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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.

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2 Answers 2

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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.

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  • $\begingroup$ (+1) Very well said -- especially, "EDA (plus deep introspection) would point me towards a model" $\endgroup$
    – suncoolsu
    Commented Sep 3, 2011 at 0:36
  • $\begingroup$ +1 as well. EDA really isn't about choosing a perspective, its about understanding your data to make more informed decisions. $\endgroup$
    – Fomite
    Commented Sep 3, 2011 at 6:44
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    $\begingroup$ I think my definition of "exploratory data analysis" is more narrow than yours. In my view, all good data analysis involves exploration. What distinguishes "exploratory data analysis" is the lack of a model or any effort towards formal inference. $\endgroup$
    – Karl
    Commented Sep 3, 2011 at 16:18
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    $\begingroup$ See Rubin (1984), and all of Gelman's work on posterior predictive checks. Exploratory data analysis can be tied much more closely to model building and checking than is typically done. These papers, in particular Rubin (1984), shows how frequentist ideas are relevant to Bayesian inference. $\endgroup$
    – Tristan
    Commented Sep 8, 2011 at 3:33
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    $\begingroup$ This, in my view, contradicts what Gelman, Hullman, and many other Bayesians are talking about recently. Their argument is that EDA is always a comparison against what you expected to be true (your prior beliefs) and what appears in the data, regardless of whether you made the prior beliefs explicit (through a generative model) or not (through internal comparisons and visual inspection). This is what I think @Tristan is alluding to. Bayesian analysis seeks to make these comparisons explicit, and "insights" in EDA are more formally defined as deviations from one's prior beliefs. $\endgroup$
    – aranglol
    Commented Apr 24, 2021 at 18:31
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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.

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