
We are getting our sources in the SOUTH country well but elsewhere we are at a loss.
Map of Difference Regions for NORTH & SOUTH countires, country borders, and overal "Plate Land"