Results!

I had a fairly productive date in that I was able to obtain estimates for all the parameters in my model; I briefly ran into a problem of identifiability which is when you aren't sure what inputs give your the output you observed. I will give a simple example of this issue: Suppose I want to find a value of "x" such that 10=2*x, you can clearly see that x=5 is the only possible answer; this system is identifiable. However if I ask you to find the values of "x" and "y" such that 10=x+y, there are many possible values 10=3+7,10=4+6,...etc. This system in not identifiable.

In order to fix this problem I had to respecify my model to give me more information about the estimates. For example, if you had know that y=2*x, then you could find unique values of "x" and "y" such that 10=x+y, but you had to add that extra information. The results look really promising and if proven true, this might be my greatest accomplishment yet. I now need to verify my equations, there will be two steps in this verification process; the first step will be the easiest to implement and the second step might take some time. So how does verification work? Well let's say that you claim to have some tool (which in my case is the equation) that can tell how fast a car is going. One way to verify the tool is to drive the car at a speed that you know, say 60 miles and hour, then use your 'tool' estimate the speed. If the tool gets a value close to 60 like 59 or 61 then it is probably working, if you get a value like 100 or 10 then it is probably not working and you need to fix the tool. So tomorrow we test the tool.