At the beginning of last century, the physicist and Nobel Prize Winner Ernest Rutherford
reportedly believed that "If your experiment needs statistics, you ought to have done a
better experiment". If he were alive today, he probably would not recognize the way
cosmology (the study of the Universe on its largest scale) has developed: essentially all of
the exciting discoveries in the last two decades have relied on sophisticated statistical
analyses of very large and complex datasets. Today, advanced astrostatistical methods
belong to the toolbox of almost every cosmologist.
In this talk I will give an overview of how cosmologists have established a "cosmological
concordance model" that explains extraordinarily well very accurate observations ranging
from the relic radiation from the Big Bang to the distribution of galaxies in the sky in the
modern Universe. The emerging picture of a cosmos remains puzzling: 95% of the Universe
is constituted of unknown components, dark matter and dark energy. Our understanding of
the Universe is -- already today -- limited by our statistical and computational methods. I will
discuss how astrostatistics will meet the challenges posed by upcoming extremely large data
sets and thereby be instrumental in answering some of the most fundamental questions
about the physical reality of the cosmos.