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Register a new userCharacterising Improvements in Photometric Redshift Probability Density Functions with Galaxy Morphology
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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 Sersic 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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We introduce an ordinal classification algorithm for photometric redshift estimation, which significantly improves the reconstruction of photometric redshift probability density functions (PDFs) for individual galaxies and galaxy samples. As a use case we apply our method to CFHTLS galaxies. The ordinal classification algorithm treats distinct redshift bins as ordered values, which improves the quality of photometric redshift PDFs, compared with non-ordinal classification architectures. We also propose a new single value point estimate of the galaxy redshift, that can be used to estimate the full redshift PDF of a galaxy sample. This method is competitive in terms of accuracy with contemporary algorithms, which stack the full redshift PDFs of all galaxies in the sample, but requires orders of magnitudes less storage space. The methods described in this paper greatly improve the log-likelihood of individual object redshift PDFs, when compared with a popular Neural Network code (ANNz). In our use case, this improvement reaches 50% for high redshift objects ($z geq 0.75$). We show that using these more accurate photometric redshift PDFs will lead to a reduction in the systematic biases by up to a factor of four, when compared with less accurate PDFs obtained from commonly used methods. The cosmological analyses we examine and find improvement upon are the following: gravitational lensing cluster mass estimates, modelling of angular correlation functions, and modelling of cosmic shear correlation functions.
The use of photometric redshifts in cosmology is increasing. Often, however these photo-zs are treated like spectroscopic observations, in that the peak of the photometric redshift, rather than the full probability density function (PDF), is used. This overlooks useful information inherent in the full PDF. We introduce a new real-space estimator for one of the most used cosmological statistics, the 2-point correlation function, that weights by the PDF of individual photometric objects in a manner that is optimal when Poisson statistics dominate. As our estimator does not bin based on the PDF peak it substantially enhances the clustering signal by usefully incorporating information from all photometric objects that overlap the redshift bin of interest. As a real-world application, we measure QSO clustering in the Sloan Digital Sky Survey (SDSS). We find that our simplest binned estimator improves the clustering signal by a factor equivalent to increasing the survey size by a factor of 2-3. We also introduce a new implementation that fully weights between pairs of objects in constructing the cross-correlation and find that this pair-weighted estimator improves clustering signal in a manner equivalent to increasing the survey size by a factor of 4-5. Our technique uses spectroscopic data to anchor the distance scale and it will be particularly useful where spectroscopic data (e.g, from BOSS) overlaps deeper photometry (e.g.,from Pan-STARRS, DES or the LSST). We additionally provide simple, informative expressions to determine when our estimator will be competitive with the autocorrelation of spectroscopic objects. Although we use QSOs as an example population, our estimator can and should be applied to any clustering estimate that uses photometric objects.
Accurate photometric redshift calibration is central to the robustness of all cosmology constraints from cosmic shear surveys. Analyses of the KiDS re-weighted training samples from all overlapping spectroscopic surveys to provide a direct redshift calibration. Using self-organising maps (SOMs) we demonstrate that this spectroscopic compilation is sufficiently complete for KiDS, representing $99%$ of the effective 2D cosmic shear sample. We use the SOM to define a $100%$ represented `gold cosmic shear sample, per tomographic bin. Using mock simulations of KiDS and the spectroscopic training set, we estimate the uncertainty on the SOM redshift calibration, and find that photometric noise, sample variance, and spectroscopic selection effects (including redshift and magnitude incompleteness) induce a combined maximal scatter on the bias of the redshift distribution reconstruction ($Delta langle z rangle=langle z rangle_{rm est}-langle z rangle_{rm true}$) of $sigma_{Delta langle z rangle} leq 0.006$ in all tomographic bins. We show that the SOM calibration is unbiased in the cases of noiseless photometry and perfectly representative spectroscopic datasets, as expected from theory. The inclusion of both photometric noise and spectroscopic selection effects in our mock data introduces a maximal bias of $Delta langle z rangle =0.013pm0.006$, or $Delta langle z rangle leq 0.025$ at $97.5%$ confidence, once quality flags have been applied to the SOM. The method presented here represents a significant improvement over the previously adopted direct redshift calibration implementation for KiDS, owing to its diagnostic and quality assurance capabilities. The implementation of this method in future cosmic shear studies will allow better diagnosis, examination, and mitigation of systematic biases in photometric redshift calibration.
Using a suite of self-similar cosmological simulations, we measure the probability distribution functions (PDFs) of real-space density, redshift-space density, and their geometric mean. We find that the real-space density PDF is well-described by a function of two parameters: $n_s$, the spectral slope, and $sigma_L$, the linear rms density fluctuation. For redshift-space density and the geometric mean of real- and redshift-space densities, we introduce a third parameter, $s_L={sqrt{langle(dv^L_{rm pec}/dr)^2rangle}}/{H}$. We find that density PDFs for the LCDM cosmology is also well-parameterized by these three parameters. As a result, we are able to use a suite of self-similar cosmological simulations to approximate density PDFs for a range of cosmologies. We make the density PDFs publicly available and provide an analytical fitting formula for them.
We present a determination of the effects of including galaxy morphological parameters in photometric redshift estimation with an artificial neural network method. Neural networks, which recognize patterns in the information content of data in an unbiased way, can be a useful estimator of the additional information contained in extra parameters, such as those describing morphology, if the input data are treated on an equal footing. We use imaging and five band photometric magnitudes from the All-wavelength Extended Groth Strip International Survey. It is shown that certain principal components of the morphology information are correlated with galaxy type. However, we find that for the data used the inclusion of morphological information does not have a statistically significant benefit for photometric redshift estimation with the techniques employed here. The inclusion of these parameters may result in a trade-off between extra information and additional noise, with the additional noise becoming more dominant as more parameters are added.
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