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Topic Title: Modelling Uncertainty
Topic Summary: Understanding the terminology used when modelling stochastic systems
Created On: 14 April 2013 01:58 PM
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 14 April 2013 01:58 PM
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I am having trouble understanding the terms structural uncertainty and parameter uncertainty when it comes to modelling stochastic systems. I have tried looking through PDF files, websites and books, but I can't find one which explains it in a way that I can understand clearly.

Can someone please try and explain the terms to me?
 30 April 2013 04:36 PM
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If the existing terminology doesn't quite fit the application you are interested in try to build your own, then look to make it consistent with other approaches.

For example one method would be to build on the existing engineering definitions of Accuracy, Error, Precision, and Uncertainty


However this sort of error analysis alone doesn't tell you much about what is going on in terms of frequency domain analysis, i.e. for sampled measurements resulting in aliasing, phase distortion, frequency response errors, measurement resolution errors etc.

Systematic error from the measurement point of view seems to be analogous to structural uncertainty in the model building point of view i.e. design flaws in the model used.

Random error from the measurement point of view seems to be analogous to parameter uncertainty in the model building point of view. Instead of a measurement error, parameter uncertainty refers to the range of values or likely distribution of values that a model parameter might take.

But whatever the definition you use for the input uncertainty (the nature of the model and its parameter values), you have to be able to relate this uncertainty to the output uncertainty, that is the uncertainty in the numbers coming out of the model. It is these that have to be compared with measured reality. I have no idea what terminology is best for doing this, I expect you will know more about this than me.

I presume that some parameters may be independent of all others and some parameters may correlate with others (i.e. not be independent of others).

I expect you can't just read a text book definitions on this and expect to know a formula that works for every problem you meet. I am not an expert on modelling stochastic systems, so all I am really saying is, try to keep an open mind and give priority to understanding the problem at hand.

When encountering definitions that are confusing, it may mean you are missing something or it may mean that they are somehow incomplete and you have unknowingly started on the path of discovering why.

James Arathoon

James Arathoon
 24 June 2013 11:36 AM
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Good to see a question on Statistics/ Probability modelling.

Structural uncertainty: this relates to the mathematical model made to describe a real life system. A mathematical model, in strict sense, can never describe the real life behaviour of a given system, but, the developed model may very closely describe a real life system. This is because of our limitation in understanding all the variables/ parameters that might impact a given system behaviour.

Parameter uncertainty: once a mathematical model is developed then the varilables in that model are required to be estimated. This estimation is done by observating the system behaviour in real life. Again, one can never be cent percent certain about the estimation of the varilables/ parameters. Hypothetically if the observations are infinite, which is actually not possible in real life, then one can make statements about the value of the parameter with cent percent certainty.

Giving you an example: Suppose that one has a measurement system. This system will have many components. Based on the design of the system together with the knowledge of its internal make up one can develop an equation/ mathematical model for the measurement uncertainty. Now there will always be incompleteness with respect to this model (e.g.: even our understanding of the simple relation describing the change in the resistance of the conductor with respect to the temperature is not complete) and this is what Structural uncertainty (i.e., Uncertainty in model structure) is all about. Once the model is ready then the calculation will involve estimation of various varilables/ parameters in the mathematical model. Uncertainty associated with the estimation of these parameters is what parameter uncertainty is all about.

Model structure uncertainty and the associated parameter uncertainty are the standard components in the uncertainty analysis problems.


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