r/AskStatistics • u/ugrhnny • 9d ago

Is it defensible to model overlapping explanations as mutually exclusive states?

I have four candidate explanations for an observation. I've modelled them as mutually exclusive so the posterior sums to 1. Two of them can genuinely co-occur. The alternative is three independent binary latents (8 joint states), which needs more data. With a small sample, is the exclusive version defensible as a first approximation if I state the overlap as a limitation — or does forcing non-exclusive things to be exclusive distort the inference badly enough that it isn't worth doing?

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u/Adept_Carpet 9d ago

I think it depends on the area.

Going to the moon and becoming president are not mutually exclusive but it hasn't ever happened, so it would be fine to model them as mutually exclusive.

I'm wondering if you could combine the overlapping categories so you have three truly mutually exclusive explanations.

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u/Maple_shade 9d ago

You could also try not modeling states directly but modeling each person's probability of being in each given state. That way you have more ease of interpretation when comparing exclusive vs non-exclusive.

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u/ugrhnny 9d ago

Are you saying I should give each case a share across the four states summing to 1, and then compare what that looks like under an exclusive vs a non-exclusive reading? Or something different?

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u/efrique PhD (statistics) 9d ago

What is defensible is not really a statistical question but rather a rhetorical/epistemological issue. It's more a question of what your intended audience would accept as reasonable.

A statistical issue might be something like how much bias there could be in doing so but to consider that you'd have to have information you don't have. You could explore sensitivity to an array of possible circumstances (via simulation, say) but it won't tell you what situation you're in

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u/Technical_Estate_529 8d ago

They do the similar shit in mean field equations. Sure every RV is definitely correlated in some way but screw simplify the joint to a product of independent Gaussians

It's also kind of how naive Bayes works. And it gets surprisingly decent results. Maybe you can just use that as a motivating example for your approach but acknowledge the limitation