Graphics Reference
In-Depth Information
Challenges Associated with the
Graphical Display of Bayesian Inferences
16.4
We expect that the quality of statistical analyses would benefit greatly if graphs were
more routinely used as part of the data analysis. Exploratory data analysis would
be more effective if it could be implemented as a part of the sotware for complex
modeling. To some extent this is done with residual plots in regression models, but
for complex models there is the potential for much more progress.
As discussed in detail in Gelman (
), we anticipate four challenges: (
) inte-
grating the automatic generation of replication distributions into the computing en-
vironment; (
) choosing the replication distribution - this is not an automatic task,
since the task involves selecting which parameters to resample and which to keep
constant; (
)choosing the testvariables; (
) displaying testvariables as graphs. In the
near future, automatic features for simulating replication distributions and perform-
ing standard model checks should become available.
Integrating Graphics and Bayesian Modeling
16.4.1
Wefit Bayesian models routinely with sotware such as BUGS (BUGSProject,
),
andmovethesimulationsovertoR(RDevelopmentCoreTeam,
)usingR
Win-
BUGS (Sturtz et al.,
). Simulations can also be summarized in R in a more natu-
ralwaybyconverting thesimulation matricesintovectorsofrandomvariable objects
(KermanandGelman,
).BUGShasalsoitslimitations; wealsofitcomplexmod-
els in R using Umacs, the “Universal Markov chain sampler,” (Kerman,
).
We are currently investigating how to define an integrated Bayesian computing
environment where modeling, fitting, and automatic generation of replications for
model-checkingispossible.hisrequiresfurtherefforttodevelopstandardizedgraph-
ical displays for Bayesian model-checking and understanding. An integrated com-
puting environment is nevertheless the necessary starting point, since functions that
generate such complex graphical displays should have full access to the models, the
data, and predictions.
he environment must also take into account the fact that we may fit multiple
modelswithdifferentsetsofobservations; withoutasystemthatcandistinguishmul-
tiple models (and the inferences associated with them) it is not possible to perform
comparisons of them.
Summary
16.5
Exploratory data analysis and modeling can work well together: in our applied re-
search, graphs are used to comprehend and check models. In the initial phase, we
create plots that show us how the models work, and then plot data and compare it to
the model to see where more work is needed.
