I have a Cartesian grid (100x100) in which some of the points are known (30 out of 10,000) and the rest are unknown. I want to use the known points and estimate the other cells. Is there any philosophies behind the way that I must use the known points to estimate the unknown cells? In other words, does it matter that where I should start the estimation? Generally speaking, I personally prefer to start from the locations where I have the maximum amount of the information rather than a random location that probably I might have one known data. However, there is another school says that I should start from a random location in order to prevent any bias. I am more interested to know your ideas about any differences between these methods. Thanks !
2026-03-31 21:48:03.1774993683
chose the best path for estimation
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A simple scheme I found very effective is to begin by letting each known point 'rule' the territory that is nearer to it than to other points. Various measures of nearness can be used and give somewhat different results. Two possible measures are actual linear distance and squared distance. (Then maybe on a subsequent path figure a way to make the inevitable boundaries have intermediate values.) This method is very naive mathematically, but in the right situation it can give very good results.
An entirely different approach is 'kriging'. Try this as a search word in Google and, with some caution, you can get a lot of authoritative info on what may turn out to be a topic of major interest to you. This method is sophisticated mathematically and take a huge amount of computation. There is a package for R statistical software devoted to the topic. I would trust that and its ancillary materials. Also Cornell. (Wikipedia is probably correct mathematically and historically, but for may taste it hardly hints at the motivation.)