Trolleys 853 and 854

Not too tired after my excursion to London to gather up this trolley from the M&S food hall on exit from Epsom Station.

I collect quite a lot of trolleys from outside the station and there are usually black taxis waiting there, which we use on a reasonably regular basis, but none of the drivers have thought to comment on my collecting habits, although some of them must have noticed. Perhaps they know from experience that it is better not to offer comments on this sort of thing.

And a second by the seats in front of the town-side exit from the Kokoro Passage.

Bag from Osprey, via T K Maxx, just behind the camera. It has served well now, for well over ten years, starting out during the months of bag life. Opsrey of London by Graeme Ellisoon, so almost certainly the people at reference 2 rather than those at reference 3.

Reference 2 mostly seeming to be a high-end video, from where I associated to the websites of big wine makers. Tricky to get a snap from this one, as the Snipping Tool takes a few seconds to click in and it seems to be a matter of luck what you get. Unless you take the time to go through the loop several times so that you know what is coming next. Pass.

But more seriously, we have the troubling case of Lucy Letby at reference 4. A young woman who has been thrown into jail for what may well turn out to be a very long time, but whom a distinguished panel of neonatal care specialists believe to be innocent. A perhaps awkward young woman who has been scapegoated by a system which failed - not forgetting that the neonates involved were very sick in the first place. One part of which system is the Criminal Case Review Commission (CCRC), the people who are supposed to deal with possible miscarriages of justice, but who are underfunded and who may take years to deal with this one. One does not want to make it easy to reopen closed cases, or the dam, as it were, might burst - but I am left worrying that there has been a miscarriage and that a conscientious young woman's life has been wrongly ruined. But what exactly should be done about it, I do not know.

I associate to being once told by a criminal barrister that the standard of proof was often very low in the case of very serious crimes - or possibly non-crimes - where the media were baying for convictions, possibly aided & abetted by the relevant Ministers, possibly aided & abetted by distraught families.

To be fair to the CCRC, it was easy enough to find where matters stood with them using the search button provided at reference 5, which led me to the short report at reference 6. It appears that the matter is being taken seriously and that significant resources have been assigned.

PS 1: almost seriously, I wonder if the rhyme and rhythm properties of  the young woman's name, which make it catchy, have contributed to her troubles?

PS 2: probably in connection with this case, I have also read recently of senior statisticians weighing in on the proper treatment of troubling coincidences. As I recall, there it a strong tendency to take coincidences more seriously than one should. Unusual things happen all the time, without anything sinister going on. Bing turns up the snap above fast enough - so perhaps now I will try to give it some time. To help me along, I have put a copy on my telephone. Maybe a quiet moment on a train?

PS 3: back with trivia, it seems that there is a lot of fuss about the new logo for Great British Railways, slated to be the new version of British Rail as the present operators - like Southwestern Trains - are nationalised over the next few years. Which all sounds like a Great British Mess to me. Another legacy from our long infatuation with Mrs Thatcher.

References

Reference 1: https://psmv5.blogspot.com/2025/05/trolley-852.html.

Reference 2: https://www.ospreylondon.com/en-gb/.

Reference 3: https://www.osprey.com/.

Reference 4: 'We did not find any murders': When Lucy Letby was convicted, a 1980s research paper was key to the prosecution case - but the author himself is fighting to show that there has been a miscarriage of justice - David Conn, Guardian - 2025.

Reference 5: https://ccrc.gov.uk/.

Reference 6: https://ccrc.gov.uk/news/lucy-letby-application-received-by-criminal-cases-review-commission/.

Reference 7: https://www.bmj.com/content/388/bmj.r250. An accessible introduction to the case - and the troubling role of a 'professional' expert witness. What I have not been able to find is the panel report.

Reference 8: https://thirlwall.public-inquiry.uk/. Nor have I bottomed out how the panel report fits in with the work of this (expensive) inquiry - which looks to be reporting early in 2026.

Reference 9: https://rss.org.uk/RSS/media/File-library/News/2022/Report_Healthcare_serial_killer_or_coincidence_statistical_issues_in_investigation_of_suspected_medical_misconduct_Sept_2022_FINAL.pdf.

Group search key: trolleysk, 20250523.

Media bits

[possibly a shot of part of the Zilch team at their offices in Buckingham Palace Road]

I was irritated by the headline in yesterday's Guardian - 'Witnesses to be forced to testify at Letby inquiry' - which for me set an unpleasantly and unnecessarily aggressive tone to the whole sorry business. The point of the inquiry is to try and do things better next time around and setting an accusing, punitive tone in this way is scarcely going to encourage those involved to be open, honest and helpful about what went on.

As I have observed before, we don't seem to be very good at these sorts of inquiry in this country, with the main beneficiaries being the all lawyers collecting fees, rather than the country at large. 

A rather different matter was the greening of all the advertising slots in a recent number of the Metro. I thought perhaps that something had gone wrong with their advertising feed and that they had decided to publish anyway.

Seemingly quite wrong, with yesterday's Metro including some green flavoured advertisements for a company called Zilch, to be found at reference 1. The fully green advertisements were probably a warm-up act. One wonders what they had to pay for it.

Lots of high-minded words from their leaders about how they want to offer a flexible service, without all kinds of hidden or unexpected rip-off charges. Buy now with your telephone, pay later with no interest charged. Get something for nothing. But despite scanning a substantial piece on the company offered at reference 2, I am none the wiser about how Zilch make their money. Are they taking a cut from the people selling you stuff? Are they offering users a regular credit service in the background? Payday lending even?

Different again is the row about the computer error in our air traffic control system which we were told will cost airlines £100m - with the suggestion that the responsible private-public company called NATS (of reference 5) should be made to pay up, if not this time, then next time. A potentially large chunk of its annual revenue. 

Was it all down, at root, to lack of a proper level of investment in the computers concerned, rather along the lines alleged for the water companies? Is the absence of dividends in the snap above just a fig leaf to cover fancy loan repayments? Who owns all the debt? Perhaps someone somewhere in the Persian Gulf?

Whatever the case, the costs will all end up back with travellers in the form of higher fares as NATS will just pass on any additional costs in the fees it charges airlines. I am reminded of the custom of extracting punitive compensation from some bit of the NHS which never had the proper amount of funding in the first place.

PS: continuing to poke at the Moroccan cookbook of reference 3, I turned up reference 4. This included some cookbooks from 14th century Andalusia, but nothing from 16th century Morocco across the water. Plus just two instances of the word 'tomato'.

References

Reference 1: https://www.zilch.com/uk/.

Reference 2: https://www.businesswire.com/portal/site/home/.

Reference 3: https://psmv5.blogspot.com/2023/08/egg-nog.html.

Reference 4a: https://newlinesmag.com/essays/medieval-arabic-culinary-literature-offers-lessons-for-the-present/.

Reference 4b: Medieval Arabic Culinary Literature Offers Lessons for the Present: Centuries-old cookbooks from the Abbasid era shed light on the lives of the upper strata of bygone Arab and Muslim societies, as well as the origins of dishes still popular today - Mahmoud Habboush - 2023.

Reference 5: https://www.nats.aero/. Not to be confused with Nordic American Tanker Ltd.

Police and crime commissioners to go

I read in this morning's FT, that police and crime commissioners are to go when their terms expire in 2028. We are told that it is an experiment that has failed and that £20m of the £100m saved will be spent on more policemen - or, at least, on 'policing'. All we are told about the case for change is the snip above. We are told that there is a White Paper to come, which will, no doubt, include all sorts of stuff, but the overall impression given is that a change has been floated to test the reactions of those involved. I don't suppose that the public at large will have much to say about it, although the media may get exercised on their account.

There appears to be no attempt to set out why the experiment was made in the first place or how it has worked out. We are not told what the Scots get up to - or indeed what anyone else gets up to. In the US, for example, I believe that they elect their chief constables, rather than electing a minder. One supposes that diligent civil servants inside the Home Office have written at length about these matters, but no-one seems to be sharing.

Bing turns up the statement at reference 2.

Google's AI assistant offers me a little essay about the whole business, more or less summarising the piece in the FT, together with a pointer to the year old statement at reference 3.

I then poke the government web site to get the promising looking screen snapped above.

But clicking on the first item does not deliver. A set of documents which has not been updated for a year, so unlikely to include anything bearing on the present matter.

As an exercise in democracy, not terribly impressive - not that I suppose other countries are much better - and I dare say plenty are a lot worse. Floating the change in this way is indeed a way to test opinion, but why can we not be given something more to bite on? Something which must exist somewhere in the Home Office. We are not a bunch of Trumps, making up policy on the hoof - at least one hopes not.

I dare say also that the standard of PCCs and their work varies a good deal across the country, but one does not envy them their job of keeping the show on the road until they are phased out in three years time.

Some time later

I vaguely remember thinking, back in 2012, that the invention of these commissioners seemed terribly half-baked, with duties, roles and resources all seeming terribly vague, at least from the outside. Checking, coverage at reference 4 all looks rather thin - but at least there is no confusion with the Parochial Church Councils of reference 5.

I then moved on to what was my only involvement with a PCC, the one for West Yorkshire. The rather unsatisfactory business of a fatal hard stop in or near Huddersfield back in 2016. An entirely proper matter for a PCC to take an interest in. A story which closed for me at reference 6.

And then there is the troubling case of Nurse Letby, last noticed at the end of reference 7. But while I dare say there are lessons for the police here, in which the PCC concerned might take an interest, the main issue now is the question of guilt, not of procedure. Quite different in that respect from Huddersfield.

From where I associate to the novel 'Thérèse Desqueyroux', last outed at reference 8. A novel which is turning out to be the story of a crime and its consequences from the inside, from inside the head of the criminal. I wonder now what sort of a splash in the media such a thing might make, were it to happen now? As it happens, a crime involving near fatal variation in the number of drops of medicine for a bad heart - the sort of thing which still happens here, in real life.

While the story at reference 9 is depressing in an entirely different way.

References

Reference 1: Police and crime commissioners to be abolished in England and Wales: Abolition of posts expected to save £100mn annually and allow £20mn each year to be reinvested in policing - Robert Wright, Financial Times - 2025.

Reference 2: https://www.gov.uk/government/news/police-and-crime-commissioners-to-be-scrapped.

Reference 3: https://www.gov.uk/government/news/home-secretary-to-announce-major-policing-reforms.

Reference 4: https://psmv2.blogspot.com/search?q=pcc.

Reference 5: https://en.wikipedia.org/wiki/Parochial_church_council.

Reference 6: https://psmv5.blogspot.com/2023/03/huddersfield.html.

Reference 7: https://psmv5.blogspot.com/2025/07/sweet-clover-and-orchids.html.

Reference 8: https://psmv5.blogspot.com/2025/11/survival.html.

Reference 9: India and Pakistan need mediators not arms suppliers: The countries that helped broker peace earlier this year are now selling advanced weapons to the nuclear-armed neighbours - Tariq Mir, Financial Times - 2025.

Unlikely crimes

This being notice of a report produced by the RSS into some of the statistical issues around unusual clusters of deaths, clusters which might result in criminal charges being made against those involved in care. This report does not mention the worrying Letby case to be found towards the end of reference 1, but the issues it raises are very much the issues raised there. It is to be found at reference 2 and its recommendations are included in the snap above.

I have read the report, but only glanced at the appendices which make up around half of the sixty pages.

The prosecutor’s fallacy

‘… Thus, the p-value of 1 in 1 million might inadvertently be taken as proof that there is only 1 chance in 1 million that the medical professional is innocent of misconduct….’. [page 6]

The report argues that when faced with an unlikely cluster of deaths, to which well-meaning people have assigned very small probabilities, we are all too likely to fall into what lawyers have known for a long time as the prosecutor’s fallacy, amongst other names. In the jargon of statisticians, conflating or confusing the probability that given A we get B with that of given B we get A. 

In the present case, A is the event that the cluster of deaths was down to bad luck and B is the event that the patients were not exposed to any unusual risks. Given event B, otherwise the hypothesis, we can compute the probability of event A, which is very small. But having event A does not tell us as much as we might think about the probability of B. For that we need some more information and the famous rule called Baye’s rule, which you can read about at appendix 4 of the present report – or at reference 5 if you want a longer treatment.

P-values come back again

 P-values are themselves a matter of some controversy. A taster for which is to be found at reference 6 – which also suggests that four years ago I thought I had got a reasonable grip on p-values. But I was prompted by the bit in the third paragraph in the snap above to have another go, turning up another chunk of the vast literature on the matter – and I found that I had lost my grip.

So when I did a bit of statistics, many years ago now, one of the things that I learned early on was that if two events were independent of each other, then the probability of their both happening was the product of the probabilities of their happening individually. In fact, this was the mathematical definition of independence. It now seems that sums of this sort are often done in the context of investigations of this sort, leading to infinitesimally small probabilities of something having happened by chance, translating more or less directly into a very high probability that there had been a crime.

When we say, conversationally, as it were, that two events are not connected in any way, that they are independent, we are not usually thinking about the product of probabilities – but, nevertheless, why should I not combine these independent probabilities by multiplication. Is that not the definition of independence?

I fairly quickly discovered that, starting around a hundred years ago with references 7 and 8, that there were lots of ways of combining p-values. Simple multiplication did not seem to be the way forward, although I was not very clear why not.

With one point of difficulty for me being that a p-value could itself be considered as a random variable which, under the null hypothesis (and a few other assumptions), had the uniform distribution over the range [0, 1]. I had, indeed, lost my grip.

Some other matters arising in no particular order

Unusual nature

The report makes the point that investigations of this nature are unusual in that one does not know at the outset whether or not there has been a crime. On the other hand, one probably does know who the supposed perpetrator is. Perhaps from that point of view, any crime here is more like a financial crime – some sort of obscure but illegal financial trickery – than a burglary, where, most of the time at least, there is little doubt that there has been a crime and the problem is rather to find the perpetrator in the haystack in which he is hiding.

Costs

It might be argued that the recommendations of this report would be expensive and time consuming to implement – as well they might be. On the other hand, crimes of this nature are only going to come to light over time and perpetrators are unlikely to make a run for it. Hurry is not indicated. And suspected crimes of this nature are apt to be very prejudicial to the lives and careers of those involved. And they are apt to result in long running and hugely expensive public inquiries. So much better to take time and trouble over the criminal part of the investigation than to get it wrong.

Scapegoats

It seems to be built into our makeup as humans to want to blame somebody when something goes wrong. Whatever has happened has to be someone’s fault, a someone who very possibly did it on purpose, with malice aforethought, to use a more or less obsolete legal term. 

With the result that all too often we go for a scapegoat. In which we don’t usually go as far as the ancients and load our scapegoat up with all the sins to hand, although there is, or at least was, the widespread practise of persuading someone about to be convicted on one offence to put his hand up for all manner of unsolved crimes sitting on the books and looking bad in statistical reports. Called ‘taking into account’.

We are not very good at accepting that we may never know what happened, why something bad happened. In the olden days, people were more content to say that it was God’s will and to leave it at that. Or, perhaps, to assign guilt to some angry spirit who needed to be appeased in one way or another, possibly by a gift or a sacrifice. While now we are more arrogant and think that we can know it all.

It helps to remember that unlikely things do happen. If, for example, you do a million experiments, it is very likely that some of them are going to give very odd results.

Observer bias

Thoughtful people have known for centuries that we see what we want to see or perhaps what we expect to see. In the present connection, this is often called observer bias. This is not necessarily a reflection on the observer, it is just the way we are made.

This report offers the prescription that, as far as is possible, those conducting forensic tests, should not know the context of those tests. So, if they are testing the blood of a known and dangerous drunk for alcohol, they should not know that. They should test the blood ‘blind’, as it is called in the trade.

This may require the lead investigator to be both tactful and firm: some medical examiners are going to resent being kept in the dark in this way.

A related issue is that of ‘tunnel vision’. An investigator gets his idea about the answer to the puzzle and chases after evidence in favour of that idea to the exclusion of all other. We can get terribly attached to what we take to be our own ideas.

From where I associate to my own behaviour leading reviews of small IT projects. The idea was to provide the owners of a project a view of how it was going from the outside, from people who had no stake in the project – although even this simple idea was corrupted by it being found that it was helpful to have the same review team look at a project through its various stages. Another idea was to use traffic lights: projects were deemed to be green, orange or red, with red being bad – which one might gloss as no action needed, action this week and action this day. At that time, reviews always took three days and one was supposed to walk away from the project with a near complete report. What this seemed to mean in practice was that on the first day one had a more or less open mind. But by the end of the second day one wanted to know where one was headed and the third day was spent confirming that diagnosis. So tunnel vision, but at least it was someone else’s tunnel vision.

Against which it was also the case that a report team wanted to have something to report: a nil report was not very exciting. I associate to the rather different world of government finance, where the people you were investigating, if they were shrewd, threw you a few bones to keep you busy.

I also associate to advice given to me a very long time ago: decide on your conclusions and then write your report. Perhaps I should give my mind to the tricky interaction between the search for the truth and the construction of an attractive report – two activities which compete for the investigator’s time.

Red teams

Getting another view is indeed a good way of mitigating the effects of tunnel vision. To which end, in the Catholic Church, when thinking about making someone a saint, they at least used to appoint a devil’s advocate whose job it was to drag out all the reasons why someone should not be made a saint. And in UK law, a lot of business is conducted on adversarial lines – which can seem a bit crude and theatrical at times, but which does provide a second view.

I associate to a well-known (and well-paid) speaker on the management consultancy circuit years ago, who made much of the idea that you should never do something important without having thought long and hard about why you should not do it.

It seems that our own Ministry of Defence is well up to the mark on all this, with their guide on what they call red teaming now running to its third edition at reference 4. And I imagine that well-run war games address a similar issue by having a team of people trying to put themselves in the shoes of the opposition, trying to think as they would.

Perhaps all rather easier when one is not working under the harsh lights of a criminal investigation. Where, although I have not come across one, I dare say that the police have training manuals which cover the ground.

References

There are more than four pages of references at the end of the report, suggestive of a great deal of prior work on the issues. One William C. Thompson scored the most entries and I picked one of his for inspection. It turns out that he is both an expert in the field and one of the authors of the report. 

The entry I chose, reference 9, reports on a substantial experiment to test the way that lay people react to DNA and footprint evidence. An important concept here is the random match probability (RMP). 

‘… DNA analysts typically use population data to estimate the probability of finding a “matching” or “consistent” profile in someone sampled randomly from various reference groups (e.g., U.S. Caucasians; African Americans; U.S. Hispanics). Although the numbers are often framed as probabilities, they can also be presented as natural frequencies—for example, the analyst might say that among U.S. Caucasians only one person in 10 million would “match” or would be “included as a possible contributor” to a DNA sample…’.

Presentation in terms of RMPs is contrasted with presentation in terms of likelihood ratios (LRs) or verbal equivalents of likelihood ratios (VEs). In this context, some statisticians prefer the use of likelihood ratios to probabilities, arguing that they avoid some of the pitfalls associated with these last.

Conclusions

The recommendations of the report have been snipped out into the snap at the head of this post. The bias of the authors is evident in the prominence of those about the need to consult statisticians!

That apart, one hopes that those involved in leading investigations of this sort will take the time to read this report – or some equivalent guidance – before getting properly stuck into the investigation. 

While for myself, maybe it is time to stop trying to get a grip on the statistical technicalities – and rest content with delegation.

PS: a digression from the present post is to be found at reference 10.

References

Reference 1: https://psmv5.blogspot.com/2025/05/trolleys-853-and-854.html.

Reference 2: Healthcare serial killer or coincidence: Statistical issues in investigation of suspected medical misconduct – RSS Statistics and the Law Section – 2022. 

Reference 3: Combining independent tests of significance – Birnbaum, A – 1954. Not freely available, but widely referenced.

Reference 4: Red Teaming Handbook (third edition) – Ministry of Defence – 2021.

Reference 5: https://en.wikipedia.org/wiki/Bayes%27_theorem. 

Reference 6: https://psmv5.blogspot.com/2021/11/the-p-value-battle-continues.html. 

Reference 7: Statistical Methods for Research Workers – R A Fisher – 1934.

Reference 8: https://en.wikipedia.org/wiki/Fisher%27s_method. 

Reference 9: Lay understanding of forensic statistics: Evaluation of random match probabilities, likelihood ratios, and verbal equivalents - Thompson WC & Newman EJ – 2015.

Reference 10: https://psmv5.blogspot.com/2025/06/on-data.html. 

Sweet clover and orchids

About ten days ago to Polesden Lacey. A hot day which meant that it was not as busy at 10:50, when we turned up, as it might otherwise have been.

Started with the now traditional tea and fruit scone, and then proceeded down the avenue leading to the back of the house and the rose garden - to find a colony of pyramid orchids getting established there. I am fairly sure that we have not come across them there before. And I have yet to see any this year outside what is now the Padel Hub in Blenheim Road  - and probably won't as they like to keep their grass short.

There were quite a lot of them, but none of my attempts at shots taking in lots of them worked. Light all wrong.

We also came across a lot of these flowers; rather past their best, but they must have looked well a few days previously. BH opted for Canterbury Bells, which Google Images more or less agrees with, although he goes for Campanula alliariifolia. I abstain, but see references 3 and 4.

A fine convolvulus, in among the ivy. The five snaps I took offered a range of contrasts between the green of the ivy and the white of the flower. You get more floral detail with high contrast, but I found them a but unnatural, so settled for a mid range one. I guess a painter has a bit more flexibility.

The rose garden, when we got there, was looking very well indeed, various beds put to fallow notwithstanding. We were told that sweet clover and buckwheat were the ground cover used.

This stuff did not look much like clover and looked even less like wheat. However, this afternoon, Google Images says buckwheat, and reference 5 explains that buckwheat has not got much to do with wheat, being more closely related to rhubarb. But you can use the seeds in the same sort of way as you can use those of wheat. 

A bit further on, we came to a bed of this yellow stuff, which did look a bit like clover. So, with a bit more help from reference 6, it looks as if Google Images is right by elimination.

Clover with roses round about.

We had missed the peonies, but the delphiniums were out, there were some fine foxgloves and there were plenty of other flowers to admire. And grist for the phyllotaxis mill, as snapped above. And plenty of benches to sit on, in shade or sun, au choix.

BH felt sure that this was borage, an identification confirmed by reference to a former neighbour who had served in HMS Borage during the war. A vegetable class corvette? I was holding out for some kind of comfrey. Google Images goes for borage, coming up with various varieties.

And we do get a back view of one of the distinctive flowers offered by Wikipedia at reference 7.

Grist for the mill of bus bodywork, the subject of a diversion of a couple of days recently. Two pressed steel frames running fore and aft, springing up from the floor, one each side? Rather feeble transverse frames between? No timber elements at all?

Having got on pretty well last time, went for lunch in the cafeteria. For me, fruit scone to keep me going while the hot food turned up, some sort of bean stew and a sausage bap. BH went for macaroni cheese. Lots of young people serving, presumably fresh out of school or college. All very satisfactory.

Home to siesta - and then out again to attend to the trolleys noticed at reference 8.

PS 1: along the way, I discovered that Pearl the chemist, who do my pills for me, have taken to customer satisfaction. They have thought it worth their while to install a floor mounted contraption with a screen, in front of the counter, which you can tell about your satisfaction. Maybe a couple of hundred pounds worth? I have yet to see anyone using it and I have no intention of using it, but I would say that I have always had good service from Pearl of Tooting since they took over from Lloyds of I know not where.

PS 2: while in the margins of this post, Microsoft brings me news of a new development in the troubling Letby case, last noticed at reference 2. For the BBC version, see reference 9.

References

Reference 1: https://psmv5.blogspot.com/2025/06/beans-with-polesden.html.

Reference 2: https://psmv5.blogspot.com/2025/06/unlikely-crimes.html.

Reference 3: https://en.wikipedia.org/wiki/Campanula_medium.

Reference 4: https://en.wikipedia.org/wiki/Campanula_alliariifolia.

Reference 5: https://en.wikipedia.org/wiki/Buckwheat.

Reference 6: https://en.wikipedia.org/wiki/Melilotus.

Reference 7: https://en.wikipedia.org/wiki/Borage.

Reference 8: https://psmv5.blogspot.com/2025/06/trolley-884.html.

Reference 9: https://www.bbc.co.uk/news/articles/c62ddkde7y5o.