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Register a new userEstimating the Redshift Distribution of Photometric Galaxy Samples II. Applications and Tests of a New Method
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In Lima et al. 2008 we presented a new method for estimating the redshift distribution, N(z), of a photometric galaxy sample, using photometric observables and weighted sampling from a spectroscopic subsample of the data. In this paper, we extend this method and explore various applications of it, using both simulations of and real data from the SDSS. In addition to estimating the redshift distribution for an entire sample, the weighting method enables accurate estimates of the redshift probability distribution, p(z), for each galaxy in a photometric sample. Use of p(z) in cosmological analyses can substantially reduce biases associated with traditional photometric redshifts, in which a single redshift estimate is associated with each galaxy. The weighting procedure also naturally indicates which galaxies in the photometric sample are expected to have accurate redshift estimates, namely those that lie in regions of photometric-observable space that are well sampled by the spectroscopic subsample. In addition to providing a method that has some advantages over standard photo-z estimates, the weights method can also be used in conjunction with photo-z estimates, e.g., by providing improved estimation of N(z) via deconvolution of N(photo-z) and improved estimates of photo-z scatter and bias. We present a publicly available p(z) catalog for ~78 million SDSS DR7 galaxies.
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We present an empirical method for estimating the underlying redshift distribution N(z) of galaxy photometric samples from photometric observables. The method does not rely on photometric redshift (photo-z) estimates for individual galaxies, which typically suffer from biases. Instead, it assigns weights to galaxies in a spectroscopic subsample such that the weighted distributions of photometric observables (e.g., multi-band magnitudes) match the corresponding distributions for the photometric sample. The weights are estimated using a nearest-neighbor technique that ensures stability in sparsely populated regions of color-magnitude space. The derived weights are then summed in redshift bins to create the redshift distribution. We apply this weighting technique to data from the Sloan Digital Sky Survey as well as to mock catalogs for the Dark Energy Survey, and compare the results to those from the estimation of photo-zs derived by a neural network algorithm. We find that the weighting method accurately recovers the underlying redshift distribution, typically better than the photo-z reconstruction, provided the spectroscopic subsample spans the range of photometric observables covered by the photometric sample.
The incompressibility method is an elementary yet powerful proof technique. It has been used successfully in many areas. To further demonstrate its power and elegance we exhibit new simple proofs using the incompressibility method.
The luminosity functions of galaxies and quasars provide invaluable information about galaxy and quasar formation. Estimating the luminosity function from magnitude limited samples is relatively straightforward, provided that the distances to the objects in the sample are known accurately; techniques for doing this have been available for about thirty years. However, distances are usually known accurately for only a small subset of the sample. This is true of the objects in the Sloan Digital Sky Survey, and will be increasingly true of the next generation of deep multi-color photometric surveys. Estimating the luminosity function when distances are only known approximately (e.g., photometric redshifts are available, but spectroscopic redshifts are not) is more difficult. I describe two algorithms which can handle this complication: one is a generalization of the V_max algorithm, and the other is a maximum likelihood approach. Because these methods account for uncertainties in the distance estimate, they impact a broader range of studies. For example, they are useful for studying the abundances of galaxies which are sufficiently nearby that the contribution of peculiar velocity to the spectroscopic redshift is not negligible, so only a noisy estimate of the true distance is available. In this respect, peculiar velocities and photometric redshift errors have similar effects. The methods developed here are also useful for estimating the stellar luminosity function in samples where accurate parallax distances are not available.
Based on the SDSS and SDSS-WISE quasar datasets, we put forward two schemes to estimate the photometric redshifts of quasars. Our schemes are based on the idea that the samples are firstly classified into subsamples by a classifier and then photometric redshift estimation of different subsamples is performed by a regressor. Random Forest is adopted as the core algorithm of the classifiers, while Random Forest and kNN are applied as the key algorithms of regressors. The samples are divided into two subsamples and four subsamples depending on the redshift distribution. The performance based on different samples, different algorithms and different schemes are compared. The experimental results indicate that the accuracy of photometric redshift estimation for the two schemes generally improve to some extent compared to the original scheme in terms of the percents in frac{|Delta z|}{1+z_{i}}<0.1 and frac{|Delta z|}{1+z_{i}}<0.2 and mean absolute error. Only given the running speed, kNN shows its superiority to Random Forest. The performance of Random Forest is a little better than or comparable to that of kNN with the two datasets. The accuracy based on the SDSS-WISE sample outperforms that based on the SDSS sample no matter by kNN or by Random Forest. More information from more bands is considered and helpful to improve the accuracy of photometric redshift estimation. Evidently it can be found that our strategy to estimate photometric redshift is applicable and may be applied to other datasets or other kinds of objects. Only talking about the percent in frac{|Delta z|}{1+z_{i}}<0.3, there is still large room for further improvement in the photometric redshift estimation.
The distribution of solar system absolute magnitudes ($H$) for the near-Earth asteroids (NEAs) observable near opposition -- i.e. Amors, Apollos, and Atens ($A^3$) -- is derived from the set of ALL currently known NEAs. The result is based only on common sense assumptions of uniformly random distributions and that the orbital phase space and $H$-magnitude distribution of known NEAs is representative of the total population. There is no population or other modeling and no assumption on albedo except in interpreting the result as a size-frequency distribution (SFD). The analysis is based on the 18355 $A^3$ NEAs cataloged by the MPC as of June 2018. The observations from 9 of the top programs (in terms of number of distinct NEAs observed) and the smaller but deeper DECam NEO Survey are used, comprising 74696 measurements of 13466 NEAs observed within 30 deg of opposition. The only parameter in the analysis is an estimate of the detection magnitude limits for each program. A single power-law slope for the cumulative distribution, $log(N<H)=0.50pm0.03H$, for $H < 27$ is found with no evidence for additional structure. A turn-over fainter than 27th magnitude may occur, but the population of known NEAs is dropping off rapidly because they are difficult to detect and so possibly is a completeness effect. Connecting to the nearly complete census of the brightest/biggest NEAs (diameter $> {sim}2$Km) provides a normalization that estimates ${sim}10^8 A^3$ NEAs with $H < {sim}27$ corresponding to NEAs greater than ${sim}10$m in diameter for reasonable typical albedos. Restricting the analysis to Earth crossing asteroids (10839 known, 7336 selected, 36541 observed) produces the same power-law slope.
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