MvNorm for several vectors at once

New to Julia
1

I’m trying to calculate some probabilities using MvNorm.

For a univariate case I would do the following to get the probabilities for a vector, all at once:

Norm_uni = Normal(2,1) #Creates the Normal dist
xvect    = [2,3,4,5]
pdf.(Norm_uni, xvect) # Resutls in a vector of length 4

I want to do the same but for a multivariate case. I have the following:

mu    = [2,4]
sigma = [1 0
         0 2]

Norm_def = MvNormal(mu,sigma)

x = [2.5,2]
pdf(Norm_def, x) #This works just fine for a single vector

But what if I want the values for two vectors?

y = [1,1]

pdf.(Norm_def, [x,y]) #This doesn't work

I get an error if I try to do just what I did with the univariate case. I also tried to use a matrix structure instead but it also didn’t work.

Thanks!

2

You don’t say what the error message is, but I’m guessing that this is because currently only univariate distributions are broadcastable (make univariate distributions broadcastable by simonbyrne · Pull Request #760 · JuliaStats/Distributions.jl · GitHub). The workaround is simply to wrap the distribution in a Ref (or a 1-component tuple), like:

pdf.(Ref(Norm_def), [x,y])
3

Great. This works. What is the Ref doing here? I don’t quite follow the description of Ref in the help.

4

From the manual:

Sometimes, you want a container (like an array) that would normally participate in broadcast to be “protected” from broadcast’s behavior of iterating over all of its elements. By placing it inside another container (like a single element Tuple) broadcast will treat it as a single value.

Ref(x) acts like a (cheap) zero-dimensional array of x.