Many scientific investigations of photometric galaxy surveys require redshift estimates, whose uncertainty properties are best encapsulated by photometric redshift (photo-z) posterior probability density functions (PDFs). A plethora of photo-z PDF estimation methodologies abound, producing discrepant results with no consensus on a preferred approach. We present the results of a comprehensive experiment comparing twelve photo-z algorithms applied to mock data produced forLarge Synoptic Survey Telescope The Rubin Observatory Legacy Survey of Space and Time (lsst) Dark Energy Science Collaboration (desc). By supplying perfect prior information, in the form of the complete template library and a representative training set as inputs to each code, we demonstrate the impact of the assumptions underlying each technique on the output photo-z PDFs. In the absence of a notion of true, unbiased photo-z PDFs, we evaluate and interpret multiple metrics of the ensemble properties of the derived photo-z PDFs as well as traditional reductions to photo-z point estimates. We report systematic biases and overall over/under-breadth of the photo-z PDFs of many popular codes, which may indicate avenues for improvement in the algorithms or implementations. Furthermore, we raise attention to the limitations of established metrics for assessing photo-z PDF accuracy; though we identify the conditional density estimate (CDE) loss as a promising metric of photo-z PDF performance in the case where true redshifts are available but true photo-z PDFs are not, we emphasize the need for science-specific performance metrics.

We conduct a comprehensive study of the effects of incorporating galaxy morphology information in photometric redshift estimation. Using machine learning methods, we assess the changes in the scatter and outlier fraction of photometric redshifts when galaxy size, ellipticity, Sérsic index and surface brightness are included in training on galaxy samples from the SDSS and the CFHT Stripe-82 Survey (CS82). We show that by adding galaxy morphological parameters to full ugriz photometry, only mild improvements are obtained, while the gains are substantial in cases where fewer passbands are available. For instance, the combination of gr z photometry and morphological parameters almost fully recovers the metrics of 5-band photometric redshifts. We demonstrate that with morphology it is possible to determine useful redshift distribution N(z) of galaxy samples without any colour information. We also find that the inclusion of quasar redshifts and associated object sizes in training improves the quality of photometric redshift catalogues, compensating for the lack of a good star-galaxy separator. We further show that morphological information can mitigate biases and scatter due to bad photometry. As an application, we derive both point estimates and posterior distributions of redshifts for the official CS82 catalogue, training on morphology and SDSS Stripe-82 ugriz bands when available. Our redshifts yield a 68th percentile error of 0.058(1+ z), and a outlier fraction of 5.2 per cent. We further include a deep extension trained on morphology and single i-band CS82 photometry.

We study the performance of the hybrid template-machine-learning photometric redshift (photo-z) algorithm delight, which uses Gaussian processes, on a subset of the early data release of the Physics of the Accelerating Universe Survey (PAUS). We calibrate the fluxes of the 40 PAUS narrow bands with 6 broadband fluxes (uBVriz) in the COSMOS field using three different methods, including a new method which utilises the correlation between the apparent size and overall flux of the galaxy. We use a rich set of empirically derived galaxy spectral templates as guides to train the Gaussian process, and we show that our results are competitive with other standard photometric redshift algorithms. delight achieves a photo-z 68th percentile error of σ68 = 0.0081(1 + z) without any quality cut for galaxies with iauto < 22.5 as compared to 0.0089(1 + z) and 0.0202(1 + z) for the bpz and annz2 codes, respectively. delight is also shown to produce more accurate probability distribution functions for individual redshift estimates than bpz and annz2. Common photo-z outliers of delight and bcnz2 (previously applied to PAUS) are found to be primarily caused by outliers in the narrowband fluxes, with a small number of cases potentially indicating spectroscopic redshift failures in the reference sample. In the process, we introduce performance metrics derived from the results of bcnz2 and delight, allowing us to achieve a photo-z quality of σ68 < 0.0035(1 + z) at a magnitude of iauto < 22.5 while keeping 50 per cent objects of the galaxy sample.

In this work, we studied the impact of galaxy morphology on photometric redshift (photo-z) probability density functions (PDFs). By including galaxy morphological parameters like the radius, axis-ratio, surface brightness and the Sérsic index in addition to the ugriz broadbands as input parameters, we used the machine learning photo-z algorithm ANNZ2 to train and test on galaxies from the Canada-France-Hawaii Telescope Stripe-82 (CS82) Survey. Metrics like the continuous ranked probability score (CRPS), probability integral transform (PIT), Bayesian odds parameter, and even the width and height of the PDFs were evaluated, and the results were compared when different number of input parameters were used during the training process. We find improvements in the CRPS and width of the PDFs when galaxy morphology has been added to the training, and the improvement is larger especially when the number of broadband magnitudes are lacking.

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