Inverse Distance Weighted (IDW) interpolation generally achieves better results than Triangular Regular Network (TIN) and Nearest Neighbor (also called as Thiessen or Voronoi) interpolation.
However, the Kriging Interpolation is statistically more sophisticated because it allows identifying distortions in the data, i.e., possible errors on the observations throughout the variance output.
The (Ordinary, Simple and Universal) Kriging Interpolation Methods are available in the Processing Toolbox of QGIS 3, as shown in the picture attached.
You must use the Geospatial extention in the ArcGis for this purpose. Then you must interpolate periciputation by different methods including: IDW, Tissen, Spline, RBF Kriging, Ordinary Kriging......
Finally you select the best method based on the stastical analyzes such as RMSE, ME.
In fact, you have to try different interpolation methods and choose the best method based on statistical analyzes that in ARCGIS and GS+ is possible.
Inverse Distance Weighted (IDW) interpolation generally achieves better results than Triangular Regular Network (TIN) and Nearest Neighbor (also called as Thiessen or Voronoi) interpolation.
However, the Kriging Interpolation is statistically more sophisticated because it allows identifying distortions in the data, i.e., possible errors on the observations throughout the variance output.
The (Ordinary, Simple and Universal) Kriging Interpolation Methods are available in the Processing Toolbox of QGIS 3, as shown in the picture attached.
You must select the interpolation method with the better results in statistical analysis. You can try different methods as Kriging or IDW and see the RMSE results for each case.
I only work with ArcGIS so I only can recommend techniques from that software; however, I believe it applies for both software if they are the same technique.
The best method will depend if you want to keep as maximum and minimum values of your data or you allow to the software to predict values over and below the real data. I believe that you will never get the maximum and minimum so I will go for IDW. If you want to keep your maximum and minimum values I would use Spline. As soon you justify why you are using one and not another, all of them are valid but also keep in mind your errors when you apply one method and another.
There are different interpolation methods to produce the spatial distribution map of environmental variables. The best results depend on your requirement of project and the interpolation accuracy. Generally, ordinary Kriging and its related other kriging could provide good results.
There are some valuable answers already added by researchers. The interpolation techniques depends upon your requirement and type of analysis you are carring out.
Note that IDW is not a statistical method, it is just heuristic (no statistical assumptions).
It takes into account the distances from the data locations to the interpolation location but not incorporate the distances and directions between data locations
Splines are a special case of Radial Basis functions and that is equivalent to universal kriging.
There is a substantial literature on interpolating precipitation data, see Water Resources Research, J. of Hydrology, Water, Mathematical Geosciences
From the above answers i would like to ask.... Does choosing the right interpolation depends upon feature(data) or the terrain of the location? I think its upon the feature.