# What is conditioning in spatial statistics?

Could someone explain to me: the concept of "conditioning" in spatial statistics in a fairly advanced context?
Here is an example to clarify the question:
Step 1) generate a 2D point process, here 6 realization are shown:

Step 2) choose a region from one realization

Step 3) try to fill the rest of same size region, here I used the same PP:

Step 4) remove the overlapped region and merge with given part:

Step 5) assume you did right!

Step 6) ask question now: Is the result is a conditioned PP on a set of given points?

Step 7) wait keeping hope that somebody will answer your question thoroughly:)

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Although the context may be "advanced," the sense of "conditioning" is elementary. To see this, simplify: focus on two locations $1$ and $2$ in the domain of a spatial process. Let the value at $1$ be $X$ and the value at $2$ be $Y$. Then the multiple realizations of step 1 are sampling from the bivariate distribution $(X,Y)$ and the steps 2-5 are observing one value $x$ of $X$ and then sampling from the conditional distribution $(X,Y) | X=x$. –  whuber Feb 6 '12 at 15:53
@whuber Could you demonstrate what you said and provide a complete answer? That can be useful for learning to me and future readers. Furthermore, it can be possible to me to narrow my question according to your answer. –  Developer Feb 7 '12 at 2:37