Graphics Reference
In-Depth Information
Introduction
16.1
Modern Bayesian statistical science commonly proceeds without reference to statis-
tical graphics; both involve computation, but they are rarely considered to be con-
nected. Traditional views about the usage of Bayesian statistics and statistical graph-
ics result in a certain clash of attitudes between the two. Bayesians might do some
exploratory data analysis (EDA) to start with, but once the model or class of models
is specified, the next analytical step is to fit the data; graphs are then typically used to
checkconvergence of simulations, or they areusedasteaching aids oras presentation
tools - but not as part of the data analysis. Exploratory data analysis appears to have
noformalplaceinBayesianstatisticsonceamodelhasactuallybeenfitted.According
to this extreme view, the only connection between Bayesian inference and graphics
occurs through convergence plots of Markov chain simulations, and histograms and
kernel density plots of the resulting estimates of scalar parameters.
On the other hand, the traditional attitude of statistical graphics users is that “all
models are wrong;” we are supposed to keep as close to the data as possible without
referencing a model, since models incorporate undesirable subjective components
and parametric assumptions into preliminary analysis. In true Tukey tradition, even
ifagraphical methodcanbederived fromaprobabilitymodel(e.g.,rootogramsfrom
the Poisson distribution), we still don't mention the model,because the graph should
stand or fall on its own.
Given these seemingly incompatible attitudes, how can we then integrate the in-
herently model-based Bayesian inference with the (apparently) inherently model-
aversive nature of statistical graphics? Our attitude is a synthesis of ideas adopted
from statistical graphics and Bayesian data analysis. he fundamental idea is that we
consider all statistical graphs to be implicit or explicit comparisons to a reference dis-
tribution; that is, to a model. his idea is introduced in Gelman (
); the article
proposes an approach that can be used to unify EDA with formal Bayesian statisti-
cal methods. he connection between EDA and goodness-of-fit testing is discussed
in Gelman (
). hese two articles formalize the graphical model-checking ideas
presented in Buja et al. (
); Buja and Cook (
); Buja et al. (
), which have
been informally applied in various contexts fora long time (e.g.,Bush and Mosteller,
; Ripley,
).
The Role of EDA in Model Comprehension
and Model-Checking
16.1.1
Exploratory data analysis, which is aided by the use of graphs, is done to look for
patterns in the data. While the reference distributions in such cases are typically im-
plicit, they are always there in the mind of the modeler. In an early article on EDA
by Tukey (
), he focused on the idea that “graphs intended to let us see what
may be happening over and above what we have already described,” which suggests
that these graphs can be built upon existing models. Ater all, to look for the un-
