[SOLVED] Variability in Turning Band Simulations

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[SOLVED] Variability in Turning Band Simulations

Postby niafall » Fri Jul 03, 2020 6:14 pm

I am using turning band simulations to produce estimates of a quantity distributed across a 2-dimensional field with uncertainty, as described in ICES' "Handbook of Geostatistics in R for Fisheries and Marine Ecology" (Petitgas et al. 2017). I am unclear as to how variability arises in the simulated realisations (i.e. how do different realisations arise from a single dataset and a deterministic variogram). Is there any literature you could point to which would give a thorough explanation of this?

Many thanks.
niafall
 
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Re: Variability in Turning Band Simulations

Postby Didier Renard » Thu Aug 06, 2020 4:03 pm

Good morning.
Sorry for the late answer to your post. And may be apologies in advance if I did not understand completely the question.
The method that you are mentioning is the geostatistical simulation technique.
As you noticed, this method offers the possibility to generate a set of equi-probable outcomes (usually called realizations) of a random variable over a field, all of them reflecting the spatial characteristics which is contained in the variogram. The limited information (i.e. the covariance or the variogram) needed to perform these simulations is due to the Gaussian framework within which the technique is provided. This means that, if necessary of pre and post transform is required (please refer to the Gaussian Anamorphosis for more details).
Moreover, each simulation can be modified to honor the data points (we called them Conditional Simulations) ... if the data have been turned to the gaussian world beforehand.
Unlike Kriging, the simulation technique does not embed any smoothing property. This conveys the ability to address problems where the whole variability of the variable is an asset (and must certainly not be smoothed out!): for example, in order to provide he probability the the variable overpasses a given threshold over the field.

The references are numerous. If I had to choose a good and very complete reference, I would certainly mention the book by:
Jean-Paul Chilès, Pierre Delfiner
ISBN: 978-1-118-13617-1 February 2012 726 Pages

Hoper this will help.
Didier Renard
 
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Re: [SOLVED] Variability in Turning Band Simulations

Postby niafall » Thu Oct 29, 2020 11:23 am

Hi Didier,

Thanks for your reply. I suppose what I am most curious about is in producing the realisations, or set of equi-probable outcomes using the turning band method, we are just using the variogram which is a fixed model, but we can produce n outcomes which are all slightly different. I do not understand where these small differences are defined, or how they are produced, given the deterministic nature of the variogram model. Perhaps the answer is very obvious...

I will try and get my hands on the reference you have provided.

Many thanks again for your reply. :)
niafall
 
Posts: 21
Joined: Tue May 17, 2016 5:46 pm


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