Finally, legal probabilists can reformulate probabilistic standards of proof using the concept of knowledge. Moss (2018) argues that a probabilistic belief, just like a full belief, can constitute knowledge.  This notion of probabilistic knowledge can be used to formulate an account of standards of proof for trial decisions (Moss, 2018: ch. 10; Moss, forthcoming). The preponderance standard for civil cases would be met if, based on the evidence presented at trial, judges or jurors have at least .5 credence that the defendant is liable, and this probabilistic belief constitutes knowledge.  The standard in criminal cases—proof beyond a reasonable doubt—would instead require knowledge of the probabilistic belief that the defendant is extremely likely to be guilty or simply full-fledged knowledge of guilt. To the extent that naked statistical evidence does not warrant full-fledged knowledge or probabilistic knowledge, knowledge-based accounts offer a solution to the puzzles of naked statistical evidence. In addition, the probabilistic knowledge account of standards of proof promises to vindicate the intuition that probability alone is not enough for legal proof while also acknowledging the key role that probability plays in decision-making at trial (however, for a critique of knowledge-based accounts of legal proof from a legal standpoint, see Allen 2021).  