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The production of complex astronomical data is accelerating, especially with newer telescopes producing ever more large-scale surveys. The increased quantity, complexity, and variety of astronomical data demand a parallel increase in skill and sophistication in developing, deciding, and deploying statistical methods. Understanding limitations and appreciating nuances in statistical and machine learning methods and the reasoning behind them is essential for improving data-analytic proficiency and acumen. Aiming to facilitate such improvement in astronomy, we delineate cautionary tales in statistics via six maxims, with examples drawn from the astronomical literature. Inspired by the significant quality improvement in business and manufacturing processes by the routine adoption of Six Sigma, we hope the routine reflection on these Six Maxims will improve the quality of both data analysis and scientific findings in astronomy. 

Abstract The acquisition of complex astronomical data is accelerating, especially with newer telescopes producing ever more large-scale surveys. The increased quantity, complexity, and variety of astronomical data demand a parallel increase in skill and sophistication in developing, deciding, and deploying statistical methods. Understanding limitations and appreciating nuances in statistical and machine learning methods and the reasoning behind them is essential for improving data-analytic proficiency and acumen. Aiming to facilitate such improvement in astronomy, we delineate cautionary tales in statistics via six maxims, with examples drawn from the astronomical literature. Inspired by the significant quality improvement in business and manufacturing processes by the routine adoption of Six Sigma, we hope the routine reflection on these six maxims will improve the quality of both data analysis and scientific findings in astronomy. 

Abstract The growth of supermassive black holes is strongly linked to their galaxies. It has been shown that the population mean black hole accretion rate ( $\overline{\mathrm{BHAR}}$) primarily correlates with the galaxy stellar mass (M_⋆) and redshift for the general galaxy population. This work aims to provide the best measurements of $\overline{\mathrm{BHAR}}$as a function ofM_⋆and redshift over ranges of 10^9.5<M_⋆< 10¹²M_⊙andz< 4. We compile an unprecedentedly large sample with 8000 active galactic nuclei (AGNs) and 1.3 million normal galaxies from nine high-quality survey fields following a wedding cake design. We further develop a semiparametric Bayesian method that can reasonably estimate $\overline{\mathrm{BHAR}}$and the corresponding uncertainties, even for sparsely populated regions in the parameter space. $\overline{\mathrm{BHAR}}$is constrained by X-ray surveys sampling the AGN accretion power and UV-to-infrared multiwavelength surveys sampling the galaxy population. Our results can independently predict the X-ray luminosity function (XLF) from the galaxy stellar mass function (SMF), and the prediction is consistent with the observed XLF. We also try adding external constraints from the observed SMF and XLF. We further measure $\overline{\mathrm{BHAR}}$for star-forming and quiescent galaxies and show that star-forming $\overline{\mathrm{BHAR}}$is generally larger than or at least comparable to the quiescent $\overline{\mathrm{BHAR}}$.