add amorized inference example

[kiante-fernandez]

This is the first of two examples I want to include for using simulation-based inference with models in SSM.jl.

Here, I am using the package NeuralEstimators.jl. Feedback is welcome at this point.

https://github.com/msainsburydale/NeuralEstimators

Next, I am working on building likelihood approximation networks in Flux based on methods from Fengler, and I will have it up and running to sample with Turing. That will be the next example.

For now, I tried to use the LCA, as similar examples have shown online (see https://bayesflow.org/stable-legacy/_examples/LCA_Model_Posterior_Estimation.html).

I was able to get this running local but I think we have to env coflict we have to resolve to get NeuralEstimators working on the docs

[github-actions]

Benchmark Results

	master	580b359...	master / 580b359...
logpdf/("SequentialSamplingModels.DDM", 10)	1.66 ± 0.12 μs	1.66 ± 0.12 μs	0.999
logpdf/("SequentialSamplingModels.DDM", 100)	15.6 ± 0.83 μs	15.7 ± 0.78 μs	0.993
logpdf/("SequentialSamplingModels.LBA", 10)	2.95 ± 0.18 μs	2.92 ± 0.19 μs	1.01
logpdf/("SequentialSamplingModels.LBA", 100)	22.4 ± 0.71 μs	22.4 ± 0.73 μs	1
logpdf/("SequentialSamplingModels.LNR", 10)	1.67 ± 0.12 μs	1.68 ± 0.12 μs	0.997
logpdf/("SequentialSamplingModels.LNR", 100)	9.47 ± 0.35 μs	9.53 ± 0.34 μs	0.993
logpdf/("SequentialSamplingModels.RDM", 10)	2.65 ± 0.21 μs	2.61 ± 0.21 μs	1.01
logpdf/("SequentialSamplingModels.RDM", 100)	24.1 ± 0.99 μs	23.8 ± 0.82 μs	1.02
logpdf/("SequentialSamplingModels.Wald", 10)	0.453 ± 0.0081 μs	0.451 ± 0.011 μs	1
logpdf/("SequentialSamplingModels.Wald", 100)	2.65 ± 0.14 μs	2.65 ± 0.13 μs	0.999
logpdf/("SequentialSamplingModels.WaldMixture", 10)	1.3 ± 0.014 μs	1.33 ± 0.013 μs	0.976
logpdf/("SequentialSamplingModels.WaldMixture", 100)	11 ± 0.19 μs	11.4 ± 0.18 μs	0.969
rand/("SequentialSamplingModels.DDM", 10)	3.15 ± 0.4 μs	3.14 ± 0.45 μs	1
rand/("SequentialSamplingModels.DDM", 100)	30.2 ± 1.6 μs	30.3 ± 1.7 μs	0.995
rand/("SequentialSamplingModels.LBA", 10)	1.62 ± 0.048 μs	1.65 ± 0.053 μs	0.982
rand/("SequentialSamplingModels.LBA", 100)	11.2 ± 0.28 μs	11.3 ± 0.34 μs	0.988
rand/("SequentialSamplingModels.LCA", 10)	0.503 ± 0.12 ms	0.52 ± 0.1 ms	0.967
rand/("SequentialSamplingModels.LCA", 100)	5.29 ± 0.13 ms	5.42 ± 0.16 ms	0.977
rand/("SequentialSamplingModels.LNR", 10)	1.14 ± 0.037 μs	1.22 ± 0.033 μs	0.933
rand/("SequentialSamplingModels.LNR", 100)	6.19 ± 2.6 μs	7.22 ± 2.9 μs	0.856
rand/("SequentialSamplingModels.RDM", 10)	1.15 ± 0.039 μs	1.22 ± 0.041 μs	0.941
rand/("SequentialSamplingModels.RDM", 100)	9.27 ± 0.27 μs	10.1 ± 0.93 μs	0.919
rand/("SequentialSamplingModels.Wald", 10)	0.394 ± 0.024 μs	0.392 ± 0.026 μs	1
rand/("SequentialSamplingModels.Wald", 100)	2.12 ± 0.066 μs	2.14 ± 0.072 μs	0.993
rand/("SequentialSamplingModels.WaldMixture", 10)	1.35 ± 0.023 μs	1.35 ± 0.022 μs	1
rand/("SequentialSamplingModels.WaldMixture", 100)	11.9 ± 0.11 μs	11.9 ± 0.11 μs	1
simulate/SequentialSamplingModels.DDM	1.95 ± 0.51 μs	1.88 ± 0.53 μs	1.04
simulate/SequentialSamplingModels.LBA	4.94 ± 3.7 μs	4.85 ± 3.7 μs	1.02
simulate/SequentialSamplingModels.LCA	0.0679 ± 0.014 ms	0.0684 ± 0.013 ms	0.992
simulate/SequentialSamplingModels.RDM	0.089 ± 0.029 ms	0.0886 ± 0.028 ms	1
simulate/SequentialSamplingModels.Wald	4.33 ± 1.8 μs	4.73 ± 2.4 μs	0.915
simulate/SequentialSamplingModels.WaldMixture	2.04 ± 0.56 μs	2.09 ± 0.55 μs	0.976
simulate/mdft	0.159 ± 0.057 ms	0.169 ± 0.066 ms	0.937
time_to_load	0.88 ± 0.0061 s	0.887 ± 0.0053 s	0.993

Benchmark Plots

A plot of the benchmark results have been uploaded as an artifact to the workflow run for this PR.
Go to "Actions"->"Benchmark a pull request"->[the most recent run]->"Artifacts" (at the bottom).

[itsdfish]

Thanks! I only gave it a cursory look, but this is nice from what I can tell.

I was able to get this running local but I think we have to env coflict we have to resolve to get NeuralEstimators working on the docs

I think that is OK. I no longer auto-generate computationally intensive docs with the @example block to cut down on run time.

By the way, I have been corresponding with the developer of NeuralEstimators.jl to get help with a few technical details. One thing I have planned is to add an example of Bayesian parameter estimation of the LNR using NormalisingFlow and comparing it to Turing (for validation). I want to let you know so we do not duplicate any work. Thanks again!

[kiante-fernandez]

Thanks! I only gave it a cursory look, but this is nice from what I can tell.

I was able to get this running local but I think we have to env coflict we have to resolve to get NeuralEstimators working on the docs

I think that is OK. I no longer auto-generate computationally intensive docs with the @example block to cut down on run time.

By the way, I have been corresponding with the developer of NeuralEstimators.jl to get help with a few technical details. One thing I have planned is to add an example of Bayesian parameter estimation of the LNR using NormalisingFlow and comparing it to Turing (for validation). I want to let you know so we do not duplicate any work. Thanks again!

Okay, I will add @example. Also, nice! I think both cases are good examples, since in one we can map it to the "ground truth" by comparing with Turing.

I want to follow up with the team, as I think some additional text on considering simulation-based calibration could be instructive. Do you know if they are working on that? I was considering opening an issue.

[itsdfish]

Okay, I will add @example.

Just to clarify, please to not use @example for long running documentation such as this. One thing that would be helpful is if you included a full, copy and paste version of the code in the following:

#```@raw html
#<details>
#<summary><b>Show Details </b></summary>
#```
#```julia
## your code here
#```
#```@raw html
#</details>
#```

Sorry for the #. It would not display at all otherwise. Anyways, this will allow users to copy and paste a full version of the code rather than multiple pieces. It also hides/reveals the code so it does not create visual clutter. I also recommend it for testing the examples locally, since @example is too slow to run each time we test the docs.

I want to follow up with the team, as I think some additional text on considering simulation-based calibration could be instructive. Do you know if they are working on that? I was considering opening an issue.

Not that I know of. It might be worth looking into.

[kiante-fernandez]

Sorry for the #. It would not display at all otherwise. Anyways, this will allow users to copy and paste a full version of the code rather than multiple pieces. It also hides/reveals the code so it does not create visual clutter. I also recommend it for testing the examples locally, since @example is too slow to run each time we test the docs.

I see understood! I will modify.

[itsdfish]

Kiante, there a few minor revisions requested below. Once we sort those out, I will merge.

[itsdfish]

@kiante-fernandez, thank you for the revisions. This looks nice. I will go ahead and merge.

The unit tests for Turing is not passing with 0.37, even though it passed before. I'm looking into a solution.