Dear R-List,
I have a set of possibilities I want to sample from:
bases <- list(c('A', 'C'), c('A', 'G'), c('C', 'T'))
possibilities <- as.matrix(expand.grid(bases))
>possibilities
Var1 Var2 Var3
[1,] "A" "A" "C"
[2,] "C" "A" "C"
[3,] "A" "G" "C"
[4,] "C" "G" "C"
[5,] "A" "A" "T"
[6,] "C" "A" "T"
[7,] "A" "G" "T"
[8,] "C" "G" "T"
If I want to randomly sample one of these rows. If I do this, I find that it is
25% likely that my choice will have an identical first and last letter (e.g.
[1,] "A" "A" "C"). It is also 25% likely that my choice will have an
identical first and third letter (e.g. [4,] "C" "G" "C"). It is not likely at
all that the second and third letter of my choice could be identical.
What I would like to do, is sample one of the rows, but given the constraint
that the probability of drawing identical letters 1 and 2 should be 50% or 0.5,
and at the same time the probability of drawing identical letters 1 and 3
should be 50%. I am unsure on how to do this, but I know it involves coming up
with a modified set of weights for the sample() function. My progress is below,
any advice is much appreciated.
Best Wishes,
Ben Ward, UEA.
So I have used the following code to come up with a matrix, which contains
weighting according to each criteria:
possibilities <- as.matrix(expand.grid(bases))
identities <- apply(possibilities, 1, function(x) c(x[1] == x[2], x[1] ==
x[3], x[2] == x[3]))
prob <- matrix(rep(0, length(identities)), ncol = ncol(identities))
consProb <- apply(identities, 1, function(x){0.5 / length(which(x))})
polProb <- apply(identities, 1, function(x){0.5 / length(which(!x))})
for(i in 1:nrow(identities)){
prob[i, which(identities[i,])] <- consProb[i]
prob[i, which(!identities[i,])] <- polProb[i]
}
rownames(prob) <- c("1==2", "1==3", "2==3")
colnames(prob) <- apply(possibilities, 1, function(x)paste(x, collapse = ",
"))
This code gives the following matrix:
A, A, C C, A, C A, G, C C, G, C A, A,
T C, A, T A, G, T C, G, T
1==2 0.25000000 0.08333333 0.08333333 0.08333333 0.25000000 0.08333333
0.08333333 0.08333333
1==3 0.08333333 0.25000000 0.08333333 0.25000000 0.08333333 0.08333333
0.08333333 0.08333333
2==3 0.06250000 0.06250000 0.06250000 0.06250000 0.06250000 0.06250000
0.06250000 0.06250000
Each column is one of the choices from 'possibilities', and each row gives a
series of weights based on three different criteria:
Row 1, that if it possible from the choices for letter 1 == letter 2, that
combined chance be 50%.
Row 2, that if it possible from the choices for letter 1 == letter 3, that
combined chance be 50%.
Row 3, that if it possible from the choices for letter 2 == letter 3, that
combined chance be 50%.
So:
If I used sample(x = 1:now(possibilities), size = 1, prob = prob[1,])
repeatedly, I expect about half the choices to contain identical letters 1 and
2.
If I used sample(x = 1:now(possibilities), size = 1, prob = prob[2,])
repeatedly, I expect about half the choices to contain identical letters 1 and
3.
If I used sample(x = 1:now(possibilities), size = 1, prob = prob[3,])
repeatedly, I expect about half the choices to contain identical letters 2 and
3. Except that in this case, since it is not possible.
Note each row sums to 1.
What I would like to do - if it is possible - is combine these three sets of
weights into one set, that when used with
sample(x = 1:nrow(possibilities, size = 1, prob = MAGICPROB) will give me a
list of choices, where ~50% of them contain identical letters 1 and 2, AND ~50%
of them contain identical letters 1 and 3, AND ~50% again contain identical
letters 2 and 3 (except in this example as it is not possible from the choices).
Can multiple probability weightings be combined in such a manner?
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