  The field of astronomy has arrived at a turning point in terms of size and
complexity of both datasets and scientific collaboration. Commensurately,
algorithms and statistical models have begun to adapt --- e.g., via the onset
of artificial intelligence --- which itself presents new challenges and
opportunities for growth. This white paper aims to offer guidance and ideas for
how we can evolve our technical and collaborative frameworks to promote
efficient algorithmic development and take advantage of opportunities for
scientific discovery in the petabyte era. We discuss challenges for discovery
in large and complex data sets; challenges and requirements for the next stage
of development of statistical methodologies and algorithmic tool sets; how we
might change our paradigms of collaboration and education; and the ethical
implications of scientists' contributions to widely applicable algorithms and
computational modeling. We start with six distinct recommendations that are
supported by the commentary following them. This white paper is related to a
larger corpus of effort that has taken place within and around the Petabytes to
Science Workshops (https://petabytestoscience.github.io/).
