Petitioner Adriano Vargas appeals from a December 19, 1994, judgment of the United States District Court for the Southern District of New York (Michael B. Mukasey, Judge) dismissing his petition for a writ of habeas corpus under 28 U.S.C. § 2254. On appeal, Vargas contends that (1) the district court erred in concluding that the trial court’s reasonable doubt instruction was not constitutionally deficient; and (2) the district court improperly deemed his challenge to the prosecutor’s summation procedurally barred.
We conclude that the challenged instruction, when taken as a whole, neither overstated the degree of doubt necessary for acquittal nor shifted the burden of proof away from the prosecution. In addition, we agree with the district court that Vargas’s challenge to the prosecutor’s summation is procedurally barred and that a denial of relief would not result in a “fundamental miscarriage of justice.” We therefore affirm.
I. Facts
The petitioner was charged with first-degree burglary and first- and second-degree robbery in connection with a February 22, 1988, incident at the Manhattan apartment of Carlos and Cecilia Carey. Two men forcibly entered the apartment, threatened Mr. and Mrs. Carey with a gun and a knife, tied the pair up with telephone cable, and ransacked the apartment. After reporting the robbery to the police and viewing police photographs, neither of the Careys was able to identify the perpetrators. Two weeks later, however, both selected a photograph of the petitioner. For reasons that are unclear, the petitioner was not apprehended. A month after the robbery, the Careys allegedly saw the petitioner on a subway car. Mr. Carey called the police, who drove him to an apartment building; Mr. Carey saw the petitioner standing at a third-floor window and identified him as one of the two robbers and as the person he had seen on the subway. The police arrested the petitioner outside of the apartment building shortly thereafter.
The Supreme Court in New York County held a suppression hearing beginning on November 7, 1988, to determine the admissibility of the Careys’ photographic identification of the petitioner and Carlos Carey’s identification of the petitioner at the scene of his arrest. When the petitioner failed to appear on the second day of the suppression hearing, the court proceeded without him, but agreed not to rule on the suppression motions until both sides had attempted to locate the petitioner. After those efforts proved unsuccessful, the court rendered its decision declining to suppress the challenged evidence and proceeded with the trial on November 16 and 17, in the petitioner’s absence but with defense counsel present and participating.
In his instructions to the jury, the trial judge defined reasonable doubt in part as follows:
A reasonable doubt is a doubt which you consciously have after the use of your powers of reasoning which arises out of the credible evidence or the lack of credible evidence.
It is a doubt for which you can give a reason if called upon to do so by a fellow juror in the jury room. The standard of reason must be prevailing. When you are convinced that you have no doubt in reason of the defendant[’]s guilt, that is when you will be justified in rendering a verdict accordingly. Consequently, after fairly and fully considering all of the evidence and the lack of evidence and using the same power of reasoning and power of thinking that would apply and do apply to weigh the importance of matters related to the [sic] important business affairs, if you then believe that each element of the crime submitted to you[] has been established beyond a reasonable doubt, you would be justified in finding the defendant guilty of that crime.
(Emphasis supplied.) After deliberating for one hour, the jury convicted the petitioner on all three counts of the indictment. The petitioner was re-arrested several weeks later, and the court imposed concurrent sentences of eight to sixteen years imprisonment on the burglary and first-degree robbery counts, and seven-and-a-half to fifteen years imprisonment on the second-degree robbery count.
*1276Vargas challenged his conviction on direct appeal. He did not challenge his trial in absentia, but claimed primarily that the trial court’s instructions on reasonable doubt were erroneous and that the proceedings had been infected by improper prosecutorial comments on summation. On July 3, 1990, the Appellate Division of the Supreme Court unanimously affirmed the conviction, finding no error in the reasonable doubt instruction and concluding that the petitioner’s challenge to the prosecutor’s summation was procedurally barred in light of his counsel’s failure to interpose an objection at trial, and (in any event) that the prosecutor’s remarks were not improper. People v. Vargas, 163 A.D.2d 39, 39, 559 N.Y.S.2d 631, 632 (1st Dep’t 1990) (mem.). The petitioner’s application for leave to appeal to the New York Court of Appeals was denied. 76 N.Y.2d 945, 563 N.Y.S.2d 74, 564 N.E.2d 684 (1990).
In June 1992, Vargas moved under §§ 440.10 and 440.20 of the New York Criminal Procedure Law for a new trial or to set aside his sentence. He claimed that the court had improperly proceeded to trial in his absence and challenged his sentencing on the ground that the Probation Department had omitted his statement from the presentence report. On July 13, 1992, the New York Supreme Court denied the petitioner’s motion, and the Appellate Division denied his application for leave to appeal.
Vargas filed the instant federal petition on November 15, 1993, claiming that the trial court’s reasonable doubt instruction was constitutionally deficient, the prosecutor’s improper summation tainted the proceedings, and the omission of his statement from the presentence report rendered his sentencing proceeding invalid. By an order of November 26, 1993, Judge Mukasey referred the petition to Magistrate Judge Michael H. Dolinger. In a Report and Recommendation filed September 21, 1994, the magistrate judge concluded that the petition should be denied, because: (1) the trial court’s reasonable doubt instruction was not constitutionally deficient, and in fact closely tracked approved New York pattern jury instructions; (2) in light of defense counsel’s failure to object to the prosecutor’s remarks during summation, the petitioner’s challenge to those remarks was procedurally barred; and (3) the petitioner’s sentencing challenge did not raise a federally cognizable claim. On December 19, 1994, Judge Mukasey adopted the report of the magistrate judge over the petitioner’s objection and issued a certificate of probable cause to appeal. We appointed counsel to brief and argue the appeal. The petitioner pursues on appeal only his claims that the trial court’s reasonable doubt instruction was constitutionally deficient and that the district court erred in treating his challenge to the prosecutor’s summation as procedurally barred.
II. Discussion
A. Reasonable Doubt Instruction
In a state criminal trial, the Due Process Clause of the Fourteenth Amendment protects the accused from conviction unless the prosecution “persuade[s] the fact-finder ‘beyond a reasonable doubt’ of the facts necessary to establish” each element of the offense charged. Sullivan v. Louisiana, 508 U.S. 275, 278, 113 S.Ct. 2078, 2080-81, 124 L.Ed.2d 182 (1993) (citations omitted); In re Winship, 397 U.S. 358, 364, 90 S.Ct. 1068, 1072-73, 25 L.Ed.2d 368 (1970). A jury instruction that permits conviction on a lesser standard — by shifting the burden of proof from the prosecution to the defendant, or by suggesting that a higher degree of doubt than “reasonable” doubt is necessary for acquittal — is constitutionally deficient. Any such deficiency would be a per se ground for reversal of a criminal conviction: because the Sixth Amendment and the Fourteenth Amendment’s Due Process Clause together require a jury verdict of guilty “beyond a reasonable doubt,” a guilty verdict rendered by a jury applying a less demanding standard of proof is not a jury verdict at all within the meaning of the Sixth Amendment. Sullivan, 508 U.S. at 278, 280, 113 S.Ct. at 2080-81, 2082. In such circumstances, harmless error analysis — which permits a reviewing court to determine whether a jury would have rendered the same verdict of guilty absent the constitutional error occurring at trial — simply cannot apply. Id.; see Chal*1277mers v. Mitchell, 73 F.3d 1262, 1267 (2d Cir.1996).
Although a constitutional infirmity in a reasonable doubt instruction is a per se ground for reversal of a criminal conviction, not every unhelpful, unwise, or even erroneous formulation of the concept of reasonable doubt in a jury charge renders the instruction constitutionally deficient. The reviewing court must examine the charge as a whole, see Cupp v. Naughten, 414 U.S. 141, 146-47, 94 S.Ct. 396, 400-01, 38 L.Ed.2d 368 (1973), and assess “whether there is a reasonable likelihood that the jury understood the instructions to allow conviction based on proof insufficient to meet” the standard of proof beyond a reasonable doubt, Victor v. Nebraska, 511 U.S. 1,-, 114 S.Ct. 1239, 1243, 127 L.Ed.2d 583 (1994). See Chalmers, 73 F.3d at 1267 (“Sometimes, erroneous portions of the jury instructions are offset when considered in context or explained by the trial court in later sections of the instruction. [At] [o]ther times, a seemingly innocuous incorrect statement becomes extremely damaging when coupled with other sections of the jury instructions or with improper conduct by counsel during the trial.” (citations omitted)). Accordingly, an asserted error in a reasonable doubt instruction may be innocuous or inconsequential when viewed in the context of the charge as a whole; surrounded by different language in a different charge, however, the same language may create a constitutional infirmity.
In the instant case, the petitioner identifies two alleged errors that, taken separately or together, are said to render the state trial court’s instruction constitutionally deficient. First, the petitioner claims that it is reasonably likely that jurors would have understood the court’s characterization of a “reasonable doubt” as a doubt “for which you can give a reason if called upon to do so by a fellow juror in the jury room”: (1) to require, for acquittal, not only a doubt that seems “reasonable” in the juror’s mind, but a doubt that is articulable to a fellow juror; and (2) to shift to the defendant or to fellow jurors the burden to supply a doubt that is both reasonable and articulable. Second, the petitioner claims that, in instructing the jurors to apply to their deliberations “the same power of reasoning and power of thinking” that they would apply “to weigh the importance of matters related to ... important business affairs,” the trial court conveyed to the jurors the impression that they would be required to vote for conviction once they had given the evidence no more consideration than they would give to their “business affairs.”
We analyze the asserted defects in turn.
1. Reasonable doubt as “a doubt for which you can give a reason if called upon to do so by a fellow juror.”
As the report of the magistrate judge noted, the trial court’s characterization of reasonable doubt as “doubt for which you can give a reason if called upon to do so by a fellow juror” is a variation on New York’s pattern jury instructions, which define reasonable doubt in part as “a doubt for which some reason can be given.” 1 Criminal Jury Instructions (New York) § 3.07, at 92 (1983); see, e.g., People v. Malloy, 55 N.Y.2d 296, 300, 303, 449 N.Y.S.2d 168, 170, 171, 434 N.E.2d 237, 238-39, 239-40 (charge defining reasonable doubt as “a doubt for which you can conscientiously express a reason” was “neither confusing nor inaccurate”), cert. denied, 459 U.S. 847, 103 S.Ct. 104, 74 L.Ed.2d 93 (1982); see also Leecan v. Lopes, 893 F.2d 1434, 1443 (2d Cir.) (rejecting habeas challenge to Connecticut trial court’s definition of reasonable doubt as “a doubt for which a reasonable man can give a valid reason”), cert. denied, 496 U.S. 929, 110 S.Ct. 2627, 110 L.Ed.2d 647 (1990). As we have previously noted, instructions tying “reasonable doubt” to a doubt “for which you can give a reason” — or, in the more passive formulation, “for which a reason can be given” — may well be unwise, because of the possibility that such an instruction will “intimidate a juror by suggesting that he may be called upon to explain his doubts.” United States v. Davis, 328 F.2d 864, 867 (2d Cir.1964) (rejecting challenge to instruction defining reasonable doubt as “a doubt for which you can give a reason”). More recently, we have had occasion to consider the constitutionality of a state trial court instruction defining reasonable doubt as “a doubt for which some good *1278reason can be given.” Chalmers, 73 F.3d at 1267 (emphasis supplied). While we noted that the “good reason” language constituted an “incorrect statement of law which should never be made,” id. at 1266, we concluded that, viewed in light of the charge as a whole, the challenged language did not raise the quantum of doubt necessary for acquittal or shift the burden of proof away from the prosecution, id. at 1268-69. Vargas argues that the trial court’s instruction in this case is more dangerous than the instruction in Chalmers or the New York pattern jury charge, because of its assertedly more direct suggestion that a juror must be prepared to expound, in the jury room, upon his reasons for doubting the defendant’s guilt. That is, the petitioner claims that even if the “doubt for which a reason can be given” formulation is appropriate, the added language here — “if called upon to do so by a fellow juror” — in substance conveyed to the jurors that they might indeed be called upon to articulate the basis for their doubts. Two constitutional deficiencies are said to follow: (1) the instruction is reasonably likely to have conveyed to the jury the idea that a doubt sufficient to justify acquittal must not only be “reasonable,” but must also be “articulable” to one’s fellow jurors; and (2) the instruction is reasonably likely to have compelled the jurors to look to the petitioner or to one another to supply an articulable doubt, thus shifting the burden of proof away from the prosecution.
Placing the challenged language in the context of the full charge, we find no reasonable likelihood that the jurors would have understood the instruction to increase the degree of doubt necessary for acquittal. The premise of the petitioner’s challenge — and, indeed, of challenges to instructions such as those in Davis and Leecan, which do not include the language “if called upon to do so by a fellow juror” — is that a juror may hold a reasonable doubt of a defendant’s guilt, based on the evidence or lack of evidence offered by the prosecution, and yet be unable to articulate that doubt. Even if we assume that there exists a category of “reasonable” yet not “articulable” doubt, we do not see how the addition of the phrase “if called upon to do so by a fellow juror” alters the substance of the instruction sustained in cases such as Davis and Leecan in any constitutionally significant way. The challenged language does not suggest — any more than the “for which a reason can be given” formulation standing alone — that a juror will be called upon to articulate his doubts, or that he must articulate them if so called upon. Moreover, language surrounding the challenged language renders it unlikely that jurors would interpret the passage to require a higher degree of doubt than “reasonable” doubt for acquittal. The challenged language was immediately preceded and followed by language giving additional content to the phrase “reasonable doubt,” emphasizing that the jurors’ task was to engage in a careful, reasoned analysis of the evidence— or lack of evidence — presented. Accordingly, the jury was unlikely to have understood the challenged language to bear upon the degree or quantum of doubt necessary for acquittal, but rather, upon the appropriate basis for the formulation of a doubt sufficient for acquittal: as the charge properly stated, a “reasonable” doubt is not “just any kind of doubt, a mere whim or a guess or a feeling, or a surmise that the accused may not be guilty,” but a doubt that “arises out of the credible evidence or the lack of credible evidence.” Viewed in context, the challenged language simply does not suggest that a doubt formulated within one’s own mind— reasonable, but not articulable — is insufficient for acquittal. Rather, it serves to emphasize, in conjunction with surrounding language, that any doubt sufficient for acquittal must be based on a reasoned evaluation of the evidence or lack of evidence, rather than on speculation, emotion, or whim.
As to the second asserted danger of the relevant language — that the jurors would look to the defendant or to one another to supply an articulable reason for doubt before voting to acquit — we conclude that, viewing the charge as a whole, there is no reasonable likelihood that the jurors interpreted the instruction as shifting the burden of proof away from the prosecution. Language preceding the challenged passage makes clear that the burden of proof “remains upon the prosecution throughout the trial and never *1279shifts to the defendant” and that “each and every element of [the] crime submitted to you ... must be proved beyond a reasonable doubt by the prosecution.” Indeed, the trial court, in the time-honored tradition of cautious trial courts, emphasized the prosecution’s burden to prove the elements of the crimes charged beyond a reasonable doubt ad nauseam — no fewer than fifteen times throughout the course of the charge.
2. Applying “the same power of reasoning” as is applied to “important business affairs.”
The petitioner also challenges a portion of the charge instructing the jurors to “use the same power of reasoning and power of thinking” as they would apply in “matters related to [their] important business affairs.” The challenged language bears some resemblance to instructions defining reasonable doubt as a doubt that would cause a reasonable person to “hesitate to act” in important personal affairs. The “hesitate to act” formulation has consistently been approved, see Victor, 511 U.S.-, 114 S.Ct. at 1250; Holland v. United States, 348 U.S. 121, 140, 75 S.Ct. 127, 137-38, 99 L.Ed. 150 (1954); Perez v. Irwin, 963 F.2d 499, 502 (2d Cir.1992), although courts have questioned the propriety of analogizing the deliberative process that jurors must undertake in a criminal trial to the thought process they undertake in weighing important personal decisions, see United States v. Reese, 33 F.3d 166, 172 (2d Cir.1994) (noting “ongoing debate” about propriety of instruction defining reasonable doubt as “a doubt which would make each of you hesitate to act in the more serious and important affairs of your own lives”), cert. denied, — U.S.-, 115 S.Ct. 756, 130 L.Ed.2d 655 (1995); United States v. Noone, 913 F.2d 20, 28-29 (1st Cir.1990) (“The momentous decision to acquit or convict a criminal defendant cannot be compared with ordinary decision-making without risking trivialization of the constitutional standard.” (citing Dunn v. Perrin, 570 F.2d 21, 24 (1st Cir.), cert. denied, 437 U.S. 910, 98 S.Ct. 3102, 57 L.Ed.2d 1141 (1978))), cert. denied, 500 U.S. 906, 111 S.Ct. 1686, 114 L.Ed.2d 81 (1991); see also Victor, 511 U.S. at-, 114 S.Ct. at 1252 (Ginsburg, J., concurring in part and concurring in the judgment) (noting observation of 1987 report to Judicial Conference of the United States that analogy underlying “hesitate to act” formulation is misplaced: “‘[The] decisions we make in the most important affairs of our lives ... generally involve a very heavy element of uncertainty and risk-taking.’”).
The petitioner claims that the instruction in the instant case is in fact considerably different from and more harmful than the ordinary “hesitate to act” formulation, in two respects. First, the jury was told to analogize not to important personal decisions, but to business decisions, which are potentially more speculative and risk-laden. Second, the jury was not told to hesitate to act, but to convict after “weighting] the evidence no more carefully than when one makes a ‘business decision.’ ” Appellant’s Br. at 27. The petitioner thus contends that the instruction: (1) trivialized the deliberative process the jurors were to undertake; and (2) diluted the concept of “reasonable doubt” by conveying that conviction was required as long as any doubts the jurors harbored were not of a kind that would prevent them from going forward with a business transaction.
Considering this language in the context of the full charge, we find no reasonable likelihood that the jury understood the instruction to permit conviction after anything but a process of careful deliberation or upon less than proof beyond a reasonable doubt. Leaving aside the general propriety of instructions analogizing a criminal jury’s deliberative process with the process involved in making important personal or business decisions, the inclusion of the reference to “important business affairs” here could not have suggested to the jurors that they were to undertake a haphazard or speculative inquiry. On the contrary, the trial court’s reference to “the power of reasoning and power of thinking” associated with important business deliberations served to reinforce its earlier instruction to decide the facts “coolly, calmly and deliberately,” not to “indulge in speculation or guesswork” or “conjecture,” and to “fairly and full[y] consider[ ] all the evidence and lack of evidence.” Similarly, the instruction did not suggest that the doubts assoeiat*1280ed with the factfinding process in a criminal trial are anything like doubts that tend to arise during consideration of business decisions, let alone that the jurors were required to convict unless they held the sort of doubts that would prevent them from acting in important business matters.1
In sum, it simply cannot be said that the asserted errors, taken separately or together, render the challenged reasonable doubt instruction constitutionally deficient. We pause only to make clear that in so holding wé do not mean to suggest that the elaboration of the concept of reasonable doubt chosen by the trial court — and particularly, the reference to reasonable doubt as a doubt “for which you could give a reason if called upon to do so by a fellow juror” — was prudent or desirable. Courts have long recognized that the concept of “reasonable doubt” is not susceptible of easy definition. See, e.g., Holland, 348 U.S. at 140, 75 S.Ct. at 138 (“Attempts to explain the term ‘reasonable doubt’ do not usually result in making it any clearer to the minds of the jury.” (quotation marks omitted)); United States v. Birbal, 62 F.3d 456, 457 (2d Cir.1995) (noting that requirement of proof beyond a reasonable doubt is “one of the least susceptible to verbal formulation”). Indeed, at least two Courts of Appeals have instructed district courts within their circuits that the concept is best left unexplained. See United States v. Adkins, 937 F.2d 947, 950 (4th Cir.1991) (“This circuit has repeatedly warned against giving the jury definitions of reasonable doubt, because definitions tend to impermissibly lessen the burden of proof____”); United States v. Hall, 854 F.2d 1036, 1039 (7th Cir.1988) (“[A]t best, definitions of reasonable doubt are unhelpful to a jury____ An attempt to define reasonable doubt presents a risk without any real benefit.”); see also id. at 1043-45 (Posner, J., concurring). There is some merit in admonitions, by courts exercising direct supervisory authority, regarding the danger of straying from tried and tested pattern jury instructions on reasonable doubt. In this instance, however, we are mindful that the challenge to the trial court’s instruction arises on habeas review, and our inquiry is whether the instruction is constitutional, not whether it is exemplary.
B. Prosecution’s Summation
The petitioner also claims that certain remarks made by the prosecutor during her summation deprived him of a fair trial. Specifically, the petitioner contends that the prosecutor (1) improperly invited the jury to convict based on the defendant’s purported “arrogance”; (2) misstated the evidence by claiming that the defendant “thought he could bully into an apartment with a gun,” when it was undisputed that only one of the perpetrators — not the defendant — had brandished a gun; and (3) suggested to the jury that the evidence in the case showed the defendant’s guilt so clearly that the trial itself was superfluous. At trial, defense counsel failed to object to the prosecutor’s remarks. On direct appeal, the Appellate Division concluded that Vargas’s challenge to those remarks was not preserved for review, and, in any event, was without merit. Vargas, 163 A.D.2d at 39, 559 N.Y.S.2d at 632.
As the district court correctly noted, the petitioner’s procedural default constitutes an adequate and independent state law ground for rejection of his claim. Accordingly, federal review of the claim is barred unless the petitioner can demonstrate cause for the procedural default and prejudice flowing therefrom, see Wainwright v. Sykes, 433 U.S. 72, 87-91, 97 S.Ct. 2497, 2506-2509, 53 L.Ed.2d 594 (1977), or that “failure to consider the claim[] will result in a fundamental miscarriage of justice,” Coleman v. Thompson, 501 U.S. 722, 750, 111 S.Ct. 2546, 2565, 115 L.Ed.2d 640 (1991). The petitioner does not attempt to show cause or prejudice, and we agree with the district court that the record does not support a conclusion that the failure to grant relief will result in a “fundamental miscarriage of justice.”
*1281Conclusion
To summarize:
1. Examining the state trial court’s jury charge as a whole, we find no reasonable likelihood that the jury understood the instruction to overstate the degree of doubt necessary for acquittal or to shift the burden of proof away from the prosecution. Accordingly, the instruction is not constitutionally deficient.
2. The petitioner’s challenge to remarks made during the prosecutor’s summation is proeedurally barred, and the record does not support a finding that a denial of relief would result in a “fundamental miscarriage of justice.”
We therefore affirm the judgment of the district court.
. Leaving aside the fact that the charge in this case underscored the need for careful deliberation, we note the dubious premise underlying the petitioner's argument — namely, that the phrase "business affairs” as used in such instructions necessarily connotes trade or commerce (and an associated decision-making process that is inherently risky or speculative). The term "business” is broad, and surely encompasses matters of personal as well as commercial concern.