A court of appeal on Thursday overturned the conviction of a woman once labeled Australia’s worst female serial killer by the tabloids for the deaths of her four young children.

The woman, Kathleen Folbigg, 56, was found guilty in 2003 of killing the children and sentenced to 30 years in prison. But Australia’s scientific community rallied around her, citing genetic evidence that indicated the children had most likely died of natural causes.

All four of Ms. Folbigg’s children died before the age of 2: Caleb, at 19 days, in 1989; Patrick, at 8 months, nearly two years later; Sarah, at 10 months, in 1993; and Laura, at 18 months, in 1999.

Andrew Bell, the chief justice for the state of New South Wales, told a court that there was “reasonable doubt” of Ms. Folbigg’s guilt, based in part on “an extensive body of new scientific evidence” that had not been available at the time of her sentencing.

“It is appropriate that her convictions be quashed,” he added.

Ms. Folbigg received a pardon in June and was freed after an official inquiry found there was a reasonable probability that three of the four children had died of natural causes, and that prosecutors had relied on “coincidence and tendency evidence” that no longer held up.

The Court of Criminal Appeal in Sydney on Thursday threw out her conviction, potentially opening the door to compensation from the state. Speaking to reporters outside the court, Rhanee Rego, Ms. Folbigg’s lawyer, suggested that compensation could be “bigger than any substantial payment that has been made before.”

Ms. Folbigg, who has long maintained her innocence, thanked supporters and criticized the “disbelief and hostility” she said she had suffered for almost a quarter century. “The system preferred to blame me rather than accept that sometimes children can and do die suddenly, unexpectedly and heartbreakingly,” she said.

At the time of her conviction, prosecutors argued that she had smothered her children, though there was no medical evidence of it, and all four had been in poor health before they died.

A doctor who served as an expert witness testified that he had never seen a case of four children dying in the same family, and prosecutors argued that four siblings’ dying so young within a decade would be so spectacularly unlikely as to be impossible.

“There has never, ever been in the history of medicine any case like this,” one prosecutor said in closing arguments. “It is not a reasonable doubt; it is preposterous.”

But the Australian Academy of Science, which acted as an independent adviser to the investigation, described the case as “Australia’s greatest miscarriage of justice” and said the outcome showed that the inquiry had “comprehensively listened to the science.”

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