OPINION
NUGENT, District Judge.
Appellant Richard Caldwell filed a petition for a writ of habeas corpus under 28 U.S.C. § 2254 in the United States District Court for the Western District of Tennessee on June 23, 1997. Upon reviewing the petition, the district court granted summary judgment in favor of Appellee and issued a certificate of appealability to this Court. Appellant filed a timely notice of appeal on August 30,1999 and an amended notice of appeal on September 7, 1999.1 For the reasons set forth below, we AFFIRM the decision of the district court in all respects.
I. BACKGROUND
In 1981, a jury in a Tennessee state trial court found Appellant Richard Caldwell guilty of first degree murder. Appellant was sentenced to life in prison. The conviction arose from the fatal shooting of Carl Lipford, a man whom Appellant accused of stealing from him. More specifically, Appellant alleged that the shooting took place in response to the victim’s act of stealing a bulldozer track from him. Appellant filed a petition for post-conviction relief, which was denied by the trial court. Subsequently, the Court of Criminal Appeals of Tennessee affirmed Appellant’s conviction and the Supreme Court of Tennessee denied his permission to appeal.
In January of 1995, Appellant filed a second petition for post-conviction relief, [475]*475which was, likewise, denied by the trial court. Once again, the Court of Criminal Appeals of Tennessee affirmed the dismissal of the petition and the Supreme Court of Tennessee denied Appellant’s application for permission to appeal. Thereafter, Appellant initiated this petition for writ of habeas corpus in the United States District Court for the Western District of Tennessee.
In an August 6, 1999 Order, the district court denied the petition and found that, despite Appellant’s assertions to the contrary, the amendments to 28 U.S.C. § 2254 in the Antiterrorism and Effective Death Penalty Act of 1996 (the “AEDPA”) govern the petition. The district court also held that Appellant procedurally defaulted on numerous claims contained in the petition. Finally, the district court addressed the merits of the remaining claims and found that those claims lacked merit. Thus, the district court denied habeas corpus relief. Appellant Caldwell now appeals the district court’s decision to this Court.
II. DISCUSSION
Appellant urges this Court to reverse the decision of the district court for several reasons. More specifically, Appellant raises the following issues in this Court: (1) whether the district court erred when it applied the 1996 AEDPA amendments; (2) whether the district applied an incorrect standard of review for claims brought pursuant to § 2254; (3) whether the district court erred in upholding a jury instruction in relation to the element of malice; (4) whether the district court incorrectly found that Appellant’s statement was given to the authorities absent any constitutional violation; (5) whether the district court erred in ruling that Appellee did not withhold material exculpatory evidence at trial; (6) whether the district court incorrectly ruled that the definition of the phrase “beyond a reasonable doubt” was appropriately given to the jury in the state trial court; and (7) whether the district court incorrectly found that Appellant was not denied the effective assistance of counsel. We now consider these issues in turn.
A. Application of the 1996
AEDPA Amendments
Appellant argues that the AED-PA amendments should not apply to the instant case because such an application would have impermissible retroactive effects and alter the significance of the various state court decisions. The 1996 amendments reflect that reviewing courts shall extend great deference to state court adjudications on the merits that reasonably apply federal law. See 28 U.S.C. § 2254. In particular, § 2254(d), as amended, states:
An application for a writ of habeas corpus on behalf of a person in custody pursuant to the judgment of a State court shall not be granted with respect to any claim that was adjudicated on the merits in State court proceedings unless the adjudication of the claim-
(1) resulted in a decision that was contrary to, or involved an unreasonable application of, clearly established Federal law, as determined by the Supreme Court of the United States; or
(2) resulted in a decision that was based on an unreasonable determination of the facts in light of the evidence presented in the State court proceeding.
Id. Thus, when applying the 1996 amendments, this Court reviews a district court’s denial of habeas corpus relief de novo and any findings of fact for clear error. See Combs v. Coyle, 205 F.3d 269, 277 (6th Cir .2000).
The argument raised by Appellant in this ease concerns the temporal issue of [476]*476when these amendments should apply. The Supreme Court specifically addressed this issue in Lindh v. Murphy, 521 U.S. 320, 320, 117 S.Ct. 2059, 138 L.Ed.2d 481 (1997), when it held that the amendments in question apply to cases filed after the date on which the AEDPA became effective. Based upon this standard, this Circuit has recognized that if a petitioner files his application for a writ of habeas corpus after the effective date of the AEDPA, which was April 24, 1996, the amendments govern the inquiry into whether habeas corpus relief was appropriate in that particular case. See Harpster v. Ohio, 128 F.3d 322, 326 (6th Cir.1997).
In this case, Appellant filed his petition for writ of habeas corpus on June 23,1997, more than a year after the enactment of the AEDPA. Accordingly, the district court correctly found that the amendments to § 2254 govern the petition. Here, as in the district court, Appellant fails to demonstrate that an application of the amendments to this case would have an impermissible retroactive effect. Other than making the general assertion that his “legal expectations and entitlements were abruptly altered on April 24, 1996” when the AEDPA was enacted, Appellant advances no reason why this case constitutes an exception to the general rule which requires the amendments to apply to petitions filed after April 24, 1996. As the district court aptly stated, “a ruling that the amendments are inapplicable here would be tantamount to declaring them inapplicable in all cases.” J.A. at 10. This Court shall make no such ruling. Because Appellant fails to demonstrate an impermissible retroactive effect, we find that the district court did not err in applying the amendments to the instant case.
B. Standard of Review Pursuant to 28 U.S.C. § 2254
Next, Appellant contends that the district court applied the incorrect standard of review pursuant to 28 U.S.C. § 2254. In particular, without making specific reference to the allegedly erroneous standard as applied in the court below, Appellant makes the general assertion that the standard of review under the AEDPA amendments “raises the question of whether the writ of habeas corpus has been constitutionally suspended.” Appellant’s Brief at 23. Thus, resolution of Appellant’s argument in this regard requires this Court to reiterate the proper standard of review under the AEDPA amendments.
As mentioned previously, this Court reviews a district court's legal decisions in habeas corpus actions de novo and reviews its factual findings for clear error. See Wolfe v. Brigano, 232 F.3d 499, 501 (6th Cir.2000). With respect to this standard arising under the AEDPA, the Supreme Court, in Williams v. Taylor, 529 U.S. 362, 120 S.Ct. 1495, 146 L.Ed.2d 389 (2000), noted that the amendments place a new constraint on the “power of a federal habeas court to grant a state prisoner’s application for a writ of habeas corpus with respect to claims adjudicated on the merits in state court.” This Circuit set forth the importance of the Williams decision in Wolfe v. Brigano, 232 F.3d 499, 501 (6th Cir.2000), wherein we explained:
The United States Supreme Court’s recent decision in Williams v. Taylor, 529 U.S. 362, 120 S.Ct. 1495, 146 L.Ed.2d 389 (2000), clarified the requirements for a federal court to grant a state prisoner’s petition for a writ of habeas corpus under 28 U.S.C. § 2254(d)(1). Under § 2254(d)(1), the writ may issue if the state court’s decision “was contrary to, or involved an unreasonable application of, clearly established Federal law, as determined by the Supreme Court of the United States.” The “contrary to” provision allows a federal habeas court to [477]*477grant the writ if the state court arrived at a conclusion “opposite to that reached by [the Supreme] Court on a question of law or if the state court decides a case differently than [the Supreme] Court has on a set of materially indistinguishable facts.” Williams, 529 U.S. at 411, 120 S.Ct. at 1523. Under the “unreasonable applications” clause, a federal habeas court may issue the -writ “if the state court identifies the correct governing legal principal from [the Supreme] Court’s decisions but unreasonably applies that principle to the facts of the prisoner’s case.” Id. Under § 2254(e)(1), the state court’s factual determinations are entitled to a presumption of correctness, rebuttable by clear and convincing evidence.
Id. at 501. Accordingly, the applicable law requires this Court to use a deferential standard of review when analyzing a habeas petition that arises under the AEDPA. See id.
In this case, Appellant does not direct this Court’s attention to a single instance in which the district court incorrectly applied the standard of review as set forth by the Supreme Court in Williams. Appellant merely makes a general assertion that, in essence, requests this Court to ignore or attempt to overrule valid precedent established in the Supreme Court of the United States. For these reasons, we find Appellant’s argument concerning the proper standard of review to be entirely lacking in merit. We shall not reverse the decision of the district court on this basis.
C. Jury Instructions Relating to Malice
Appellant further argues that “the jury instructions unconstitutionally relieved the prosecution of proving the essential element of malice.” Appellant’s Brief at 23. This claim is based upon the following jury instructions, which permitted the jury to presume the element of malice under certain instances:
If it is shown beyond a reasonable doubt that the alleged victim was killed, the killing is presumed to be malicious in the absence of evidence which would rebut the implied presumption.
Implied malice may be found to exist where the wrongdoer did not intend to slay the person killed but the death resulted from a consciously unlawful act intentionally and with knowledge on the wrongdoer’s part that the act was directly perilous to human life. In this event there is implied such a high degree of conscious and willful recklessness as to amount to that malignity of heart constituting malice.
All homicides are presumed to be malicious in the absence of evidence which would rebut the implied presumption. Thus, if the state has proven beyond a reasonable doubt that a killing has occurred, then it is presumed that the killing was done maliciously, but this presumption maybe [sic] rebutted by either direct or circumstantial evidence, or by both, regardless of whether the same be offered by the defendant, or exists in the evidence of the state.
Likewise, if a deadly weapon is handled in a manner so as to make the killing a natural or probable result of such conduct, then there is raised a presumption of malice sufficient to support a conviction of murder in the second degree unless it is rebutted by other facts and circumstances.
J.A. at 101. While the first of these jury instructions related to the first-degree murder charge, the remaining related to the second-degree murder charge. J.A. at 101.
[478]*478In reviewing Appellant’s challenge to these jury instructions, the Court of Criminal Appeals of Tennessee found the following:
The jury instruction regarding malice given by the trial judge in this case, which was tried in 1981, was held to be unconstitutional in Clark v. Rose, 762 F.2d 1006 (6th Cir.1985), in accordance with Sandstrom v. Montana 442 U.S. 510, 99 S.Ct. 2450, 61 L.Ed.2d 39 (1979). When such an instruction is given, a conviction cannot stand unless the court can find the evidence in the case is sufficiently strong to show all the elements of the offense without the necessity of the trier of fact having to apply the presumption to find guilt. In such cases, the court may apply the doctrine of harmless error beyond a reasonable doubt. Rose v. Clark, 478 U.S. 570, 106 S.Ct. 3101, 92 L.Ed.2d 460 (1986). State v. Martin, 702 S.W.2d 560 (Tenn.1985). The Court reviewed this case on direct appeal, State v. Caldwell, 656 S.W.2d 894 (Tenn.Crim.App.1983), at which time the sufficiency of the evidence was an issue. The record showed the appellant’s guilt beyond a reasonable doubt and all the essential elements of murder in the first-degree were made out by the evidence.
State v. Caldwell, C.C.A. No. 3, 1990 WL 33456, at *1 (Tenn.Crim.App. Mar. 28, 1990). Based upon these findings, the court held that this instruction, though erroneous, was harmless beyond a reasonable doubt. Id. On appeal, the district court reviewed the decision of the state court. In doing so, the district court affirmed the state court’s finding that the error in question was harmless. J.A. at 111-12. Appellant now appeals that finding to this Court.
In conducting federal habeas review of a constitutional trial error, we will consider an error to be harmless unless it had a “substantial and injurious effect or influence in determining the jury’s verdict.” Brecht v. Abrahamson, 507 U.S. 619, 637, 113 S.Ct. 1710, 123 L.Ed.2d 353 (1993). That is, if it is clear that the error had no effect or very slight effect or influence on the jury, the verdict must stand. See Kotteakos v. United States, 328 U.S. 750, 764-65, 66 S.Ct. 1239, 90 L.Ed. 1557 (1946). Conversely, if there exists grave doubt as to whether the error had a substantial and injurious effect or influence on the jury, the court shall issue the habeas writ. See id. In an instance of allegedly incorrect jury instructions, the petitioner must demonstrate that the instructions were so infirm as to render the entire trial fundamentally unfair. See Estelle v. McGuire, 502 U.S. 62, 72, 112 S.Ct. 475, 116 L.Ed.2d 385 (1991). Accordingly, this deferential standard of review requires the reviewing court to examine the effect of the error on the jury, rather than the sufficiency of the evidence at trial. See Kotteakos, 328 U.S. at 775-76, 66 S.Ct. 1239.
Here, we agree with the district court’s observation that this is not a case where the record is evenly balanced, creating grave doubt as the harmlessness of the error. J.A. at 58. In considering the effect of the error on the jury, we conclude that the jury instructions relating to malice did not have a substantial and injurious effect or influence in determining the verdict. The jury in this case is presumed to have considered the overwhelming evidence of Appellant’s intent to kill the victim. Furthermore, the evidence weighed so heavily in favor of Appellant’s culpability that any presumptions made by the jury as to mahce resulted in harmless error. Accordingly, we affirm the decision of the district court on this basis.
D. Appellant’s Statement to Police
Appellant also argues that his statement to police was obtained in viola[479]*479tion of the Fifth Amendment to the Constitution and, therefore, should not have been admitted at trial.2 More specifically, Appellant claims that the investigating officers violated his Fifth Amendment right to remain silent as explained in Miranda v. Arizona, 384 U.S. 436, 86 S.Ct. 1602, 16 L.Ed.2d 694 (1966). The statement at issue is as follows:
Bell: Before we talk to you ask any questions, it is my duty to advise you that you have the right to remain silent; anything you say can be used against you in Court. You have the right to talk to a lawyer for advice before we ask you any questions and to have him with you during any questioning. If you can’t afford to hire a lawyer, one will be appointed to represent you before any questioning, if you wish one. If you decide to answer any questions now without a lawyer present, you will still have the right to stop answering at any time. You also have the right to stop answering at any time until you talk to a lawyer. Do you understand your rights?
Caldwell: Yeah, I understand my rights.
Bell: Alright sir. Do you want to talk to us about what’s happened?
Caldwell: I’d rather not.
Bell: You’d rather not talk to us?
Cáldwell: I didn’t realize what I was doing. Pulled up and a man was stripping my dozer down. I just went crazy. That’s all I got to say about that.
Bell: Well, when you came up there, he was taking parts off of it? Caldwell: Yeah, taking parts off of it and done already had the track and sprocket wheel.
J.A. at 1015. Appellant claims that this passage demonstrates that he expressed a clear intent not to speak with the authorities. Because the investigating officers continued with the questioning after this purported expression of intent, Appellant contends that they failed to scrupulously honor his right to remain silent. For this reason, Appellant argues that his statement should not have been admitted at trial.
In examining this issue, the Court of Criminal Appeals of Tennessee found that Appellant’s statement was voluntarily given. More specifically, the court held:
Appellant argues that a statement he gave to police was obtained in violation of his Fifth Amendment rights and should not have been admitted at trial. Before being questioned, appellant was fully advised of his Miranda rights. When asked if he wanted to talk, he replied, “I’d rather not.” The sheriff repeated this statement, saying, “You’d rather not talk to us?” Without any further prompting, appellant then began giving his reasons for shooting Lipford. The evidence supports the trial court’s ruling that the statement was freely and voluntarily given.
Thus, the court affirmed the lower court’s decision to admit the statement at trial on this basis. State v. Caldwell, 656 S.W.2d 894, 897 (Tenn.Crim.App. May 26, 1983). The district court affirmed the state court’s finding that the statement was admissible at trial.
[480]*480As set forth in Miranda, a suspect in a criminal case has the right not to have a coerced self-incriminating statement used against him in a criminal proceeding. See Machacek v. Hofbauer, 213 F.3d 947, 953-54 (6th Cir.2000). The remedy for a violation of this right is the exclusion from evidence of any self-incriminating statements made in an improper custodial interrogation. See id. A suspect may, however, waive his rights under the Fifth Amendment, so long as the waiver is knowingly, voluntarily, and intelligently given. See id. at 954. In determining whether a suspect has executed a valid waiver of Miranda rights, the following factors shall be considered:
First, the relinquishment of the right must have been voluntary in the sense that it was the product of a free and deliberate choice rather than intimidation, coercion or deception. Second, the waiver must have been made with full awareness both of the nature of the right being abandoned and the consequences of the decision to abandon it. Only if “the totality of the circumstances surrounding the investigation” reveal both an uncoerced choice and the requisite level of comprehension may a court properly conclude that the Miranda rights have been waived.
Machacek, 213 F.3d at 954 (quoting Moran v. Burbine, 475 U.S. 412, 421, 106 S.Ct. 1135, 89 L.Ed.2d 410 (1986) (citation omitted)). Thus, the reviewing court must examine the “totality of the circumstances” surrounding the alleged waiver in order to determine whether it constitutes a knowing, voluntary, and intelligent waiver of the suspect’s Fifth Amendment rights. Id.
In this case, the issue is whether the questioning officer violated Appellant’s Fifth Amendment right to remain silent when he continued to question Appellant after he made the statement that he would “rather not” talk to the authorities. The questioning officer then asked the clarifying question, “You’d rather not talk to us?,” in response to which Appellant voluntarily made a statement concerning the events in question. In circumstances in which the invocation of the right to remain silent is ambiguous, questioning of the suspect need not cease entirely. See Davis v. United States, 512 U.S. 452, 459-62, 114 S.Ct. 2350, 129 L.Ed.2d 362 (1994). In the instant case, Appellant’s invocation was ambiguous and the officer’s subsequent questioning was properly limited to clarifying Appellant’s intent. Accordingly, we find that the questioning officer did not overstep Miranda and that Appellant’s statements were voluntary. Therefore, we affirm the district court’s ruling that the state trial court’s decision to admit the statement constituted a reasonable application of controlling Supreme Court precedent.
E. Alleged Withholding of Exculpatory Evidence
Appellant further contends that the district court erred in granting summary judgment to Appellee on his claim that the prosecution withheld exculpatory evidence relating to the name, whereabouts, and identity of Edward Yarborough, an alleged witness to the theft of the bulldozer track by the victim.3 The Court of Criminal Appeals of Tennessee ruled [481]*481that Appellant was not entitled to relief on this basis because “there is no evidence that the name of a witness to the theft of the bulldozer track, Edward Yarbro,4 was intentionally withheld or that his testimony would have been exculpatory.” Caldwell, 656 S.W.2d at 897. Similarly, the district court ruled that it was uncertain whether Yarborough’s testimony would have been exculpatory and, even if it was, the evidence was not material under the facts and circumstances of the instant case. J.A. at 42.
Appellant’s argument concerning the information about Yarborough falls within the scope of the well-known discovery doctrine often referred to as the “Brady ” rule. More specifically, Appellant invokes the government’s duty under Brady v. Maryland, 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963), which permits a criminal defendant to inspect any material evidence which may be considered to be exculpatory (“Brady material”) in time for its effective use at trial. The evidence is considered to be material “only if there is a reasonable probability that, had the evidence been disclosed to the defense, the result of the proceeding would have been different.” United States v. Bagley, 473 U.S. 667, 682, 105 S.Ct. 3375, 87 L.Ed.2d 481 (1985). A “reasonable probability” is defined as “a probability sufficient to undermine confidence in the outcome.” Id. Accordingly, in order to fall within the scope of the Brady rule, the evidence must be both exculpatory and material. See id.
Even assuming that the evidence in question was exculpatory, we agree with the district court’s finding that such evidence was not material. Viewing the record as whole, the defense was able to establish the victim’s alleged theft by presenting testimony from other witnesses. As observed by the district court, “[a]ny evidence Yarborough could have given about the theft would have added little to the proof already in the record, except perhaps to provide further details about the manner of the theft.” J.A. at 42. Accordingly, there is no reasonable probability that, had the evidence been disclosed to Appellant in time for its effective use at trial, the result of the proceeding would have been different. Stated another way, this evidence does not present a reasonable probability sufficient to undermine confidence in the jury’s verdict. For this reason, we find that Petitioner is not entitled to relief on this basis.
F. Definition of “Beyond a Reasonable Doubt”
Next, Appellant claims that he is entitled to relief on the ground that the state trial court gave an unconstitutional definition of the phrase “beyond a reasonable doubt” in the jury instructions. The record reflects that although Appellant initially raised this claim in his first post-conviction petition, he did not raise this issue in his subsequent appeals to the Court of Criminal Appeals of Tennessee or the Tennessee Supreme Court. J.A. at 15. Appellant did, once again, raise this issue in his second post-conviction petition; however, the Court of Criminal Appeals of Tennessee dismissed the claim as barred by the statute of limitations. J.A. at 15. Because neither the state trial court nor the Court of Criminal Appeals considered the merits of this claim under federal law prior to determining that the state statute of limitations barred the claim, Appellant proeedurally defaulted on this claim. Furthermore, because Appellant fails to dem[482]*482onstrate cause for that default, he is procedurally barred from bringing the instant claim in this Court.
G. Effective Assistance of Counsel
Finally, Appellant argues that he is entitled to relief for ineffective assistance of counsel in violation of his Fifth, Sixth, and Fourteenth Amendment rights. In his first post-conviction petition, Appellant claimed ineffective assistance of counsel because of an alleged failure to: (1) meaningfully investigate the facts of the offense; (2) meaningfully voir dire jurors; and (3) seek expert assistance in evaluating, preparing, and presenting certain defenses. Appellant, however, failed to pursue these issues in the Court of Criminal Appeals or the Tennessee Supreme Court. Because Appellant fails to demonstrate cause for not pursuing these issues, the district court correctly found that he has procedurally defaulted on them.
In his second post-conviction petition, Appellant claimed ineffective assistance of counsel because of an alleged failure to develop and present certain defenses. Appellant acknowledges procedural default with respect to this claim, but argues that there is cause for the default because, as an indigent defendant, he did not have funds for expert and investigative services. Such a reason does not constitute cause for procedural default. See Coleman v. Thompson, 501 U.S. 722, 752-55, 111 S.Ct. 2546, 115 L.Ed.2d 640 (1991) (stating that because there is no constitutional right to an attorney in state post-conviction proceedings, a petitioner cannot claim constitutionally ineffective assistance of counsel in such proceedings).
Appellant also argued ineffective assistance of counsel in his second post-conviction petition based upon an alleged failure to make a meaningful, reasonable argument in support of him at the conclusion of the trial and to object to a jury instruction concerning reasonable doubt. These claims were dismissed by the state court as barred by the relevant statute of limitations. Because Appellant fails to show cause for the default of these claims, the district court properly ruled that he is not entitled to relief on his ineffective assistance of counsel claim.
III. CONCLUSION
For the reasons stated herein, we AFFIRM the district court’s grant of summary judgment against Appellant and in favor of Appellee. Accordingly, we hereby AFFIRM the district court’s denial of Appellant’s petition for writ of habeas corpus in all respects.