What is the test for imperfect self-defense in a murder case?

With regard to imperfect self-defense, the jury was instructed: "A person who kills another person in the actual but unreasonable belief in the necessity to defend against imminent peril to life or great bodily injury kills unlawfully but does not harbor malice aforethought and is not guilty of murder." (Italics added.) "[I]n a murder case, unless the People's own evidence suggests that the killing may have been provoked or in honest response to perceived danger, it is the defendant's obligation to proffer some showing on these issues sufficient to raise a reasonable doubt of his guilt of murder. [Citations.]" (People v. Rios, supra, 23 Cal.4th at pp. 461-462.) Defendant failed to do so.