Lucy Letby: Guilty or Innocent - a Bayesian analysis
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- Опубліковано 11 вер 2024
- Mathematician Richard Gill (a colleague and friend) put out a tweet with a number of assumptions abou the case of Lucy Letby (the UK nurse convicted in 2023 of multiple baby murders), using a Bayesian analysis to conclude that a sepsis outbreak was much more likely to have been the cause of the baby deaths than Lucy. He claimed that, with his assumptions the posterior odds of sepsis outbreak rather than Lucy being the killer was about 4000:1. Using a simply Bayesian network I show that the posterior odds are more like 166:1 (if I have understood Richard's assumptions). Of course the critical assumptions Richard makes (which were not accepted during the trial) are that a) there was little evidence of malicious harm to the babies; and b) there was much evidence of a sepsis outbreak. Whether or not these assumptions are reasonable this is nevertheless a nice example of a Bayesian network in action.
The Bayesian network program used is www.agena.ai
Nice. Thank you.
Not that it means anything to anyone else, and it’s a while ago now, but the details I heard surrounding the case and my gut feel led me to think that there was a very high probability that Lucy Letby was completely innocent and that a great injustice has been done to her.
I very much hope that the case will be looked at again with cold reason and any errors of judgment will be corrected.
Leaking sewage pipes
@@rocklover7437 Yes, that was a killer point, and most likely the ‘culprit’ by far!
How much would they NHS have to have paid out if they couldn’t pin her down for this?
@@joetodd4351a very pertinent question, thanks for bringing it up. I believe that Lucy is innocent.
There seems to be the customary misinformation around Lucy's case in the comments. No babies died from insulin poisoning and the so-called 'confession' note referred to contained the words "I haven't done anything wrong" which must be unique for a confession.
Whatever way you look at this they’re are more questions than answers.. How much would they have had to pay out if they couldn’t pin it on her?
It always worries me when someone is convicted without any actual evidence. Beyond reasonable doubt?
More like 'Someone's got to take the blame, we think she did it so she must be guilty'.
Two of the baby deaths were caused by insulin injection and totally unrelated to sepsis. The insulin in the babies is confirmed by blood tests and the markers for man made insulin is totally different to human insulin. Also these two deaths were 8 months apart. All the nurses that were present when these insulin deaths occurred were investigated and it was Letby that aroused suspicion. On searching her property, notes were found which stated "I did it" and other such nonsense indicating a mental disturbance and this led to her being charged and convicted by jury. Hardly beyond reasonable doubt. Sadly there is no doubt about the fact that 7 children are dead with Letby being the common denominator.
A lot doesn’t add up about the trial. None of the other nurses she worked believed she’d done any wrong but , weren’t allowed to give evidence. Why? Blaming it on Lucy apparently saved a lot of moneys money from parents being able to sue for large amounts. Leaking sewage pipes seems to be a real problem that hasn’t been seriously looked into
Thank you Norman -hope this can be sent to the relevant people in government - there mist be a retrial -🙏 so much evidence was left out previously ............
When are you going to analyse the change in reporting of excess deaths by the ONS ?
I was away when that all broke and so have linked to other good analyses of that on my twitter feed. I will try to do a summary on our substack wherearethenumbers.substack.com/ rather than youtube
It looks very arbitrary... Do You expect to analyze neighboring coefficients?
@@NormanFenton81
I too would be anxious to see your appraisal of the new method.
Thank you for your work 🙏
It’s not like the British State hasn’t got previous.
Poor Girl 🙏
So because there have been previous miscarriage's of justice then this case is one?
This reminded me of the Dutch nurse Lucia de Berk who was sentenced to life in prison. Looked it up on Wikipedia to refresh my memory and there in the section about the statistical arguments, the name Richard Gill pops up. He's doing the Lords work!
Of course it does. Maybe you need to look at the other case with a Nurse he helped. She got another Nurse to take photos of her with an older person with her mouth open and imitated her.
That poor woman. These corrupt courts make me sick.
How refresshing to see a well put together video with insightful and intelligent comments arranged in a well organised manner. Great work. Thank you both for all the effort you put into this. Its a stand alone piece of work of great merit. I thank you sincerely.
I wonder if it is justified to state the initial assumptions as they are. I can accept the statement that on average one cluster of sepsis deaths in neonatal ward occurs per year. Here, there is a repeated set of circumstances, each with their own risk, that combined lead to a comparable risk of an occurrence of a cluster of sepsis.
I have a problem with the average of one serial killer nurse in neonatal ward per 10 years. This is a sporadic event, depending on a decision by, in each case, a different person with, in each case, an unknow set of circumstances. It feels wrong to use an average for this type of event.
This is complete separate of course from the need to have clear evidence of wrongdoing in a case like this.
I make no judgment about the case. I was simply correcting the calculations made by Richard. As I said in the description, the critical assumptions Richard makes were not accepted during the trial and I make no judgement about whether or not these assumptions are reasonable
@@NormanFenton81maybe your problem is using Richard's analysis. He thinks it's ok for a person running a non-profit organisation to use for money to pay their rent and buy food. None of his calculations take into account human beings and the different methods of death in these cases. None of his information takes into account Baby O's liver damage, over-feeding, the embulisms etc. I understand Richard is respected for stats, but he doesn't even touch on Baysien analysis for circumstancial evidence. He uses statistics the same way a Government does in relation to employment stats. I'm waiting for a person who follows me around
@@lesley9989 The reason I did this was simply to point out that, even with Richards’s massively oversimplified assumptions, there was an error in his calculations
@@normanfenton oh thankyou for explaining. I apologise. It just becomes exceptionally frustrating when he keeps saying he has all this evidence and he also thinks it's ok for Adams on Science on Trial to ask for donations and says she needs to pay her rent!
So how does any of this explain the fact that the likelihood of an incident occurring was at least 600% higher when LL was present compared to when she wasn't? I can understand it being a mere coincidence if there was just a handful of cases over a 3 or 4 week maximum spell of her working there, but it was a total of 34 incidents if you include the other 9 over a period of at least a year. I just cant find any other explanation for it?
Thanks.
What about the possibility there was both? Or something other killed the babies? Or there was a killer, but not her?
Yes indeed these should be considered, and a full BN model would incorporate these additional possibilities.
Norman! 😁👍👍👍
Makes you wonder why the defense counsel didn’t use this analysis.
No one would be convicted if such analysis was used. Thankfully they instead focused on the indisputable facts in this case.
Hopefully, it wouldn’t be admissible. Sally Clark was convicted partly on the basis of statistical evidence that the expert got wrong.
I make no judgment about the case. I was simply correcting the calculations made by Richard. As I said in the description, the critical assumptions Richard makes were not accepted during the trial and I make no judgement about whether or not these assumptions are reasonable
@@NormanFenton81I'm delighted that you're analysing this case. Let's hope her appeal sets her free. Lucy will have lost years of freedom by this time....
Because, by all accounts, it was a shit show. 10 month trial and only the hospital plumber called. The jury must have thought the defence had gone on holiday.
His tweet says '1 million to 1 that she was innocent' - I don't understand this - did he mean to say she has 1 in a million chance of being guilty?
I agree . It is very badly worded. I assumed at first that Norman was about to do a critique, disagreeing with the tweet!
@@johnstewart3244 yes - so did I
@@johnstewart3244I did exactly that. Instead of odds of a million to one against guilt using his own assumptions I showed the odds were 166 to 1. I make no judgment about the case. I was simply correcting the calculations made by Richard. As I said in the description, the critical assumptions Richard makes were not accepted during the trial and I make no judgement about whether or not these assumptions are reasonable
Like all conspiracy theorists, he points to a hole in the wall of evidence and then says there's no wall. Letby was not convicted on the spreadsheet alone.
Using an average of one cluster of sepsis deaths per year doesn't mean there will be exactly one cluster per year. Some years none; some years two or three, maybe. Same with the SKs. The variance/consistency of clusters provides opportunities for SKs or for opportunists. SKs think and their thinking cannot be removed from the equation. In fact, the frequency and expectation of clusters provides a 'golden opportunity' for the SK. One would expect them to take advantage of those conditions.
That may well be true, but then why would we assume a SK nurse could spot a sepsis cluster if the Doctors couldn't?
@@joshradcliffe8563 The SK nurse is actively looking for clusters/opportunities while the doctors aren't. Experience matters.
I hope you commented this on his twitter so others can see
I did
Beautiful
I am surprised you have posted this as both the approaches covered seem to set out to simply show that Letby was extremely improbable to have committed the offences by omitting the most important facts. Two of the baby deaths were caused by insulin injection and totally unrelated to sepsis. The insulin in the babies is confirmed by blood tests and the markers for man made insulin is totally different to human insulin. Also these two deaths were 8 months apart. All the nurses that were present when these insulin deaths occurred were investigated and it was Letby that aroused suspicion. On searching her property, notes were found which stated "I did it" and other such nonsense indicating a mental disturbance and this led to her being charged. So run this Bayesian analysis again but this time add another dimension concerning the presence of insulin in the dead babies and the fact that Letby was the consistent nurse present and see how the probability comes out then. I loom forward to seeing this video!
The scribbled notes did not say “I did it” in isolation. It was part of a longer doodle which suggested nothing of the kind.
I make no judgment about the case. I was simply correcting the calculations made by Richard. As I said in the description, the critical assumptions Richard makes were not accepted during the trial and I make no judgement about whether or not these assumptions are reasonable
@@NormanFenton81 Thank you for your reply. I am a big fan of your work.
The two babies that were alleged to have been injected with insulin are still alive.
@excelnow4442 If you’re going to write a long spiel about the case at least get your facts straight. 😂
Nurses get short shrift on authoritative professional activity. unless you are a recognised physician ...back off when you have ticked your boxes and let the gods take over... .
I am not arguing that Letby was innocent or guilty. The doctors found that someone must have injected babies with insulin and that babies had been given lethal injections of air. Premature babies can die of pathogens in hospitals but in this case we know they died of insulin poisoning & air emboli, do you not agree? I don't know what Letby did when she was feeding the babies milk. After Letby's feeding, on several occasions, other nurses fed the babies and saw projectile vomiting from them; the claim being that Letby had deliberately overfed babies. The doctors' examinations show that babies had been harmed by being overfed milk.
No - there is no proof that any child died that way
All of the autopsies were completely normal
The two babies that were alleged to have been injected with insulin are still alive.
The pathology report was at pains to point out that the insulin levels did NOT indicate that the babies were injected with insulin.
No, the doctors did NOT find that someone poisoned babies with insulin. The doctors did the wrong test. And even when this was pointed out to them, they did not do the correct test. It was never done. Sorry, but we need to be factual. Both babies alive BTW.