add arviz plot for posterior predictive

[sbidari]

Add 'hdi_type' plot with equal tailed credible intervals to demonstrate posterior predictive distribution using arviz

(second try after closing previous one due to mangled commit history)

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[sbidari]

Did you try anything with plot_lm, plot_ppc, or plot_ts?

I couldn't get the 'timeseries' type plots (plot_lm and plot_ts) to work for the hospital admissions model. I suspect it has something to do with the padding as those plots work for the basic model implementation. The output from plot_lm would be similar to figure generated here.

I was not sure if we wanted multiple posterior predictive plots. I can include figures using plot_ppc if you'd like. @damonbayer

[damonbayer]

I couldn't get the 'timeseries' type plots (plot_lm and plot_ts) to work for the hospital admissions model. I suspect it has something to do with the padding as those plots work for the basic model implementation.

Can you demonstrate those plots working somewhere? In this tutorial or a different one.

I was not sure of we wanted multiple posterior predictive plots. I can include figures using plot_ppc if you'd like. @damonbayer

Yes, please.

[sbidari]

I couldn't get the 'timeseries' type plots (plot_lm and plot_ts) to work for the hospital admissions model. I suspect it has something to do with the padding as those plots work for the basic model implementation.

Can you demonstrate those plots working somewhere? In this tutorial or a different one.

Ok! I will add demonstration of these to getting started tutorial.

[sbidari]

I do not understand why the posterior predictive distribution for the hospital admissions model does not have the same dimension as the observation.

Am I missing something here? @damonbayer

[damonbayer]

Am I missing something here? @damonbayer

It is because of the padding and/or seeding. I would try padding in the data in InferenceData with missing values for now. If that doesn't work, we can change the model a bit or manually modify the samples.

All of this will be handled better once we have time incorporated throughout the project.

[sbidari]

That's what I thought too but this is for the model fit without padding shown below:

hosp_model.run(
    num_samples=1000,
    num_warmup=1000,
    data_observed_hosp_admissions=dat["daily_hosp_admits"].to_numpy(),
    rng_key=jax.random.PRNGKey(54),
    mcmc_args=dict(progress_bar=False,num_chains=1),
)

Since we are not padding the observation data here, padding shouldn't come into play, right?

[damonbayer]

Since we are not padding the observation data here, padding shouldn't come into play, right?

It's just because of the seeding, then.

[damonbayer]

I do not understand why the posterior predictive distribution for the hospital admissions model does not have the same dimension as the observation.

Am I missing something here? @damonbayer

Try with the argument supplying the argument data_observed_hosp_admissions instead of n_timepoints_to_simulate

I think it would be hosp_model.posterior_predictive(data_observed_hosp_admissions=dat["daily_hosp_admits"].to_numpy().astype(float).

You could save that as its own variable somewhere, since we have now used it twice.

[sbidari]

Try with the argument supplying the argument data_observed_hosp_admissions instead of n_timepoints_to_simulate

I think it would be hosp_model.posterior_predictive(data_observed_hosp_admissions=dat["daily_hosp_admits"].to_numpy().astype(float).

This solves the dimension issue but now the posterior predictive samples are just observed data.

[damonbayer]

This solves the dimension issue but now the posterior predictive samples are just observed data.

Oops. We will need to change the model code.

[sbidari]

I noticed for both prior_predictive and posterior_predictive if called using data_observed_hosp_admissions=dat["daily_hosp_admits"].to_numpy().astype(float) argument then the predictive distributions returned is simply the observed data.