Working with numbers smaller tha 10^-308

Hi,

I would like to know if it is possible to use Matlab for very small numbers (smaller than 10^-308 ). It's very important for my application "statistical genetics". in this field, somes probabilities are smaller than 10^-500.

Thank you

[John Doe]

I'm sorry, but I just have to ask: How can a probability of 10^-500 be of any relevance, ever? (I'm actually curious)

[Sean de Wolski]

+1 @Robert's comment

[sadoune sadoune]

Hi Robert,

You can imagine a vector length 500, each case represent a probability, and the probability i would like to compute is the product of all this probabilities (independance).

[John Doe]

Ok, then I see where you get the number from, but if you are ending up with a probability that low, it is literally impossible for it to happen. Isn't OK to just let it be equal to 0?

I don't mean to be rude or condescending, I just don't get how it would make sense to keep working with numbers that low.

Anyhow, I hope someone can provide an answer for you, and good luck =)

Answer 1

[Sean de Wolski]

You can do this using vpa() in the Symbolic Math Toolbox:

v = vpa('3.14159^-5000')

And for more info:

doc vpa

You could also use exact symbolic arithmetic:

sym('3.1415^-34334')

doc sym

[sadoune sadoune]

Thank you for your answer,

I tried vpa function with the following example:

 for i=1:400
tab(i)=0.1;
end

v = vpa(prod(tab))

and the result was v =0.0 :(

[Sean de Wolski]

That's because you're doing the computation as a double and then converting it to vpa(). Convert it to vpa before doing the computation:

for i=400:-1:1
  tab(i)=vpa(0.1);
end
v = (prod(tab))

[sadoune sadoune]

Thank you Wolski. it's OK now

Answer 2

[Peter Perkins]

Quite often in statistics when one has very small probabilities, one works on the log scale. That's why one typically maximizes the LOG-likelihood, and not the likelihood.