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What do you do to visualize uncertainty?

Howard Wainer writes:

What do you do to visualize uncertainty?
Do you only use static methods (e.g. error bounds)?
Or do you also make use of dynamic means (e.g. have the display vary over time proportional to the error, so you don’t know exactly where the top of the bar is, since it moves while you’re watching)?

Have you any thoughts on this topic?
I assume that since a Bayesian generates a posterior dist’n the output should not be point but rather a dist’n; and you being the most prolific Bayesian I know that you’ve got three or four old papers that you’ve written on it.

OK, sure, when you put it that way, my collaborators and I do have a few papers on the topic:

Visualization in Bayesian data analysis

Visualizing distributions of covariance matrices

Multiple imputation for model checking: completed-data plots with missing and latent data

A Bayesian formulation of exploratory data analysis and goodness-of-fit testing

All maps of parameter estimates are misleading

But I don’t really have much else to say right now. Dynamic graphics seem like a good idea but I’ve never programmed them myself. In many settings it will work to display point estimates, but sometimes this can create big problems (as discussed in some of the above-linked papers) because Bayesian point estimates will tend to be too smooth—less variable—compared to the variation in the underlying parameters being modeled.

So I’m kicking this one out to the commenters to see if they can offer some useful suggestions.


  1. My supervisor uses animated samples which I find very useful. He has written a tech report on his method which you can find on his homepage:

    Hope you find this useful.

  2. jrg says:

    Here’s an example from a recent JASA paper on Bayesian forecasting of cohort fertility. We tried hard to depict certainty (narrow and heavy coloring) and uncertainty (wide and lighter coloring), but I leave it to the blog readers to suggest improvements.

    For the full paper,

  3. Tomi says:

    Here’s a dynamic graphic demonstrating Gaussian processes with one-dimensional input:

    Incidentally, one can see that the mean function tends to be a lot smoother than random draws from the processes.

  4. Rahul says:

    I’m no expert but all the links to visualizations posted in this thread look pretty cool to me.

  5. John Brennan says:

    I am not sure.

  6. Keith O'Rourke says:

    This line “In the Bayesian sense, looking at inferences and deciding whether they “make sense” can be interpreted to be a comparison of the estimates to our prior knowledge, that is, to a prior model” suggests to me that posterior predictive estimates need to be compared to prior predictive estimates?
    (OK, if prior predictive estimates are _known_ to be just vague noise, perhaps that need not be explicitly plotted.)

    Also, not sure plotting in the data space is always most informative, though I must admit I was not able to be very convincing about the value of plotting in the parameter space

  7. Here’s a UK Government Statistical Service take on communicating uncertainty:

  8. Guy Abel says:

    I am a big fan of this plot for showing the uncertainty of UK migration estimates…

    Similar as previous comments, the fanplot package in R for shading sequential densities. Code is in the paper…

    More details on using the fan function here…

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