Aviv’s article had nothing to do with the appeal case. It was written in response to the original trial.
Looking further at the appeal judgement, I see it doesn't deal with all the questions in Aviv’s article. It doesn’t mention the possibility of errors in statistical reasoning, or why a particular defence witness was not called to testify at the first trial, or the state of the neonatal unit where the deaths took place. But it does go into great detail on two issues that were used as grounds for appeal.
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Whether evidence given by one expert witness, Dr Dewi Evans, should have been disregarded, and further evidence from him not admitted.
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Questions about how good the evidence on air embolism was. E g, was air embolism diagnosed just because other causes of sudden collapse had been ruled out?
The appeal judges say that they found it necessary ‘to read a vast volume of material (including from the transcripts of evidence) well beyond the material specifically relied on by the defence, in order to examine the matters complained of in their full context.’
An appeal is not an evaluation of the science.
The judges do explain why they agree with the prosecution that the evidence about embolism was not too vague or inherently weak to be admissible. (Points 140-150.)
For instance, the judges say it is not true that the expert witnesses wrongly based a diagnosis of air embolus ‘solely on an exclusion of other possible causes’. They give grounds for this.
Another example: the defence had argued that a reliable diagnosis of air embolus could not be made solely on the basis of a particular type of skin discolouration, other than one specific type. But the appeal judges say that this is not what the prosecution expert witnesses did - again, with grounds.