What is the test for a judge's denial of a recusal motion for abuse of discretion?

The law provides that a judge "shall disqualify himself in any proceeding in which his impartiality might reasonably be questioned." 28 U.S.C. 455(a). Specific instances where recusal is required include situations in which the judge has "a personal bias or prejudice concerning a party, or personal knowledge of disputed evidentiary facts concerning the proceeding." Id. 455(b)(1). We review a judge's denial of a recusal motion for abuse of discretion. See, e.g., United States v. Thompson, 76 F.3d 442, 451 (2d Cir.1996).

As we have stated,