Are there differences in Bayesian and frequentist approaches to EDA?

Question

Very simply put: Are there any differences in Bayesian and Frequentist approaches to Exploratory Data Analysis?

I know of no inherent biases in EDA methods as a histogram is a histogram, a scatterplot is a scatterplot, etc., nor have I found examples of differences in how EDA is taught or presented (ignoring a particularly theoretical paper by A. Gelman). Finally, I looked at CRAN, the arbiter of all things applied: I haven't found packages tailored to a Bayesian approach. However, I thought CV might have a few people who could shed a light on this.

Why should there be differences?

For starters:

1. When identifying appropriate prior distributions, shouldn't one investigate this visually?
2. When summarizing data and suggesting whether to use a frequentist or Bayesian model, shouldn't the EDA suggest which direction to go?
3. The two approaches have very clear differences on how to handle mixture models. Identifying that a sample likely comes from a mixture of populations is challenging and directly related to the methodology used to estimate the mixture parameters.
4. Both approaches incorporate stochastic models and the selection of model is driven by understanding the data. More complex data or more complex models necessitates more time in EDA. With such distinctions between stochastic models or generating processes, there are differences in EDA activities, so shouldn't there be distinctions arising from different stochastic approaches?

Note 1: I'm not concerned with the philosophies of either "camp" - I only want to address any gaps in my EDA toolkit and methods.

Answer 1

In my mind, Bayes vs frequentist is about formal inference, and exploratory data analysis is neither.

Certainly, when it comes to model assessment/goodness-of-fit and sensitivity analysis, in which I'd classify your points (1), (3), and (4), there will be differences in how one would proceed, but that's because the nature of the differences between the analysis and computational methods rather than about philosophy.

Regarding your (2), I don't generally see the results of the EDA as pointing you towards the Bayesian or frquentist approach, but rather I'd think it was the goal of the study that mattered most.

For me personally, the EDA (plus deep introspection) would point me towards a model, and if I could find a natural frequentist approach that answered the scientific question reasonably well, I'd go with that, but if by the nature of the situation, no frequentist method would work well, and if there were a reasonable prior, I'd use Bayes.

Answer 2

I thinks that, EDA helps you to build a model, make some assumptions and (if required) update the model and its assumptions. I select a pragmatics approach to use for model fitting and assessment.