Graphics Reference
In-Depth Information
expected is to look for something that differs from something that we were expect-
ing - the reference model. For example, even simple time series plots are viewed
implicitly as comparisons to zero, a horizontal line, linearity, monotonicity, and so
forth. Viewing two-way scatterplots usually implies areference toan assumed model
of independence. Before looking at a histogram, we have certain baselines of com-
parison (symmetric distribution, bimodal, skewed) in our minds. In the Bayesian
sense, looking at inferences and deciding whether they “make sense” can be inter-
preted as a comparison of the estimates with our prior knowledge; that is, to a prior
model.
he ideas that EDA gives us can be made more powerful if used in conjunction
with sophisticated models. Even if one believes that graphical methods should be
model-free, it can still be useful to have provisional models that make EDA more
effective. EDA can be thought of as an implicit comparison to a multilevel model; in
addition, EDA can be applied to inferences as well as to raw data.
InBayesian probability modelcomprehension and model-checking, the reference
distribution can beformally obtained bycomputing thepredictive distribution ofthe
observables, which is also called the replication distribution. Draws from the poste-
rior predictive distribution represent our previous knowledge of the (marginal) dis-
tributionoftheobservables.hemodelfitcanbeassessedbycomparingtheobserved
values with posterior predictive draws; discrepancies represent departures from the
model. Comparisons are usually best made via graphs, since the models used for
the observables are usually complex. However, depending on the complexity of the
model,highly sophisticated graphical checksoten need tobedevised and tailored to
the model.In this article, we review these principles, show examples of how to apply
them to data analysis, and discuss potential extensions.
Comparable Non-Bayesian Approaches
16.1.2
Our Bayesian data visualization tools make use of posterior uncertainty, as summa-
rized by simulated draws of parameters and replicated data. A similar non-Bayesian
analysis might compute point estimates for parameters and then simulate data using
a parametric bootstrap. his reduces to (Bayesian) posterior predictive checking if
the parameter estimates are estimated precisely (if the point estimate has no poste-
rior variance).
A confidence interval (the point estimate plus or minus the standard error) ap-
proximately summarizes the posterior uncertainty about a parameter. In multilevel
models, a common non-Bayesian approach is to compute point estimates for the hy-
perparameters and then simulate the modeled parameters.
he visualization tools described in this article should also work in these non-
Bayesian settings.
