Photometric redshift estimation is becoming an increasingly important technique , although the currently existing methods present several shortcomings which hinder their application .
Here it is shown that most of those drawbacks are efficiently eliminated when Bayesian probability is consistently applied to this problem .
The use of prior probabilities and Bayesian marginalization allows the inclusion of valuable information , e.g .
the redshift distributions or the galaxy type mix , which is often ignored by other methods .
It is possible to quantify the accuracy of the redshift estimation in a way with no equivalents in other statistical approaches ; this property permits the selection of galaxy samples for which the redshift estimation is extremely reliable .
In those cases when the a priori information is insufficient , it is shown how to ‘ calibrate ’ the prior distributions , using even the data under consideration .

There is an excellent agreement between the \sim 100 HDF spectroscopic redshifts and the predictions of the method , with a rms error \Delta z / ( 1 + z _ { spec } ) = 0.08 up to z < 6 and no systematic biases nor outliers .
Note that these results have not been reached by minimizing the difference between spectroscopic and photometric redshifts ( as is the case with empirical training set techniques ) , which may lead to an overestimation of the accuracy .
The reliability of the method is further tested by restricting the color information to the UBVI filters .
The results thus obtained are shown to be more reliable than those of standard techniques even when the latter include near-IR colors .

The Bayesian formalism developed here can be generalized to deal with a wide range of problems which make use of photometric redshifts .
Several applications are outlined , e.g .
the estimation of individual galaxy characteristics as the metallicity , dust content , etc. , or the study of galaxy evolution and the cosmological parameters from large multicolor surveys .
Finally , using Bayesian probability it is possible to develop an integrated statistical method for cluster mass reconstruction which simultaneously considers the information provided by gravitational lensing and photometric redshift estimation .