Need help on structuring a problem with stochastic algebra...

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Dear all,

I am stuck at structuring the general outline of a programming project and could use some fresh thoughts :)

I have a value D = 12.03

Then I have a set of other values
H1 = 11.91
H2 = 11.91
H3 = 10.54
H4 = 15.23

which should be substituting the value "D" depending on their similarity to "D".

I have therefore calculated probabilities, which value H1-H4 would be best suited as substitution for "D", using the following formula:
Px = (1-Hx/(H1+H2+H3+H4)/3)

P1 = 0.325
P2 = 0.325
P3 = 0.236
P4 = 0.117

So far everything went well - now the problem is: There is another condition for the usability of H1-H4 as substitution for "D", I designate this S1-S4:

S1 = 0.59
S2 = 5.5
S3 = 3.0
S4 = 24.8


I now want to modulate the calculated probabilites P1-P4, taking into account the additional information given by S1-S4.
How can this be achieved?

I thought about calculating the probabilities in analogy to P1-P4 as P1b-P4b and then simply add the probabilities up and divide by 2 to make them sum up to 1 again:

P1_total = (P1 + P1b)/2
P2_total = (P2 + P2b)/2
P3_total = (P3 + P3b)/2
P4_total = (P4 + P4b)/2

Would this be correct? Or should the probabilities be multiplied or otherwise processed?

Thank you very much in advance for any help! :)

Regards,
Peter
I'm not really sure what sort of answers you are expecting so I'll just pick at the obvious first issue:

PeterR wrote:
now the problem is: There is another condition for the usability of H1-H4 as substitution for "D", I designate this S1-S4:


In calculating probabilities one would ask if the conditions are statistically dependent or independent. The easiest is if you can assume they are independent. In that case the combined probability is the product of the two individual probabilities, not their average. You might want to check out Bayes' theorem (http://en.wikipedia.org/wiki/Bayes%27_theorem).

A.G.
WaveMetrics, Inc.

March 16, 2015 at 01:26 pm - Permalink