EVANS, Circuit Judge.

Today, we resolve Chas Simonson's appeal from a district court judgment denying his petition for a writ of habeas corpus. As per usual, we start with the facts, which, despite a few editorial comments along the way, we set out in the light most favorable to the State of Wisconsin.

Simonson went to trial in Wisconsin state court in 2002 on charges that he sexually assaulted his seven-year-old daughter. The primary evidence against him came from the alleged victim, who we will call Donna. Donna, who was nine years old when the trial rolled around, testified that Simonson placed his penis in her vagina on two separate occasions, first in the spring of 1999 and again in the spring of 2000. Simonson's counsel tried to impeach Donna's testimony by pointing out that she recanted (twice) and had given inconsistent statements regarding the timing and location of the assaults. Simonson also presented proof of a motive to lie. He was living on and off with his wife — Donna's mother, Kristina Simonson — at the time of the incidents, and the couple ultimately divorced in July 2000. In the fall of that year, Simonson decided to seek full custody of Donna and her younger sister. Simonson testified that he informed Kristina of his intentions on December 1, 2000. Although Kristina could not recall that conversation, one of her friends testified that Kristina had told her Simonson was threatening to take the kids away. The timing is key. It was on December 3, 2000, just two days after Simonson disclosed his plan, that Donna first supposedly told Kristina about the assaults. And three days later Kristina took Donna to the police station, where Donna shared her story with the authorities. Simonson's take on all this: Kristina coaxed her daughter into making false statements to block Simonson from gaining custody.

The State offered corroborating evidence from Julie Kennedy-Oehlert, a nurse specializing in sexual assault who had examined Donna in January 2001. Kennedy-Oehlert testified that Donna's hymenal tissue along the lower portion of her vagina was "virtually missing." In her opinion, the only explanation was insertion of an object, such as a man's penis. Although a girl's hymen is extremely sensitive prior to puberty, Kennedy-Oehlert testified that it generally stays intact "unless there is some pressure put directly on that tissue or near that tissue. . . ." When Kennedy-Oehlert asked Donna "if someone had put anything in her vagina," Donna said her dad had put "his wiener in."

To counter this testimony, Simonson sought to develop an alternative explanation for the hymenal damage. He made an offer of proof that Donna was severely constipated when she was one year old, and that Kristina and Donna's grandmother attempted to extract the stool by pressing their thumbs against Donna's rectal and vaginal areas as if they were trying to "pop a pimple." The state trial judge was not impressed. Without expert testimony to buttress Simonson's theory — to prove that these actions could in fact cause a tear in Donna's hymen — the judge believed the jury would be left to speculation. In the judge's opinion, "[o]rdinary experience and common sense" did not reveal the link between the alleged cause and effect. He therefore prohibited Simonson from presenting this theory.

The jury convicted Simonson as charged and the judge sentenced him to ten years' imprisonment followed by an equal period of extended supervision. At the sentencing hearing, the State asked the judge to consider the fact that the presentence report showed Simonson's involvement in the sexual assault of a 13-year-old girl. Because Simonson was never charged, however, the court "place[d] little significance" on that conduct, focusing instead on the gravity of the crime, the damage to the victim, and the need to protect both the victim and the public from future assaults. With respect to the last consideration, the judge pointed to, among other things, the high recidivism rates for offenders like Simonson:

[B]ased on my experience, individuals who undertake this type of behavior typically do it more than once with more than one victim, unlike charges like homicide where statistically the likelihood is they're never going to do it again. But in these kinds of cases, if it happened once, it's very likely going to happen again. Or at least the temptation to do it again is going to be there. So I see a very, very high need to protect the public.

Simonson wanted to appeal both his conviction and sentence, but his attorney dropped the ball, failing to file either a timely post-conviction motion or a notice of appeal. Fortunately for Simonson, the Wisconsin Court of Appeals reinstated his appellate rights in 2005, State ex rel. Chas Simonson v. Randall Hepp, Case No. 2005AP1354-W (Wis.Ct.App. Sept. 29, 2005), and Simonson filed a motion for post-conviction relief with the trial court raising two claims: (1) that the court infringed upon his right to present a defense when it barred him from offering an alternative explanation for Donna's hymen injury; and (2) that the court relied upon inaccurate information in sentencing. The trial court rejected both claims. With respect to the first claim, the judge reiterated his opinion that "expert testimony would be necessary . . . to explain how `rectal' or other stimulation applied to dislodge fecal matter . . . would, or even could, be the cause of tearing and disruption of the hymen, without causing the jury to improperly speculate." The gist of Simonson's second claim — then and now — is that the judge relied on recidivism rates for child molestation, as opposed to incest. Recidivism by incest offenders is lower, he says, and the judge should have figured that into his calculus. The trial judge wasn't entirely dismissive of this argument, but he denied relief because the recidivism information (pertinent or otherwise) occupied only a peripheral role in his analysis.

Things went similarly in the state appellate court. In affirming the trial judge's decision requiring expert testimony, the appellate court echoed his sentiments: "[E]xpert testimony was required because making a causal link between the alleged treatment and the torn hymen is not within the realm of ordinary experience and common sense." State v. Chas S., 2006 WI App 244, 297 Wis.2d 585, 724 N.W.2d 704 (2006). And Simonson couldn't just use Kennedy-Oehlert's testimony — "unless there is some pressure put directly on [the hymen] or near that tissue it generally stays intact" — because it was at once too general and unique to its context. As the Wisconsin Court of Appeals put it:

That single sentence does not provide an adequate foundation for Chas's alternate theory. The nurse was not asked whether placing thumbs on the exterior of the vagina could result in the damage she found in her examination. The nurse's single reference to damage "near that tissue" would not sufficiently enlighten the jury to allow it to accept Chas's alternate theory.

Absent expert testimony, in other words, the appellate court determined that the proffered evidence was irrelevant. And because a defendant has no right to use that sort of evidence, its exclusion did not abridge Simonson's right to present a defense.

Moving on to sentencing, the appellate court found no error in the trial judge's post-conviction analysis. The appellate court assumed for the sake of argument that the trial judge considered the wrong recidivism data. However, it determined that the information played no role in the judge's analysis, which focused on the particular circumstances of Simonson's history and behavior. Simonson's contention that the lower rates for incest should control did not sway the appellate court: "The fact that perpetrators of incest may have a lower rate of recidivism than other sexual abusers does not establish that he presents a low risk to his children or others." Id. at *3, 724 N.W.2d 704.

Simonson's petition for review in the Supreme Court of Wisconsin was denied. State v. Chas S., 299 Wis.2d 328, 731 N.W.2d 638 (Jan. 9, 2007).

With his state remedies exhausted, Simonson filed a petition for a writ of habeas corpus in federal district court. Chief Judge Barbara Crabb referred the petition to Magistrate Judge Stephen Crocker for preparation of a report and recommendation and then adopted the latter's suggestion to dismiss. The judge approved the state courts' rationale on the evidentiary issue — without expert testimony to bridge the gap between cause (attempted removal of a stool) and effect (torn hymen), Simonson's theory "would have been highly speculative." Simonsm v. Hepp, 07-00397, 2007 WL 5490149, *2 (W.D.Wis. Nov. 21, 2007). With respect to the sentencing issue, on the other hand, the district court's review contained a healthy dose of criticism. Considering the record, the district court could not accept the view that the trial judge had not factored in recidivism rates at all. However, the court found the error harmless (the sentence would have been the same without that information) and the ultimate conclusion supported by the facts (Simonson was likely to re-offend), so the petition for relief was denied. Now on to this appeal.

We review a federal habeas court's factual findings for clear error and its legal conclusions de novo. Rizzo v. Smith, 528 F.3d 501, 505 (7th Cir. 2008). Under the Antiterrorism and Effective Death Penalty Act of 1996 (AEDPA), a petitioner is only entitled to habeas relief when the decision of the last state court to consider the case is either "contrary to" or "an unreasonable application of clearly established federal law as determined by the United States Supreme Court. 28 U.S.C. § 2254(d)(1). A decision is contrary to clearly established federal law if the state court applies a rule that conflicts with a rule identified by the Supreme Court, or if the state court reaches a different conclusion than the Supreme Court in a case with materially indistinguishable facts. Williams v. Taylor, 529 U.S. 362, 405-06, 120 S.Ct. 1495, 146 L.Ed.2d 389 (2000). A decision involves an unreasonable application of clearly established law if the state court "identifies the correct governing legal principle . . . but unreasonably applies that principle to the facts of the prisoner's case." Id. at 413, 120 S.Ct. 1495. Under both tests, mere error is not sufficient; a state court's decision must be "objectively unreasonable." Lockyer v. Andrade, 538 U.S. 63, 76, 123 S.Ct. 1166, 155 L.Ed.2d 144 (2003).

Measured against the rubric of AEDPA, Simonson's claims have little chance of success. That's not to say the case against him was airtight. It's simply to say that the decision of the Wisconsin Court of Appeals was not objectively unreasonable.

Simonson first argues that the exclusion of his alternative theory deprived him of the ability to contest the charge against him. The Sixth Amendment, through its spirit if not its words, guarantees a criminal defendant the right to present a defense. Chambers v. Mississippi 410 U.S. 284, 302, 93 S.Ct. 1038, 35 L.Ed.2d 297 (1973). At a minimum, this means a defendant may "put before a jury evidence that might influence the determination of guilt." Taylor v. Illinois, 484 U.S. 400, 408, 108 S.Ct. 646, 98 L.Ed.2d 798 (1988). Like most rights, however, the right to present a defense is not unlimited and may "bow to accommodate other legitimate interests in the criminal trial process." Chambers, 410 U.S. at 295, 93 S.Ct. 1038; United States v. Knox, 540 F.3d 708, 719 (7th Cir. 2008). Among these interests are "fairness and reliability in the ascertainment of guilt and innocence." Chambers, 410 U.S. at 302, 93 S.Ct. 1038; Horton v. Litscher, 427 F.3d 498, 504 (7th Cir. 2005). To further these interests, states have broad latitude to adopt rules excluding evidence so long as they are not "arbitrary or disproportionate to the purpose they are designed to serve." Johnson v. Bett, 349 F.3d 1030, 1035 (7th Cir. 2003). Rules that prohibit irrelevant or speculative evidence are kosher. Hood v. Uchtman, 414 F.3d 736, 738-39 (7th Cir. 2005); Morgan v. Krenke, 232 F.3d 562, 566 (7th Cir. 2000).

And that's where Simonson runs into trouble. To repeat, the state trial court prohibited him from telling the jury that the injury to Donna could have been caused by her mother and grandmother's efforts to relieve constipation because it would have required speculation. We tend to agree. While there is some intuitive merit to the idea that pressure near the vaginal and rectal areas could result in tearing of the hymen, it is far from obvious. It is not like asking a jury to consider, say, the fact that a blow from a baseball bat can lead to a broken limb. Nevertheless, it is tempting to buy Simonson's argument that there was relevant expert testimony available — Kennedy-Oehlert's statement that the hymen generally stays intact "unless there is some pressure put directly on that tissue or near that tissue." It is tempting, we say, but not wholly convincing. It was reasonable to hold that this testimony did not suit the purpose because Kennedy-Oehlert announced this general proposition only as background to her specific conclusion (that the injury was caused by insertion of an object). Kennedy-Oehlert probably would have been surprised to learn Simonson's application of her testimony. That's how the state courts saw it, and we are not prepared to label that view "objectively unreasonable."

Under the federal and state rules of evidence alike, expert testimony is appropriate if "specialized knowledge will assist the trier of fact to understand the evidence or to determine a fact in issue. . . ." Fed.R.Evid. 702; Wis. Stat. § 907.02. Although these rules do not require expert testimony — they only say when it is permissible — they point to a basic truth of trial practice: expert testimony is often needed to eliminate speculation. See, e.g., Owen v. General Motors Corp., 533 F.3d 913, 924 (8th Cir. 2008); United States v. Han, 230 F.3d 560, 564 (2d Cir. 2000). Preventing speculation is undoubtedly a legitimate state interest, and excluding evidence in the name of that interest did not abridge Simonson's right to present a defense in this case. The state appellate court's decision to this effect was neither contrary to nor an unreasonable application of clearly established federal law.

On to the next claim, then, where Simonson argues that his sentence was infected by false information. Due process demands that a court sentence a defendant upon accurate information. United States v. Artley, 489 F.3d 813, 821 (7th Cir. 2007). To obtain the remedy of resentencing, a defendant must establish that the sentencing court relied on critical inaccurate information when announcing the sentence. See Lechner v. Frank, 341 F.3d 635, 639 (7th Cir. 2003).

Did the state trial judge rely on inaccurate information about recidivist rates of run-of-the-mill child molesters vis-à-vis incestuous child molesters when he imposed the 10-year sentence in this case? Simonson says yes — and, he argues, that made a difference here because recidivist rates are lower for those who assault their own children as opposed to those who assault other children. The Wisconsin Court of Appeals said no.

The first problem with Simonson's argument is that the sentencing judge here did not rely on any hard statistical data; he did not consult recidivism studies or charts but rather based his view on his own "experience" in these sorts of cases. The Supreme Court has rejected the idea that this is somehow improper. In Barclay v. Florida, 463 U.S. 939, 103 S.Ct. 3418, 77 L.Ed.2d 1134 (1983), the Court upheld a judge's decision imposing the death penalty where the judge explained his decision by comparing the defendant's crimes to what he had witnessed in Nazi camps. The Court observed that "[i]t is neither possible nor desirable for a person to whom the State entrusts an important judgment to decide in a vacuum, as if he had no experiences." Id. at 950, 103 S.Ct. 3418.

But, even assuming the sentencing judge did rely on undisclosed "statistical" data — and that is a wild assumption — the nature of that data is unclear. Simonson contends that the sentencing court "confused recidivism rates of child molesters in general, for which there is a relatively high rate of re-offense, with the low recidivism rate for incest offenders. . . ." The sentencing transcript very much implies that the sentencing judge viewed Simonson not just as any child molester, but as an incestuous child molester. Before reaching the recidivism factor, the judge had this to say about the gravity of the offense: "Frankly, I can't think of many more worse offenses than sexually assaulting a seven-year-old child that is the product of you and your wife." That remark was made only a moment before the judge concluded that "individuals who undertake this type of behavior typically do it more than once." So the notion that the judge was talking about child molesters in general seems questionable at best.

But, for the sake of argument, let's assume the sentencing judge actually considered hard statistics regarding recidivism by molesters of nonfamilial victims. The studies Simonson presented to the trial court when seeking post-conviction relief, the same studies he cites to us, do tend to establish that child molesters in general are more likely to re-offend (or at least be convicted again) than incest offenders. However, they do not establish that conclusively, and, in any event, they also suggest that perpetrators like Simonson are likely to strike again. According to a Department of Justice report offered by Simonson, incest offenders have a reconviction rate of 6 percent, while the rate for child molesters is between 25 and 30 percent depending on the victim's gender. Recidivism of Sex Offenders (May 2001) at http://www.csom.org/pubs/recidsexof.html (last visited October 9, 2008). However, because it uses the term "incest" — as opposed to "incestuous child molestation" or the like — the incest data could be read not as a subset of the child molestation data, but as an entirely separate category (including incidents with minors and adults), in which case it might be just as appropriate to apply the higher child molestation figures to Simonson. Nevertheless, the other study Simonson cites clears the air a bit, reporting that "[t]he risk for sexual offense recidivism . . . increase[s] for those who ha[ve] . . . an extrafamilial victim." R. Karl Hanson Monique T. Bussiere, Predicting Relapse: A Meta-Analysis of Sexual Offender Recidivism Studies, 66 Journal of Consulting and Clinical Psychology 348, 351 (1998). But that report also identifies "sexual interest in children" as the "single strongest predictor" of sexual-offense relapse, id., and the DOJ study warns that recidivism in the case of incest is severely under reported because victims fear the disruption it may cause to their families. Considered in the aggregate, these studies do little to undermine the trial court's conclusion that Simonson was likely to re-offend. Perhaps the man who has sex with his adult sister is unlikely to do it again, but that, of course, is not at all comparable to the assault here, where Donna testified that her dad carried her into his bedroom, removed her pajamas, put some kind of clear liquid from a bottle on her crotch area and on his penis, put her on top of him, and put his penis "inside her crotch."

In sum, we believe the sentencing judge did rely on something — his experience revealing that offenders like Simonson tend to have a high rate of recidivism — but Simonson has failed to prove that "something" was inaccurate. The state appellate court's decision upholding the sentence, regardless of the rationale, was neither contrary to nor an unreasonable application of clearly established federal law.

The district court's judgment denying Simonson's petition for habeas corpus is AFFIRMED.