Hi Alexandre Wadoux,

Thank you for your detail explanation. It helps me a lot.

Dear    Yahya.  In my opinion Bayesian Kriging potentially is more powerful. This is true if you have a good a priory information about you observations. If this is not true sometimes regression   Kriging may be more preferable

Please, you could check this interesting article about empirical bayesian kriging in ArcGIS.

http://www.esri.com/news/arcuser/1012/files/ebk.pdf

You should also consider cokriging. Exactly what do you mean by "more powerful"? I.e., how would you quantify "power"?

Regression kriging usually means combining in some way regression and kriging. In particular where the expected value of the random function is nonconstant, e.g. it is a polynomial function of the position coordinates or is function (usually a low degree polynomical) of another spatially distributed variable, e.g. elevation in the case of precipitation.

Precipitation data is nearly always "point" data whereas satellite data is non point data  (there is a pixel size) so you must compensate for the difference in data support. Regression doesn't do that and in general Bayesian modeling doesn't either. I suggest that you need to look more at the literature on combining rain gage data with Doppler rain data, this is more analogous to your problem. You will see that cokriging has most often been used

Dear Prof Donald Myers,

In term of "more powerful", I mean is about the accuracy or bias. Thank you for your advice. I will read more about cokriging method. 

Th Simple kriging, Ordinary kriging and Universal kriging estimators are all unbiased by construction. Depending on your version of regression kriging, it is probably not and likewise for Bayesian kriging. As for accuracy. to determine that you would have to know the true values to compare with the interpolated values but if the true values were known then it would not be necessary  to interpolate. SK, OK and UK are all exact  interpolators, i.e. at a data location the interpolated value is the data value and hence the errors at data locations are all zeros. So unfortunately you still do not have a criterion to determine the "power" of the methods or your interpretation of "bias" and "accuracy" are not the usual ones.

The attached paper link has a comparison between RK and BK approaches in spatial geological data.

Conference Paper Comparative Geostatistical Simulation of Formation Permeabil...