# Defining input marginal/probabilistic distribution for uncertainty in model correlation

Hi,
Generally one needs to define moments or the parameters for the uncertain inputs. In my case, I would like to define a model correlation used in the model as the uncertain inputs. So for e.g. the density of liquid is calculated by a model correlation of lets say, y = x +m+c, instead of saying the parameter of (x, m and c) are uncertain, I am looking at it this way, that the density (y) is uncertain about ± 15% for whatever the values are being computed using the correlation.
Hence, I am little unsure or would like your inputs on how I can define the marginal distribution in this case or even state that the uncertainty in the density values follows gaussian distribution? Based on how we input in the UQLab as below:

InputOpts.Marginals(1).Parameters = [1 0.15];

I am using the mean as 1 and use std.dev for a gaussian distribution as 0.15. Do you think this is the way to do it?

Visha

Hi

The input parameters of your computational model should be clearly identified first. That is, when you run your code, do you give a value of (x,m,c) separately, or do you give a value of y?

If you need to define the three values of (x,m,c) to get your code run, then you should define three variables in the UQLab INPUT.

However, you can define that two of them are of `'Constant'` type, say (m, c), and that x is of `'Gaussian` type. This way you can handle the variability of y through the (Gaussian) distribution of x.
Whether this makes sense from the physics of your problem is, however, another story…

Best regards
Bruno

1 Like

Hi Bruno,
So the y is a physical properties, and it is calculated based on a correlation that requires the inputs of other values (x, m, c) for e.g. molecular weights and etc. And each of these values (x , m and c) are also can be based on other equations to compute those values before giving a final value for y.
In the problem, I want to state that I have a variability in the value y or I am uncertain about the value y because it is based on experimental correlation. And I would like to state that this value is about ±20% uncertain for e.g. So in this case, I am unsure how I can input in the UQLab for the initialization part.

Yes, so in the end can I define the variability in y as uncertain input without accounting the distribution in x? So can I state that x, m and c are constant instead?

Thank you so much for your explanation regarding to this topic.

BR,
Visha