I'm having a hard time figuring out what the output of fitted() applied to a rbart object means. Specifically, I fit my data using the rbart_vi() function in the R package dbarts, and I'm trying to understand what fitted(rbartFit) returns. The documentation says it returns the "posterior mean of a predicted quantity". Can someone please explain what this means and how it is calculated? I don't have much background in either Bayesian stats or machine learning so am spending a lot of time figuring out but with very little progress :( Thanks!!
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1 I don’t have experience with this package, so for the software specific details you’d need to check the documentation or asks it’s developers, however I can help you with the “posterior mean of a predicted quantity”.
Unlike non-Bayesian models, in Bayesian setting we usually find not the point estimates, but their distributions. For example, in frequentist setting you would be calculating mean of a sample to estimate the mean of the population. In Bayesian setting, you would end up with a distribution of the possible values for the mean. Since in some cases you need a point estimate, you can use a summary statistic to reduce this posterior distribution to single point, for example mean, median, or mode of the posterior distribution. So the Bayesian estimator finds the distribution of the predictions, so called posterior predictive distribution, and the quote means that the fitted function returns mean of this distribution.
Of course, the model would make predictions for each sample, so this would be mean of the distribution predicted per each sample.
If this is still not clear, I’d highly recommend referring to one of the many great Bayesian textbooks before proceeding further, as otherwise it might be tough for you to understand what’s going on.
- $\begingroup$ This is super helpful! Thanks! $\endgroup$spring– spring2020-12-29 09:41:47 +00:00Commented Dec 29, 2020 at 9:41