Graphics Reference
In-Depth Information
Using Visualization to Understand
and Check Models
16.2
he key to Bayesian inference is its unified treatment of uncertainty and variability;
wewouldlike tousethisindata visualization (e.g.,Wilkinson,
,Chap.
)aswell
as in data analysis in general (Kerman and Gelman,
).
Using Statistical Graphics in Model-Based Data Analysis
16.2.1
EDAisthesearchforunanticipated areasofmodelmisfit.Confirmatory data analysis
(CDA),ontheotherhand,quantifiestheextenttowhichthesediscrepanciescouldbe
expected to occur by chance. We would like to apply the same principles to the more
complex models that can now be fitted, using methods such as Bayesian inference
and nonparametric statistics. Complex modeling makes EDA more effective in the
senseofbeingabletocapturemoresubtlepatternsindata.Conversely,whencomplex
modelsare used, graphical checks are even more desirable in order to detect areas of
model misfit.
We, like other statisticians, do statistical modeling in an iterative fashion, explor-
ing our modeling options, starting with simple models, and expanding the models
into more complex and realistic models, putting in as much structure as possible,
trying to find deficiencies in our model at each stage, building new models, and iter-
ating this process until we are satisfied. We then use simulation-based model checks
(comparisons ofobserved data toreplications underthe model);tofindpatterns that
represent deviations from the current model. Moreover, we apply the methods and
ideas ofEDAtostructures otherthan rawdata, suchasplots ofparameterinferences,
latent data, and completed data (Gelman et al.,
); Fig.
.
illustrates this.
At a theoretical level, we look at the model,identifying different sorts of graphical
displays with different symmetries or invariancies in an explicit or implicit reference
distribution of the test variables. his serves two purposes: to add some theoretical
structure to the graphics and EDA, so that graphical methods can be interpreted in
terms of implicit models, and to give guidelines on how to express model checking
as a graphical procedure most effectively.
Bayesian Exploratory Data Analysis
16.2.2
Bayesian inference has the advantage that the reference distribution - the predic-
tive distribution for the data that could have been observed - arises directly from
the posterior simulations (which are typically obtained using iterative simulation).
Consequently, we can draw from this distribution and use these simulations to pro-
duce a graph comparing the predictions to the observed data. Such graphs can be
customized to exploit symmetries in the underlying modelto aid interpretation. he
inclusionofimputedmissingandlatent data canresultinmoreunderstandable com-
pleted-data exploratory plots.
