“The plaintiff bears the initial burden of proving by the preponderance of the evidence a prima facie case of discrimination. ... In order to meet this burden, the plaintiff must present evidence that gives rise to an inference of unlawful discrimination. ... If the plaintiff meets this initial burden, the burden then shifts to the defendant to rebut the presumption of discrimination by producing evidence of a legitimate, nondiscriminatory reason for its actions. ... If the defendant carries this burden of production, the presumption raised by the prima facie case is rebutted, and the factual inquiry proceeds to a new level of specificity. . . . The plaintiff then must satisfy [his] burden of persuading the factfinder that [he] was the victim of discrimination either directly by persuading the court . . . that a discriminatory reason more likely motivated the employer or indirectly by showing that the employer’s proffered explanation is unworthy of credence.” (Citations omitted; internal quotation marks omitted.) Id., 53-54.