```
tags:
- data-assimilation
- transport
- algorithm
```

Parameter estimation

Suppose we have the model

However, we may not know our *infinite number* of distributions we may care about. Contrast this with how

For more of discussion of a state-augmentation approach, see my thesis.

Another idea would be to form a map

- We then have to perform a proper
analysis step using the "correct" . These then will properly come from . - We need
to be associated with the distribution . I qualitatively like the average (it seems nice!), but another very reasonably idea would be to just take a sample . - There's a statistic that we, in some sense, disregard here:
, the parameters of . It would be extraordinarily curious to instead perform inference on the pair .- Then,
, where .

- Then,

Flipping some notation, suppose we have a joint distribution

Interactive Graph

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