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Merge pull request #33 from CDCgov/toy-model-generate-data
Toy model generate data
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EpiAware/test/predictive_checking/toy_model_log_infs_RW.jl
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| using Pkg: generate | ||
| #= | ||
| # Toy model for running analysis: | ||
| This is a toy model for demonstrating current functionality of EpiAware package. | ||
| ## Generative Model without data | ||
| ### Latent Process | ||
| The latent process is a random walk defined by a Turing model `random_walk` of specified length `n`. | ||
| _Unfixed parameters_: | ||
| - `σ²_RW`: The variance of the random walk process. Current defauly prior is | ||
| - `init_rw_value`: The initial value of the random walk process. | ||
| - `ϵ_t`: The random noise vector. | ||
| ```math | ||
| \begin{align} | ||
| X(t) &= X(0) + \sigma_{RW} \sum_{t= 1}^n \epsilon_t \\ | ||
| X(0) &\sim \mathcal{N}(0, 1) \\ | ||
| \epsilon_t &\sim \mathcal{N}(0, 1) \\ | ||
| \sigma_{RW} &\sim \text{HalfNormal}(0.05). | ||
| \end{align} | ||
| ``` | ||
| ### Log-Infections Model | ||
| The log-infections model is defined by a Turing model `log_infections` that takes the observed data `y_t` (or `missing` value), | ||
| an `EpiModel` object `epimodel`, and a `latent_process` model. In this case the latent process is a random walk model. | ||
| It also accepts optional arguments for the `latent_process_priors`, `transform_function`, `pos_shift`, `neg_bin_cluster_factor`, and `neg_bin_cluster_factor_prior`. | ||
| ```math | ||
| \log I_t = \exp(X(t)). | ||
| ``` | ||
| ### Observation model | ||
| The observation model is a negative binomial distribution with mean `μ` and cluster factor `r`. Delays are implemented | ||
| as the action of a sparse kernel on the infections $I(t)$. The delay kernel is contained in an `EpiModel` struct. | ||
| ```math | ||
| \begin{align} | ||
| y_t &\sim \text{NegBinomial}(\mu = \sum_s\geq 0 K[t, t-s] I(s), r), | ||
| r &\sim \text{Gamma}(3, 0.05/3). | ||
| \end{align} | ||
| ``` | ||
| ## Load dependencies in `TestEnv` | ||
| =# | ||
|
|
||
| split(pwd(), "/")[end] != "EpiAware" && begin | ||
| cd("./EpiAware") | ||
| using Pkg | ||
| Pkg.activate(".") | ||
|
|
||
| using TestEnv | ||
| TestEnv.activate() | ||
| end | ||
|
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| using EpiAware | ||
| using Turing | ||
| using Distributions | ||
| using StatsPlots | ||
| using Random | ||
| using DynamicPPL | ||
| Random.seed!(0) | ||
|
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| #= | ||
| ## Create an `EpiModel` struct | ||
| Somewhat randomly chosen parameters for the `EpiModel` struct. | ||
| =# | ||
|
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| truth_GI = Gamma(1, 2) | ||
| truth_delay = Uniform(0.0, 5.0) | ||
| neg_bin_cluster_factor = 0.05 | ||
| time_horizon = 100 | ||
|
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| epimodel = EpiModel( | ||
| truth_GI, | ||
| truth_delay, | ||
| neg_bin_cluster_factor, | ||
| time_horizon, | ||
| D_gen = 10.0, | ||
| D_delay = 10.0, | ||
| ) | ||
|
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| #= | ||
| ## Define a log-infections model | ||
| The log-infections model is defined by a Turing model `log_infections`. | ||
| In this case we don't have observed data, so we use `missing` value for `y_t`. | ||
| =# | ||
| toy_log_infs = log_infections( | ||
| missing, | ||
| epimodel, | ||
| random_walk; | ||
| latent_process_priors = EpiAware.STANDARD_RW_PRIORS, | ||
| ) | ||
|
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| #= | ||
| ## Sample from the model | ||
| I define a fixed version of the model with initial infections set to 10 and variance of the random walk process set to 0.1. | ||
| We can sample from the model using the `rand` function, and plot the generated infections against generated cases. | ||
| =# | ||
| cond_toy = fix(toy_log_infs, (init_rw_value = log(10.0), σ²_RW = 0.1)) | ||
| random_epidemic = rand(cond_toy) | ||
|
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| # We can get the generated infections using `generated_quantities` function. Because the observed | ||
| # cases are "defined" with a `~` operator they can be accessed directly from the randomly sampled | ||
| # process. | ||
| gen = generated_quantities(cond_toy, random_epidemic) | ||
| plot( | ||
| gen.I_t, | ||
| label = "I_t", | ||
| xlabel = "Time", | ||
| ylabel = "Infections", | ||
| title = "Generated Infections", | ||
| ) | ||
| scatter!(X.y_t, lab = "generated cases") |
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| Original file line number | Diff line number | Diff line change |
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| @@ -0,0 +1,40 @@ | ||
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| @testitem "`log_infections` with RW latent process" begin | ||
| using Distributions, Turing, DynamicPPL | ||
| # Define test inputs | ||
| y_t = missing # Data will be generated from the model | ||
| epimodel = EpiModel([0.2, 0.3, 0.5], [0.1, 0.4, 0.5], 0.8, 10) | ||
| latent_process_priors = EpiAware.STANDARD_RW_PRIORS | ||
| transform_function = exp | ||
| n_generate_ahead = 0 | ||
| pos_shift = 1e-6 | ||
| neg_bin_cluster_factor = 0.5 | ||
| neg_bin_cluster_factor_prior = Gamma(3, 0.05 / 3) | ||
|
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| # Call the function | ||
| test_mdl = log_infections( | ||
| y_t, | ||
| epimodel, | ||
| random_walk; | ||
| latent_process_priors, | ||
| transform_function, | ||
| pos_shift, | ||
| neg_bin_cluster_factor, | ||
| neg_bin_cluster_factor_prior, | ||
| ) | ||
|
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| # Define expected outputs for a conditional model | ||
| # Underlying log-infections are const value 1 for all time steps and | ||
| # any other unfixed parameters | ||
|
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| fixed_test_mdl = fix( | ||
| test_mdl, | ||
| (init_rw_value = log(1.0), σ²_RW = 0.0, neg_bin_cluster_factor = 0.05), | ||
| ) | ||
| X = rand(fixed_test_mdl) | ||
| expected_I_t = [1.0 for _ = 1:epimodel.time_horizon] | ||
| gen = generated_quantities(fixed_test_mdl, rand(fixed_test_mdl)) | ||
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| # Perform tests | ||
| @test gen.I_t ≈ expected_I_t | ||
| end |