Thanks Sven for the detailed explanstion.. I had eventually arrived at the conclusion that the mean value of the density was the point estimate being output albeit that the densities for each parameter were also an output plot option. It would seem then that the residuals from the mean values are not retrievable (yet) from running the GUI version, which incidentally has now attached itself permanently as an option within univariate options.

 It would appear in many applied studies that the parameter means with credible intervals are employed. In a forecasting or projection context with Bayesian estimation of time series data, one might suppose that the residuals would clearly still be important for post estimation diagnosis regarding stationarity and serial correlation.


On Mon, 1 Apr 2024, 20:55 Sven Schreiber, <> wrote:
Am 16.03.2024 um 17:22 schrieb Brian Revell:
I have tried using the BayTool package with some success (in terms of getting output),
I have read (perhaps not well enough)  the detailed paper by Luca Pedini.
Luca has had some email problems lately, perhaps he didn't get this one.
However,  I am puzzled why when simply using the linear model with conjugate prior, as a default  I get two sets of  posterior mean parameter and se estimates -NI-post m and I post-m and NI-Pst se and I-post se. . Looking at the graphs of the Gaussian Posterior density estimates, they appear to more closely centred on  the I-pos -mean.  Although the difference s between the N & O posterior estimates is small, what is the basis for selecting one rather than the other?
I believe that NI stands for non-informative and I for informative, which typically refers to the prior used. So basically the NI results should be purely data-driven, which usually means the max-likelihood or frequentist quantities. This is just for comparison, a Bayesian would of course go for the informative ones. (Provided she really believes in the prior, which for some reason doesn't seem to happen all that often in reality, but that's a different story.)

Second question  - how can I retrieve the fitted values and residuals from theB-Took Package. Hopefully it resides somewhere to be retirieved post estimation. Or is iit necessary to run the input data through the equation to generate it onself -and if so, which set of posterior mean estimates does one use?

Luca may correct me eventually, but it seems those things are not directly available. I guess this makes sense from a Bayesian perspective since it gives you densities, not point estimates. For example, do you want to consider the posterior mean, median or mode as your quasi-point estimate? All imply different sets of residuals. In principle they could all be stored of course, but it's not clear whether that's the most practical thing to do.

Having said that, it looks like for the coefficients (in the sub-bundle post_summ) the means are stored, so in that context this arbitrary choice was made, apparently.

So for the CASE 1 in the sample script with covariates list X, I guess you could try:

 lincomb(X, out.post_summ.post_betamean)

to get the fitted values. (Untested.)

PS -the BayTool package does not seem to attach permanently to the URL "model" list of options.

Sorry, I don't understand. What URL?



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