  The estimation and utilization of photometric redshift probability density
functions (photo-$z$ PDFs) has become increasingly important over the last few
years and currently there exist a wide variety of algorithms to compute
photo-$z$'s, each with their own strengths and weaknesses. In this paper, we
present a novel and efficient Bayesian framework that combines the results from
different photo-$z$ techniques into a more powerful and robust estimate by
maximizing the information from the photometric data. To demonstrate this we
use a supervised machine learning technique based on random forest, an
unsupervised method based on self-organizing maps, and a standard template
fitting method but can be easily extend to other existing techniques. We use
data from the DEEP2 and the SDSS surveys to explore different methods for
combining the predictions from these techniques. By using different performance
metrics, we demonstrate that we can improve the accuracy of our final photo-$z$
estimate over the best input technique, that the fraction of outliers is
reduced, and that the identification of outliers is significantly improved when
we apply a Na\"{\i}ve Bayes Classifier to this combined information. Our more
robust and accurate photo-$z$ PDFs will allow even more precise cosmological
constraints to be made by using current and future photometric surveys. These
improvements are crucial as we move to analyze photometric data that push to or
even past the limits of the available training data, which will be the case
with the Large Synoptic Survey Telescope.
