Quasar Photometric Redshifts and Candidate Selection: A New Algorithm Based on Optical and Mid-Infrared Photometric Data

We present a new algorithm to estimate quasar photometric redshifts (photo-$z$s), by considering the asymmetries in the relative flux distributions of quasars. The relative flux models are built with multivariate Skew-t distributions in the multi-dimensional space of relative fluxes as a function of redshift and magnitude. For 151,392 quasars in the SDSS, we achieve a photo-$z$ accuracy, defined as the fraction of quasars with the difference between the photo-$z$ $z_p$ and the spectroscopic redshift $z_s$, $|\Delta z| = |z_s-z_p|/(1+z_s)$ within 0.1, of 74%. Combining the WISE W1 and W2 infrared data with the SDSS data, the photo-$z$ accuracy is enhanced to 87%. Using the Pan-STARRS1 or DECaLS photometry with WISE W1 and W2 data, the photo-$z$ accuracies are 79% and 72%, respectively. The prior probabilities as a function of magnitude for quasars, stars and galaxies are calculated respectively based on (1) the quasar luminosity function; (2) the Milky Way synthetic simulation with the Besan\c{c}on model; (3) the Bayesian Galaxy Photometric Redshift estimation. The relative fluxes of stars are obtained with the Padova isochrones, and the relative fluxes of galaxies are modeled through galaxy templates. We test our classification method to select quasars using the DECaLS $g$, $r$, $z$, and WISE W1 and W2 photometry. The quasar selection completeness is higher than 70% for a wide redshift range $0.5<z<4.5$, and a wide magnitude range $18<r<21.5$ mag. Our photo-$z$ regression and classification method has the potential to extend to future surveys. The photo-$z$ code will be publicly available.Comment: 22 pages, 17 figure, accepted by AJ. The code is available at https://doi.org/10.5281/zenodo.101440

Contribuições ao estudo de dados longitudinais na teoria de resposta ao item

Orientador: Caio Lucidius Naberezny AzevedoTese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação CientíficaResumo: Na presente tese desenvolvemos classes de modelos longitudinais da Teoria de Resposta o Item (TRI) considerando duas abordagens. A primeira é baseada na decomposição de Cholesky de matrizes de covariância de interesse, relacionadas aos traços latentes. Essa metodologia permite representar um amplo conjunto de estruturas de dependência de maneira relativamente simples, facilita a escolha de distribuições a priori para os parâmetros relacionados à estrutura de dependência, facilita a implementação de algoritmos de estimação (particularmente sob o enfoque Bayesiano), permite considerar diferentes distribuições (multivariadas) para os traços latentes de modo simples, torna bastante fácil a incorporação de estruturas de regressão para os traços latentes, entre outras vantagens. Desenvolvemos, adicionalmente, uma classe de modelos com estruturas de curvas de crescimento para os traços latentes. Na segunda abordagem utilizamos cópulas Gaussianas para representar a estrutura de dependência dos traços latentes. Diferentemente da abordagem anterior, essa metodologia permite o total controle das respectivas distribuições marginais mas, igualmente, permite considerar um grande número de estruturas de dependência. Utilizamos modelos dicotômicos de resposta ao item e exploramos a utilização da distribuição normal e normal assimétrica para os traços latentes. Consideramos indivíduos acompanhados ao longo de várias condições de avaliação, submetidos a instrumentos de medida em cada uma delas, os quais possuem alguma estrutura de itens comuns. Exploramos os casos de um único e de vários grupos como também dados balanceados e desbalanceados, no sentido de considerarmos inclusão e exclusão de indivíduos ao longo do tempo. Algoritmos de estimação, ferramentas para verificação da qualidade de ajuste e comparação de modelos foram desenvolvidos sob o paradigma bayesiano, através de algoritmos MCMC híbridos, nos quais os algoritmos SVE (Single Variable Exchange) e Metropolis-Hastings são considerados quando as distribuições condicionais completas não são conhecidas. Estudos de simulação foram conduzidos, os quais indicaram que os parâmetros foram bem recuperados. Além disso, dois conjuntos de dados longitudinais psicométricos foram analisados para ilustrar as metodologias desenvolvidas. O primeiro é parte de um estudo de avaliação educacional em larga escala promovido pelo governo federal brasileiro. O segundo foi extraído do Amsterdam Growth and Health Longitudinal Study (AGHLS) que monitora a saúde e o estilo de vida de adolescentes holandesesAbstract: In this thesis we developed families of longitudinal Item Response Theory (IRT) models considering two approaches. The first one is based on the Cholesky decomposition of the covariance matrices of interest, related to the latent traits. This modeling can accommodate several dependence structures in a easy way, it facilitates the choice of prior distributions for the parameters of the dependence matrix, it facilitates the implementation of estimation algorithms (particularly under the Bayesian paradigm), it allows to consider different (multivariate) distributions for the latent traits, it makes easier the inclusion of regression and multilevel structures for the latent traits, among other advantages. Additionally, we developed growth curve models for the latent traits. The second one uses a Gaussian copula function to describes the latent trait structure. Differently from the first one, the copula approach allows the entire control of the respective marginal latent trait distributions, but as the first one, it accommodates several dependence structures. We focus on dichotomous responses and explore the use of the normal and skew-normal distributions for the latent traits. We consider subjects followed over several evaluation conditions (time-points) submitted to measurement instruments which have some structure of common items. Such subjects can belong to a single or multiple independent groups and also we considered both balanced and unbalanced data, in the sense that inclusion or dropouts of subjects are allowed. Estimation algorithms, model fit assessment and model comparison tools were developed under the Bayesian paradigm through hybrid MCMC algorithms, such that when the full conditionals are not known, the SVE (Single Variable Exchange) and Metropolis-Hastings algorithms are used. Simulation studies indicate that the parameters are well recovered. Furthermore, two longitudinal psychometrical data sets were analyzed to illustrate our methodologies. The first one is a large-scale longitudinal educational study conducted by the Brazilian federal government. The second was extracted from the Amsterdam Growth and Health Longitudinal Study (AGHLS), which monitors the health and life-style of Dutch teenagersDoutoradoEstatisticaDoutor em Estatística162562/2014-4,142486/2015-9CNPQCAPE

Skew t Mixture Latent State-Trait Analysis: A Monte Carlo Simulation Study on Statistical Performance

This simulation study assessed the statistical performance of a skew t mixture latent state-trait (LST) model for the analysis of longitudinal data. The model aims to identify interpretable latent classes with class-specific LST model parameters. A skew t-distribution within classes is allowed to account for non-normal outcomes. This flexible function covers heavy tails and may reduce the risk of identifying spurious classes, e.g., in case of outliers. Sample size, number of occasions and skewness of the trait variable were varied. Generally, parameter estimation accuracy increases with increasing numbers of observations and occasions. Larger bias compared to other parameters occurs for parameters referring to the skew t-distribution and variances of the latent trait variables. Standard error estimation accuracy shows diffuse patterns across conditions and parameters. Overall model performance is acceptable for large conditions, even though none of the models is free from bias. The application of the skew t mixture model in case of large numbers of occasions and observations may be possible, but results should be treated with caution. Moreover, the skew t approach may be useful for other mixture models