positive_infinity()

[Juan]

Hello.

The manual speaks about positive_infinity() but no example is provided.

Could anybody explain how to use it properly.

Thanks.

[Daniel Lee]

positive_infinity() is a function. It returns the value of \infty.

It really doesn't have much purpose. One place you can use it is in a variable declaration. Suppose you have scale variable, sigma, that's lower bounded by 0. This is how I'd write it:

parameters {

  real<lower = 0> sigma;

}

You could write this, which isn't recommended, but you could still do this:

parameters {

  real<lower = 0, upper = positive_infinity()> sigma;

}

Since Stan is a language, I'm sure there are many other use cases that I haven't thought about.

Daniel

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[Pi]

OK, thanks.

Then it's just a constant containing a number?

Why does Stan use positive_infinity()  and not just positive_infinity without the parenthesis?

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[Daniel Lee]

positive_infinity is a function. You need to evaluate the function to get the value out of it.

[Pi]

I guess it's like  pi() or e().

Why are they defined as functions, and not just a constant containing a number?

[Bob Carpenter]

Because users like to declare variables named
pi and e and they'd otherwise be illegal or
they'd mask the built-in values.

The generated C++ will be compiled so as
not to involve a function call at run time. It's
a wonderful language that way (but it's part of
why the compile times are so long with optimization).

- Bob