In a criminal trial the government's burden of persuasion is to establish a criminal defendant's guilt beyond a reasonable doubt. This is a federal constitutional requirement that is applicable to the states as well to the federal government.

United States v. Mitchell, 328 F.3d 77, 82-83 (2d Cir. 2003) (upholding trial court's admission into evidence of accused's prior firearm arrest where to rebut accused's claim of ignorance, such evidence "was therefore relevant to whether [accused] knew that his conduct was illegal and,...Evidence of a criminal or wrongful act apart from the act that at issue at trial Is not barred by the prohibition against circumstantial use of character if intent, knowledge, mistake, or accident is a legally-material factual issue, the opposing party suggests the non-existence of knowledge or urges mistake or accident as a defense, and evidence of another crime, wrong, or act is offered to prove the knowledge or the absence of mistake or accident by a criminal defendant or other person.

Fed. R. Evid. 801(d)(2).Personal and vicarious admissions are exempt from Federal Rule of Evidence 802's prohibition against the admission of hearsay evidence.

King v. Harrington, 447 F.3d 531, 533 (7th Cir. 2006) (holding, in plaintiff injured parties' personal injury action against defendant pick-up truck driver that evidence of defendant's liability insurance was....Evidence of the existence or non-existence of liability insurance is not admissible on the issue of negligence or wrongful conduct.