Add a page on predictive distributions #658
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Preview the changes: https://turinglang.org/docs/pr-previews/658 |
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Nov 6, 2025
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| ::: {.callout-note} | ||
| If you want to specify `X` as an argument to the model, then to mark it as being unobserved, you have to instantiate the model again with `X = missing` or `X = fill(missing, N)`. | ||
| Whether you use `missing` or `fill(missing, N)` depends on whether `X` is treated as a single distribution (e.g. with `filldist` or `product_distribution`), or as multiple independent distributions (e.g. with `.~` or a for loop over `eeachindex(X)`). |
| Statistically, this is defined as | ||
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| $$ | ||
| p(\tilde{x} | \theta, \mathbf{X}) = \int p(\tilde{x} | \theta) p(\theta | \mathbf{X}) d\theta, |
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If you integrate out \theta on the right hand side, it shouldn't be a "free" parameter on the left hand side.
This should be correct:
p(\tilde{x} | \mathbf{X}) = \int p(\tilde{x} | \theta) p(\theta | \mathbf{X}) d\theta,
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| This means that when the model is evaluated, it will sample a new value for `X`. | ||
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| ```{julia} | ||
| predictive_model = decondition(model) |
| ::: {.callout-tip} | ||
| ## Reproducibility | ||
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| `predict`, like many other Julia functions, takes an optional `rng` as its first argument. |
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this could also be "like many other random generation Julia functions" - taking that qualifier from the Random.jl docs at https://docs.julialang.org/en/v1/stdlib/Random/#Random-generation-functions
Though I feel that's a bit clunky as well 🤷
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Only 3 years late (!), but closes #332.
View here: https://turinglang.org/docs/pr-previews/658/usage/predictive-distributions/