I. Selection method and number counts based on redshift PDFs

Based on observations collected at the German-Spanish Astronomical Center, Calar Alto, jointly operated by the Max-Planck-Institut für Astronomie (MPIA) at Heidelberg and the Instituto de Astrofísica de Andalucía (CSIC).-- et al.[Context]: Most observational results on the high redshift restframe UV-bright galaxies are based on samples pinpointed using the so-called dropout technique or Ly-α selection. However, the availability of multifilter data now allows the dropout selections to be replaced by direct methods based on photometric redshifts. In this paper we present the methodology to select and study the population of high redshift galaxies in the ALHAMBRA survey data. [Aims]: Our aim is to develop a less biased methodology than the traditional dropout technique to study the high redshift galaxies in ALHAMBRA and other multifilter data. Thanks to the wide area ALHAMBRA covers, we especially aim at contributing to the study of the brightest, least frequent, high redshift galaxies. [Methods]: The methodology is based on redshift probability distribution functions (zPDFs). It is shown how a clean galaxy sample can be obtained by selecting the galaxies with high integrated probability of being within a given redshift interval. However, reaching both a complete and clean sample with this method is challenging. Hence, a method to derive statistical properties by summing the zPDFs of all the galaxies in the redshift bin of interest is introduced. [Results]: Using this methodology we derive the galaxy rest frame UV number counts in five redshift bins centred at z = 2.5,3.0,3.5,4.0, and 4.5, being complete up to the limiting magnitude at mUV(AB) = 24, where mUV refers to the first ALHAMBRA filter redwards of the Ly-α line. With the wide field ALHAMBRA data we especially contribute to the study of the brightest ends of these counts, accurately sampling the surface densities down to mUV(AB) = 21-22. [Conclusions]: We show that using the zPDFs it is easy to select a very clean sample of high redshift galaxies. We also show that it is better to do statistical analysis of the properties of galaxies using a probabilistic approach, which takes into account both the incompleteness and contamination issues in a natural way.K. Viironen acknowledges the Juan de la Cierva fellowship of the Spanish government. We acknowledge funding from the FITE (Fondos de Inversiones de Teruel) and support from the Spanish Ministry for Economy and Competitiveness and FEDER funds through grants AYA2012-30789, AYA2006-14056, AYA 2003-00128, AYA 2006-01325, AYA 2007-62190, AYA2010-15169, AYA2010-22111-C03-02 and AYA2013-48623-C2-2. We also acknowledge Junta de Andalucía through the grant TIC 114 and Generalitat Valenciana projects Prometeo 2009/064 and PROMETEOII/2014/060, and the financial support from the Aragón Government through the Research Group E103. I. Oteo acknowledges support from the European Research Council (ERC) in the form of Advanced Grant, cosmicism. A. J. Cenarro acknowledges the Ramón y Cajal fellowship of the Spanish government. M. Povic acknowledges financial support from JAE-Doc program of the Spanish National Research Council (CSIC), cofunded by the European Social Fund.Peer Reviewe