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Over the past century, major advances in astronomy and astrophysics have been largely driven by improvements in instrumentation and data collection. With the amassing of high quality data from new telescopes, and especially with the advent of deep and large astronomical surveys, it is becoming clear that future advances will also rely heavily on how those data are analyzed and interpreted. New methodologies derived from advances in statistics, computer science, and machine learning are beginning to be employed in sophisticated investigations that are not only bringing forth new discoveries, but are placing them on a solid footing. Progress in wide-field sky surveys, interferometric imaging, precision cosmology, exoplanet detection and characterization, and many subfields of stellar, Galactic and extragalactic astronomy, has resulted in complex data analysis challenges that must be solved to perform scientific inference. Research in astrostatistics and astroinformatics will be necessary to develop the state-of-the-art methodology needed in astronomy. Overcoming these challenges requires dedicated, interdisciplinary research. We recommend: (1) increasing funding for interdisciplinary projects in astrostatistics and astroinformatics; (2) dedicating space and time at conferences for interdisciplinary research and promotion; (3) developing sustainable funding for long-term astrostatisics appointments; and (4) funding infrastructure development for data archives and archive support, state-of-the-art algorithms, and efficient computing., Comment: Submitted to the Astro2020 Decadal Survey call for science white papers

Structures in Warm Dark Matter (WDM) models are exponentially suppressed below a certain scale, characterized by the dark matter particle mass, $m_{\rm x}$. Since structures form hierarchically, the presence of collapsed objects at high-redshifts can set strong lower limits on $m_{\rm x}$. We place robust constraints on $m_{\rm x}$ using recent results from the {\it Swift} database of high-redshift gamma-ray bursts (GRBs). We parameterize the redshift evolution of the ratio between the cosmic GRB rate and star formation rate (SFR) as $\propto (1+z)^\alpha$, thereby allowing astrophysical uncertainties to partially mimic the cosmological suppression of structures in WDM models. Using a maximum likelihood estimator on two different $z>4$ GRB subsamples (including two bursts at $z>8$), we constrain $m_{\rm x} \gtrsim 1.6$-1.8 keV at 95% C.L., when marginalized over a flat prior in $\alpha$. We further estimate that 5 years of a SVOM-like mission would tighten these constraints to $m_{\rm x} \gtrsim 2.3 $ keV. Our results show that GRBs are a powerful probe of high-redshift structures, providing robust and competitive constraints on $m_{\rm x}$., Comment: 11 pages, 7 figures, accepted for publication in MNRAS