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 ∼ 100 HDF spectroscopic redshifts and the predictions of the method, with a rms error ∆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.

We present aperture-matched PSF-corrected BV i ′ z ′ JH photometry and Bayesian photometric redshifts (BPZ) for objects detected in the Hubble Ultra Deep Field (UDF), 8,042 of which are detected at the 10-σ level (e.g., i ′ < 29.01 or z ′ < 28.43). Most of our objects are defined identically to those in the public STScI catalogs, enabling straightforward object-by-object comparison. We have combined detections from i ′ , z ′ , J+H, and B+V +i ′ +z ′ images into a single comprehensive segmentation map. Using a new program called SExSeg we are able to force this segmentation map into SExtractor for photometric analysis. The resulting photometry is corrected for the wider NIC3 PSFs using our ColorPro software. We also correct for the ACS z ′ -band PSF halo. Offsets are applied to our NIC3 magnitudes, which are found to be too faint relative to the ACS fluxes. Based on BPZ SED fits to objects of known spectroscopic redshift, we derived corrections of −0.30 ± 0.03 mag in J and −0.18 ± 0.04 mag in H. Our offsets appear to be supported by a recent recalibration of the UDF NIC3 images combined with non-linearity measured in NICMOS itself.The UDF reveals a large population of faint blue galaxies (presumably young starbursts), bluer than those observed in the original Hubble Deep Fields (HDF).

We measure the morphology-density relation ( MDR) and morphology-radius relation (MRR) for galaxies in seven z $ 1 clusters that have been observed with the Advanced Camera for Surveys (ACS) on board the Hubble Space Telescope. Simulations and independent comparisons of our visually derived morphologies indicate that ACS allows one to distinguish between E, S0, and spiral morphologies down to z 850 ¼ 24, corresponding to L /L Ã ¼ 0:21 and 0.30 at z ¼ 0:83 and 1.24, respectively. We adopt density and radius estimation methods that match those used at lower redshift in order to study the evolution of the MDR and MRR. We detect a change in the MDR between 0:8 < z < 1:2 and that observed at z $ 0, consistent with recent work; specifically, the growth in the bulge-dominated galaxy fraction, f EþS0 , with increasing density proceeds less rapidly at z $ 1 than it does at z $ 0. At z $ 1 and AE ! 500 galaxies Mpc À2 , we find h f EþS0 i ¼ 0:72 AE 0:10. At z $ 0, an E+S0 population fraction of this magnitude occurs at densities about 5 times smaller. The evolution in the MDR is confined to densities AE k 40 galaxies Mpc À2 and appears to be primarily due to a deficit of S0 galaxies and an excess of Sp+Irr galaxies relative to the local galaxy population. The f E -density relation exhibits no significant evolution between z ¼ 1 and 0. We find mild evidence to suggest that the MDR is dependent on the bolometric X-ray luminosity of the intracluster medium. Implications for the evolution of the disk galaxy population in dense regions are discussed in the context of these observations.