BOTSFORD, J.

After a jury trial, the defendant, Mikolaj Letkowski, was convicted of aggravated kidnapping, aggravated rape, armed robbery, assault and battery by means of a dangerous weapon, and intimidation of a witness. The defendant appealed, and the Appeals Court affirmed the convictions. Commonwealth v. Letkowski, 83 Mass.App.Ct. 847 (2013). We granted the defendant's application for further appellate review, limited to issues concerning the prosecutor's references to the defendant's invocation of his rights as set forth in Miranda v. Arizona, 384 U.S. 436, 444-445 (1966), at trial. We conclude that the prosecutor's references to the defendant's invocation of his Miranda rights were improper. We conclude also, however, that in the particular circumstances of this case, the improper references, which were not objected to at trial, did not raise a substantial risk of a miscarriage of justice. We affirm the defendant's convictions.

1. Background. a. Facts. The jury could have found the following. At approximately 11:30 P.M. on April 17, 2006, the victim, a student at a college in Springfield, drove from her off-campus job and entered the parking lot of her campus dormitory. When she pulled into the parking lot, she noticed the defendant walking on the sidewalk near one of the dormitories. The victim parked her car. While she was collecting her belongings from it, the defendant approached her and asked whether she knew where a set of nearby dormitories was located. After answering him, the victim returned to gathering her belongings; when she turned around again, the defendant had a knife in his hand and ordered the victim back into her car. He then ordered the victim to give him one hundred dollars, but she told him that she did not have that much money on her. The defendant drove the victim's motor vehicle (with the victim in the front passenger seat) to an automated teller machine (ATM) in West Springfield, declining to go to the ATM across from the college because, as he later told the police, it was too well lit and was close to a coffee shop which was frequented by the police.2

Once they arrived at the ATM, the defendant ordered the victim to switch places with him; she complied and moved into the driver's seat. He placed a black winter hat over his face as the victim drove through the ATM and aimed his face toward the passenger's side door to avoid being detected by video cameras. The victim removed sixty dollars from her bank account; the defendant removed the hat from his face only after they left the ATM.

The defendant then directed the victim to an apartment complex in Agawam where his former girl friend used to live. He took the victim to the woods behind the complex and twice forced her to perform oral sex; he also digitally penetrated her. During the second instance of oral sex, a car pulled into the apartment complex, which prompted the defendant to have the victim stop and to tell her that, if anyone came into the woods, she should tell them that they were just "making out." The defendant then hit the victim with a belt, directed her to get dressed, brought her to the bottom of a hill, and told her that he did not believe that she would not go to the police and that he could just stab her then and throw her in some nearby water.

They returned to the car, and the victim drove back toward campus. The defendant made her enter campus from a particular direction that had fewer lights and video cameras. Once the victim parked her car near her dormitory, the defendant escorted her to her door. Before leaving, he insisted that, should the victim go to the police, he knew her home address and where she lived on campus so he could find her.3

The next day, Longmeadow police officers seized both a knit hat and a knife from the defendant's car during a valid traffic stop of the defendant, but did not arrest him at that point. The defendant later admitted to police that the knit hat recovered was the one used during the robbery.4 In addition, a piece of paper containing the victim's name and information was recovered from a trash barrel outside the defendant's home during the execution of a search warrant. Analysis of fingerprints lifted from the victim's car revealed that the fingerprints located on the driver's front door window and passenger's front door window matched the defendant's prints. The defendant's deoxyribonucleic acid (DNA) was also a match with a vaginal swab taken from the victim.5

b. The defendant's statement to police.6 On April 19, 2006, the defendant was arrested in his parents' home. The defendant's mother provided the arresting officers with the defendant's prescription pain medication,7 and he was thereafter taken to the Springfield police department. On arrival, the defendant was read the Miranda warnings, as well as his right to a prompt arraignment. He told the officers that he understood those rights but stated that he did not wish to speak with them.8 After this invocation, the officers took the defendant to be booked; in conjunction with the booking process, he was photographed and fingerprinted, and submitted to a DNA test. While he was in the booking area, the defendant received some of his prescription pain medication.

After his fingerprints had been taken and the DNA swab obtained, the defendant told the officers that he wanted to give a statement. Accordingly, two hours after he had initially invoked his Miranda rights, the defendant was escorted back to the police interview room where he again was advised of his Miranda rights and his right to prompt arraignment. He indicated that he understood the rights and that he wanted to talk with the officers. The defendant's resulting statement contained portions that implicated him in the robbery of the victim but denied sexually assaulting and beating her.

c. The references to the defendant's invocation of his Miranda rights. Before trial, the defendant moved to suppress his statements to the police, asserting, in part, that his statements were not voluntary because the officers withheld the defendant's prescription pain medication and told him they would provide the defendant with his medication if he reconsidered talking to them. After an evidentiary hearing, the motion judge, who was not the trial judge, did not accept the defendant's allegation about withheld medication, concluded that the defendant's statements were voluntary based on the totality of the circumstances, and ultimately denied the motion to suppress in its entirety. The defendant based his defense at trial on his claim that he lacked criminal responsibility, and informed the prosecutor and the trial judge at the outset of the trial that voluntariness of the defendant's statements to the police remained a live issue.

In three different portions of the trial, the prosecutor referred to the defendant's initial invocation of his Miranda right to remain silent and not to speak with police: during her direct examination of Detective Eugene Dean of the Springfield police department; in her cross-examination of the defendant's expert witness, Dr. Melvin Lurie; and in her closing argument.

(i) Detective Dean. On the first day of Dean's testimony, the prosecutor elicited in her direct examination the following:

The prosecutor thereafter introduced into evidence the "Miranda Warning" and "Arraignment Warning" forms, both of which evidenced the defendant's initial invocation of his right to remain silent in his own handwriting. This testimony of Dean and these forms provided the first references to the defendant's invocation of his Miranda rights at trial.9

On the second day of Dean's testimony, the prosecutor again referred to the defendant's invocation through her questioning:

(ii) Dr. Lurie. During her cross-examination of the defendant's expert, the following exchange occurred:

(iii) Closing argument. In her closing, the prosecutor rehearsed the various actions taken by the defendant during the criminal events that, the prosecutor argued, showed that the defendant was criminally responsible and described them as "calculated" actions. The prosecutor then stated:

2. Discussion. a. Prosecutor's use of defendant's invocation of right to silence. At trial, the defendant conceded that he committed the acts of aggravated kidnapping, aggravated rape, assault and battery with a dangerous weapon, and intimidation of the victim that were at issue in the case; his defense, and the question in dispute, was whether he was criminally responsible for those acts. Relying principally on Doyle v. Ohio, 426 U.S. 610, 617-619 (1976), and Commonwealth v. Mahdi, 388 Mass. 679, 694-697 (1983), he argues that the prosecutor's several references to his initial invocation of his right to remain silent violated his constitutional due process rights in that the prosecutor was using the defendant's invocation to argue, impermissibly, that he was indeed criminally responsible.13 We agree with the defendant. We begin with the governing constitutional principles.

"There is no question that, under the fundamental principles of jurisprudence, evidence of a criminal defendant's postarrest, post-Miranda silence cannot be used for the substantive purpose of permitting an inference of guilt...." Mahdi, 388 Mass. at 694, citing United States v. Hale, 422 U.S. 171, 175, 181 (1975). This prohibition exists because

Commonwealth v. Cobb, 374 Mass. 514, 520-521 (1978), quoting Doyle, 426 U.S. at 617-618. See Commonwealth v. Beneche, 458 Mass. 61, 73 (2010), quoting Commonwealth v. Peixoto, 430 Mass. 654, 658-659 (2000). See also Commonwealth v. Waite, 422 Mass. 792, 797 (1996). Moreover, "[f]undamental unfairness results from the use of evidence of such silence regardless whether the person exercising his or her constitutional right to remain silent claims insanity as a defense." Mahdi, supra at 695.14

There are, however, "rare instances where evidence of a defendant's postarrest, post-Miranda silence ... may be admissible." Commonwealth v. DePace, 433 Mass. 379, 383 (2001), overruled on other grounds, Commonwealth v. Carlino, 449 Mass. 71, 80 (2007). Such instances include explaining why a police interview of the defendant abruptly ended and the jury would be confused without the explanation, see Commonwealth v. Habarek, 402 Mass. 105, 110 (1988), S.C., 421 Mass. 1005 (1995); rebutting the defendant's suggestion at trial that some impropriety on the part of the police prevented him from completing his statement to them, see id.; and rebutting a claim by the defendant that he had given the police at the time of his arrest the same exculpatory explanation as he was presenting to the jury at trial. See DePace, supra at 383-384. None of these exceptions applies in this case.

(i) Direct examination of Detective Dean. The Commonwealth contends that the prosecutor was justified in eliciting that the defendant initially invoked his right to remain silent during her direct examination of Dean to (1) "provide a complete picture of the defendant's interaction with the police," and in particular to explain why the first interview ended in very short order; and (2) rebut the defendant's theory that the statements elicited during his second police interview were not voluntary. We disagree.

When a defendant gives a statement to the police, it is permissible for the Commonwealth to present a fair and reasonably complete picture of the interaction between police and the defendant, including the administration of Miranda warnings and the defendant's responses to questions posed to him during that process. See, e.g., Commonwealth v. Toolan, 460 Mass. 452, 472 (2011); Habarek, 402 Mass. at 110. In this case, the defendant gave a statement to the police when they brought him back to the interview room in response to his request near the end of the booking process. The Commonwealth was entitled to, and did, present a full account of that interrogation through the prosecutor's direct examination of Dean. The defendant's earlier invocation of his right to remain silent was a distinct event, separated by time and circumstances; clearly, there was no need, in the name of fairness or completeness, to include a description of that event in presenting evidence about the defendant's postbooking waiver of Miranda rights and police interview.

In addition, the Commonwealth's reliance on Habarek, 402 Mass. at 109-110, is misplaced.15 Unlike that case, where the defendant waived his Miranda rights and spoke to the police about the alleged crime in question for at least a short while (see note 15, supra), in this case, Dean did not conduct any interview of the defendant the first time he and the defendant spoke, precisely because upon receiving the Miranda warnings, the defendant stated he did not want to speak with the police. See DePace, 433 Mass. at 384 ("The rule in Habarek does not apply to the present case .... Here, there was no evidence of any interview, much less one that ended abruptly"). See also Commonwealth v. King, 34 Mass.App.Ct. 466, 469 (1993).16 The prosecutor's references to the defendant's desire to remain silent were not justified under Habarek.

That the voluntariness of the defendant's statement to police remained a live issue at trial likewise did not justify the prosecutor's use of the defendant's exercise of his right to silence during her direct examination of Dean. It is true that "under the Commonwealth's `humane practice' rule, where the voluntariness of a statement is a live issue at trial, the jury may hear evidence that a defendant was informed of and understood his Miranda rights." Toolan, 460 Mass. at 471. But evidence that Miranda warnings were provided and that the defendant understood them does not itself require reference to the fact that the defendant earlier exercised the rights included in those warnings. See id. at 472-473.17 This is particularly the case where, as here, the prosecutor introduced the evidence of the defendant's exercise of his Miranda rights at a time when the defendant had yet to raise the issue of voluntariness before the jury. The references to the fact that the defendant initially declined to speak to police during the prosecutor's direct examination of Dean constituted error.

(ii) Cross-examination of the defendant's expert. In cross-examining Dr. Lurie, the prosecutor again mentioned the defendant's initial assertion of his right to remain silent.18 The Commonwealth argues that in doing so, the prosecutor was clearly addressing the voluntariness of the defendant's statement, and that she was careful to distinguish the "voluntariness" line of questioning from her questions that dealt with the defendant's criminal responsibility. The defendant disputes this characterization. He contends that the true focus of the prosecutor's references to the defendant's assertion of his right to silence and then waiver was on his capacity to appreciate the wrongful nature of his conduct and to take steps post hoc to exculpate himself — that is, the focus was on the defendant's criminal responsibility.19

It is true Dr. Lurie testified that, in his opinion, the defendant's statement to the police was not voluntary. But just as it was not necessary for the prosecutor to refer to the defendant's initial invocation of his rights in order to address the voluntariness issue with Detective Dean, it was equally unnecessary in cross-examining Lurie. The prosecutor could have asked questions to challenge Lurie's view on voluntariness without the reference, and certainly could have posed the same hypothetical question whether a person in the defendant's position who had been fingerprinted would want to tell his story to the police without any mention of the defendant's earlier exercise of his right not to speak. See Wainwright v. Greenfield, 474 U.S. 284, 295 (1986) (carefully framed questions can accomplish same task as comment on silence).

Moreover, assuming for the sake of argument that it would have been permissible to introduce evidence of the defendant's initial invocation in order to respond to his claim of involuntariness, cf. Habarek, 402 Mass. at 110, contrary to the Commonwealth's claim, the prosecutor's questions were not so focused. As the defendant points out (see note 19, supra), right before the prosecutor referred to the defendant's initial decision not to speak to police, she listed a series of the defendant's actions on the night the crimes were committed to show that he understood the consequences of his actions. The Commonwealth argues that the prosecutor paused following these questions before turning to the voluntariness issue. The transcript does reflect a pause, but we question whether that pause, by itself, was sufficient to signal to the jury that the prosecutor was no longer addressing the defendant's lack of criminal responsibility defense. Moreover, the prosecutor followed her reference to the defendant's invocation of his right to silence with more questions about particular aspects of the criminal episode that arguably showed appreciation and control (i.e., criminal responsibility). Cf. Commonwealth v. Acevedo, 427 Mass. 714, 716-717 (1998) (prejudice created by correct jury instruction sandwiched between two incorrect instructions on same issue).

In sum, the prosecutor's references to the defendant's invocation of the right to silence in the cross-examination of Lurie were improper.

(iii) Prosecutor's closing argument. The portion of the prosecutor's closing argument challenged by the defendant followed the same pattern as her cross-examination of Lurie, and indeed built on it. As earlier described, the prosecutor in her closing listed actions by the defendant that reflected his capacity for appreciation and control in relation to his conduct, characterizing them for the jury as "calculated" actions; she then moved to the defendant's initial exercise of his right to silence and subsequent decision to speak to the police after being fingerprinted, describing the defendant's thought pattern in essentially the same words as she had in her hypothetical question earlier posed to Lurie, and then labeling the entire invocation-waiver sequence as a "calculated... scenario."

The Commonwealth asserts that the prosecutor's challenged remarks were addressing the voluntariness of the defendant's statement, not his criminal responsibility, and that she was entitled to do so to reply to the defendant's contrary position. Again, assuming the propriety of raising the defendant's initial invocation of Miranda rights as a response to a defense challenge to voluntariness, the Commonwealth's argument ignores the close proximity and significant degree of parallelism between the portion of the prosecutor's closing argument countering the defendant's contention that he lacked criminal responsibility, and the portion purporting to address the voluntariness of the defendant's statement. We agree with the defendant that the prosecutor's closing left the impression that the defendant's invocation in significant part demonstrated that he was criminally responsible.20 This is precisely what Mahdi prohibits. See Mahdi, 388 Mass. at 694-695.

b. Effect of errors. With one partial exception, the defendant did not object at trial to the prosecutor's references to his invocation.21 Both the defendant and the Commonwealth agree, as do we, that the proper standard of review is whether the errors created a substantial risk of a miscarriage of justice. See Commonwealth v. Alphas, 430 Mass. 8, 13 (1999). Cf. Commonwealth v. Fowler, 431 Mass. 30, 42 & n.20 (2000) (unpreserved error concerning admission of evidence of defendant's invocation of right to remain silent in first degree murder appeal was properly reviewed under substantial likelihood of miscarriage of justice standard).

In Alphas, 430 Mass. at 13, this court stated:

See Commonwealth v. Randolph, 438 Mass. 290, 297-298 (2002) (review of denial of motion for new trial; articulation of factors for reviewing substantial risk of miscarriage of justice).22

We first review the considerations set forth in Alphas. As to the strength of the Commonwealth's case, the defendant admitted to committing the acts constituting the crimes charged, and even without the evidence of the defendant's invocation of his Miranda rights, the Commonwealth's case that the defendant was criminally responsible was very strong. The testimony of the victim, as well as the defendant's own statement to the police, provided detailed, compelling evidence that the defendant understood and appreciated that what he was doing was criminal and that he had the capacity to direct and control his behavior.23 Turning to the nature of the error and the failure of defense counsel to object, for all the reasons we have discussed previously, the prosecutor's various references to the defendant's initial invocation constituted a constitutional error that at least in part related to the premise of the defense. Nevertheless, in the context of the other evidence presented at trial, the error does not create a plausible inference that if it had not occurred, the jury would have decided the case differently. See Commonwealth v. Miranda, 22 Mass.App.Ct. 10, 21 (1986). In these circumstances, we conclude that no substantial risk of a miscarriage of justice occurred in this case.

Finally, we turn to the factors that the court set out in Mahdi, 388 Mass. at 696-697, for assessing the degree of harm caused by constitutional evidentiary errors. See note 22, supra. The Mahdi factors are: "(1) the relationship between the evidence and the premise of the defense; (2) who introduced the issue at trial; (3) the weight or quantum of evidence of guilt; (4) the frequency of the reference; and (5) the availability or effect of curative instructions." Id. (footnotes omitted). Many of the factors weigh against the Commonwealth here. The prosecutor's references to the defendant's invocation of Miranda rights, when used to suggest criminal responsibility, directly connected to the premise of the defendant's defense (factor 1); the Commonwealth introduced the evidence at trial (factor 2); the prosecutor referred to the invocation in three contexts (factor 4); and there were no targeted curative instructions by the judge (factor 5) — although the absence of such instructions is consistent with the evidence being admitted without objection. See Commonwealth v. Adams, 434 Mass. 805, 812 (2001).24 But as discussed, the victim's testimony and, significantly, the defendant's own statement described the series of intentional actions he took during the criminal episode and offered explanations for those actions (see note 23, supra), and these explanations provided very powerful evidence of the defendant's ability to appreciate both the wrongfulness of his actions and his ability to conform his actions to the requirements of law — i.e., that he possessed criminal responsibility while committing the crimes (factor 3). See id. at 814 ("lengthy laundry list of rational, calculating, nondelusional conduct ... admittedly engaged in by [the defendant] before, during, and just after the crime" supported "[the Commonwealth's] expert's testimony that [the defendant] was fully capable of complex thought and action when he committed the murders, and was able to appreciate the wrongfulness of his conduct and form it to the requirements of the law" [footnote omitted]). See also Fowler, 431 Mass. at 42-43.25 In light of the strength of the evidence of the defendant's criminal responsibility, even considering the Mahdi factors, we conclude that there was no substantial risk of a miscarriage of justice, and reversal of the defendant's convictions is not warranted.

3. Conclusion. The prosecutor's references to the defendant's invocation of his right to remain silent constituted error but they did not create a substantial risk of a miscarriage of justice. For the reasons stated by the Appeals Court, Letkowski, 83 Mass. App. Ct. at 858-859, the case is remanded to the Superior Court for further proceedings.

So ordered.