Parameter finding - can you give me a basic guide?

[AdamHunyadi]

Hey there,

I started working with a detector, and I was asked to model the efficiency of this it. I have collected lots of data about the efficiency of this detector, and have lots of sampled datasets like efficiency vs "some important parameter". The number of important independent parameters is 6. What I want to achieve is to be able to give an answer to the question: "What would likely to be the efficiency if the 6 parameters were the following: (...)"?

Can you give me a basic guideline, how to approach this problem, or what kind of books I should try and read?

Thank you very much!

 

[Stu]

When you say efficiency, are you talking about statistical efficiency, or the efficiency of some physical sensor (i.e. detector) that is collecting data on something? If you are doing the latter, it sounds like you're doing basic scenario analysis, and simply need to change your input values to get estimates. For example, if you have a dataset:

DATASET
_______________________
y x1 x2 x3  b1  b2  b3
. 30 50 60  10  20  30
.  .  .  .  10  20  30

where b1, b2 and b3 are parameter estimates for x1, x2, and x3 respectively, you would simply put in custom values of x1-x3. Let's say you want to try two scenarios:

1. What if x1 increases by 10%, and x2 decreases by 5%?
2. What if x1, x2, and x3 are 15, 25, and 35?

For (1), take all known values of x1 and x2 and modify them, then multiply each by their parameter estimates.

For (2), create 3 new values for x1, x2, and x3, then multiply each by their parameter estimates.

DATASET
______________________________
y   x1   x2    x3  b1  b2  b3
.   33   47.5  60  10  20  30
.   15   25    35  10  20  30

y for scenario 1: (10*33) + (20*47.5) + (30*60)
y for scenario 2: (10*15) + (20*25) + (30*35)

 

[AdamHunyadi]

Thank you for your quick response. I don't exactly understand what you are saying, but I think what you mean is, that if I have independent variables, on what the sensor-efficiency is dependent, then I should just multiply the expected dependency from each of the independent variables and I will get the correct results. In other words, If i have samples from most of the regions of the 6 dimensional parameter-space, then I can just simply interpolate to get the result for any point in-between.

I'm sorry, I'm really unexperienced in these kinds of problems, I might be misinterpreting your answer. I have two questions with about approach: I don't have the enough sampling points, and they are from really different regions of the parameter space. Also I don't really know how I could sort their individual dependencies out (eg. separating the dependencies of a dataset). I think this kind-of means, that I don't have pure b1, b2, b3, just some mixed values. Is there a way to sort this out efficiently?
The other question is about the following: I would like to simulate this sensor-efficiency, so I cannot really store big datasets to do this interpolation. Do you think if there is a way to sort out the dependencies and the just give polynomial estimations to them.

Thank you again!
Adam Hunyadi