Does Squiggle treat multiple instances of the same variable as independent variables?

[RationalityEnhancement]

Hi,

I am getting the impression that Squiggle treats multiple instances of the same variable as independent variables. Here is a fairly minimal example of this problem. I want to calculate the variance of a random variable. The correct answer is 1. Obviously, the variance can never be negative. But the answer I get from Squiggle is -0.023. Can you confirm that this happens because Squiggle treats x and x as two independent variables even though it is the same variable? If so, is this a bug or am I fundamentally misunderstanding the semantics of Squiggle code?

var(x) ={
x_bar = mean(x)
mean((x-x_bar)*(x-x_bar))
}

var(normal(0,1))

[OAGr]

Yea, this part is confusing.

Squiggle treats SampleSets as independent, but it has no way of doing this for Symbolic or PointSet dists. In this case, there was no call forcing the distributions to be SampleSets until fairly late.

Try this:

var(x) ={
y = SampleSet.fromDist(x)
x_bar = mean(y)
mean((y-x_bar)*(y-x_bar))
}

var(normal(0,1))

See this for more:
https://www.squiggle-language.com/docs/Guides/Gotchas#sample-set-correlations

[Hazelfire]

See also #1442, which is a possible solution to this problem.

[joel-becker]

are there any solutions to this problem for variables over time?

take geometric discounting: discount_over_time(r, t) = r^t. atm, squiggle seems to be taking independent draws from the random variable r (at each point in time). but it seems more intuitive to me to fix my uncertain draws of r, then ask how they progress through time.

atm i don't think i have a way to implement this in squiggle? discount_over_time(truncate(normal(0.9, 0.1), 0, 1), t) = discount_over_time(SampleSet.fromDist(truncate(normal(0.9, 0.1), 0, 1)), t).

[OAGr]

I don't really follow that last example, but about over-time tracking -

I assume what you are describing is something like,
"Every year, I earn income X=normal(5,1). I want to simulate my earnings in point in time (t) in the future."

With Squiggle, you could use integration to calculate this. However, it's messy to plot the total over time. Our current function plots calculate each X point independently.

You could use a reducer statement to take an aggregation and save it at each point (like, you start with year 1, save the result for year 1, do the same for year 2, and so on), but it would be more work. As I think about this, I think we can do it in Squiggle code, but it is a bit messy.

[OAGr]

I would be curious to get a better example here though, I'm not sure if I really understood your use case.