[I may have made a mess of replying first time. This is the second
try. Apologies if any duplication results]
On 22-Jul-06 Digby Millikan wrote:
> Hello,
>
> I am reading some geostatisitics texts, and they introduce random
> functions.
>
> Some texts say;
>
> A deposit D is made of a set of random variables Z(x) which make
> up a random function.
>
> Z(x) is hence a set of possible realizations e.g. z(x)
>
> I understand this, however in Geostatisitics: Modeling Spatial
> Uncertainty and Geostatisitics for Engineers and Earth Scientists
>
> The term w is introduced representing the sample space(?)
>
> i.e. a random variable is Z(x,w)
>
> This I do not understand. If w is part of the sample space e.g.
> a range of possible grades at a point then this is saying the
> grade Z(xi,wi) is a function of itself w. Is this how this
> term is supposed to interpreted? What is w?
The second statement is in fact the more precise version of the
first, provided the second one is properly interpreted.
First of all, for any particular value of w, Z(x,w) is a particular
function of x. The values of w do not need to be of any particular
kind -- all that is needed is that they serve to index the functions
Z(x,w). The set of all possible values of w can be denoted by W, say
(this bit is not explicit in what you say).
So the set of all available functions of x is
{Z(x,w) for w in W}
Next, Z(x,w) will be a random function of x if w has been chosen
at random from amongst the values in W. To do this, you need to
have a probability distribution defined on W. That is why W is
called the "sample space". So a probability distribution P is
defined on W.
Thus to "realise" a random function from {Z(x,w) for w in W} when
the probability distribution P is defined on W, use P to sample
a value at random from W and let this value be w. Then the random
function is Z(x,w).
Does this help?
Best wishes,
Ted.
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E-Mail: (Ted Harding) <[EMAIL PROTECTED]>
Fax-to-email: +44 (0)870 094 0861
Date: 22-Jul-06 Time: 14:07:46
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