
Court of Appeal bans Bayesian probability - leephillips
http://understandinguncertainty.org/court-appeal-bans-bayesian-probability-and-sherlock-holmes
======
blauwbilgorgel
This reminds me of the case of Lucia de B., a nurse once suspected of killing
her patients.

There never was solid evidence against her. She was a suspect because nearly
everytime someone died in the hospital she was on her shift.

The initial chance of her being present when these supposed murders happened,
and being innocent, was estimated at 1 in 7 billion. This number caused the
police to focus their research completely on Lucia de B.

Eventually she was convicted for the murders based not on hard evidence or
witnesses, but on statistics. The chance of innocence was put on 1 in 342
million.

The econometrist Aart de Vos was the first to notice that the initial Bayesian
analysis was plain wrong. For example they had presumed the murderer had to be
found amongst the nurses, other possibilities were neglected. They also hadn't
corrected for combined P-values. He reduced the chance Lucia was innocent to 1
in a million.

The court said they had abandoned the statistical "proof", but remained of the
view that it couldn't be a coincidence. Possible murder cases were chosen when
they were negative for Lucia, other possible murder cases were left out of the
equation. This further reduced the chance to 1 in 50.

Statisticians Richard Gill and Piet Groeneboom further reduced the chance to 1
in 9.

In my opinion statistics alone can never be adequate for conviction. It can
muddy research and lead to confirmation bias. And the difference between a
Bayesian chance of 1 in 7 billion and 1 in 9 is so big as to doubt the initial
use of statistics even further.

[http://en.wikipedia.org/wiki/Lucia_de_Berk#Statistical_argum...](http://en.wikipedia.org/wiki/Lucia_de_Berk#Statistical_arguments)

~~~
davorak
I do not think I understand your argument. In the case as you describe it the
statistics are done incorrectly and cause a potential false conviction.

How is this different then an expert on autopsies incorrectly does the job
which leads to a potential false conclusion.

In both case an expert made a mistake or did their job poorly leading to a
potentially unfortunate outcome. Why should one be banned and not the other?

~~~
DanBC
For a criminal trial, with a jury? People are hopeless at statistics.

Even on HN you'll find people making simple mistakes.

Someone confidant presenting a mathematical argument would be persuasive to a
jury, even if their numbers are totally bogus.

> _In both case an expert made a mistake or did their job poorly leading to a
> potentially unfortunate outcome. Why should one be banned and not the
> other?_

People doing the job poorly should be banned. But the nurse case is
interesting because poor statistics became self-fulfilling.

"We have some deaths, and this nurse is present when they happen, and so they
are all suspicious", becomes "all the deaths that happen when this nurse is
working are suspicious, and the deaths that don't happen when this nurse is
working are not suspicious". And that sloppy thinking gets turned into
"probability is 1 in a gajillion that these happen normally by chance."

~~~
davorak
>People doing the job poorly should be banned. But the nurse case is
interesting because poor statistics became self-fulfilling.

>"We have some deaths, and this nurse is present when they happen, and so they
are all suspicious", becomes "all the deaths that happen when this nurse is
working are suspicious, and the deaths that don't happen when this nurse is
working are not suspicious". And that sloppy thinking gets turned into
"probability is 1 in a gajillion that these happen normally by chance."

Investigators have been known to be unduly influenced by pretty much any kind
of evidence imaginable and then all further evidence is construed to support
the original assumption/assertion. I need a more concrete difference or
divider to promote other methods above statistics.

~~~
pseut
> Investigators have been known to be unduly influenced by pretty much any
> kind of evidence imaginable and then all further evidence is construed to
> support the original assumption/assertion.

A different way of phrasing this is that investigators have been known to
incorrectly apply even standard tools that they've been explicitly trained in.

> I need a more concrete difference or divider to promote other methods above
> statistics.

If by "promote" you mean that we should try to increase the statistical
literacy of lawyers, police, judges, and the general public, than hells yeah.
But encouraging armchair statisticians to try to determine causality and guilt
from badly-collected observational data that's analyzed by financially-
invested parties...? In the highest stakes setting we have? Really?

------
Anderkent
The quotations in this article are taken out of context and presented
incomplete. For example, the article quotes

 _The chances of something happening in the future may be expressed in terms
of percentage. Epidemiological evidence may enable doctors to say that on
average smokers increase their risk of lung cancer by X%. But you cannot
properly say that there is a 25 per cent chance that something has happened:
Hotson v East Berkshire Health Authority [1987] AC 750. Either it has or it
has not._

And the judgement continues:

 _In deciding a question of past fact the court will, of course, give the
answer which it believes is more likely to be (more probably) the right answer
than the wrong answer, but it arrives at its conclusion by considering on an
overall assessment of the evidence (i.e. on a preponderance of the evidence)
whether the case for believing that the suggested event happened is more
compelling than the case for not reaching that belief (which is not
necessarily the same as believing positively that it did not happen)._

Which is _exactly_ the bayesian approach of 'probability as state of
knowledge'.

~~~
bo1024
The quotes are contradictory. The Bayesian approach agrees with the second and
disagrees with the first.

I suppose you could weasel in some sort of consistency about the wording ...
something like "You cannot properly say there is a 25 percent chance that
something has happened, but you _can_ properly say you _believe_ there is a 25
percent chance that something has happened." OK, fine, but what's the
difference? You still assign a percent probability to the chance that
something happened, and you still rule on the basis of those beliefs. Or do
you? (It's not clear to me from those quotes.)

~~~
rayiner
Its post facto versus a priori. There is a 25% chance of something happening,
but after the fact, it either did or did not happen. Averaged over many cases
we can say that after the fact there is a 25% chance it happened, but criminal
trials look at one specific instance, and its accurate to say that in an
instance something either did or did not happen.

~~~
jules
You should still use probability to quantify that belief. Whether it happened
in the past or is going to happen in the future doesn't matter. If you throw a
coin, and the coin is flying in the air, what is the probability that it lands
heads? By your reasoning, the motion is already in place, and it's either
going to land heads or it isn't. With a high speed camera and some physics we
might even be able to predict which side it will fall. Even if we go back to a
little before you threw the coin, the electrons in your brain are already in
place and it's already determined which way you'll throw the coin. Would it be
invalid to say that there is a 50% chance that it will land heads? So even
when we are talking about the future, we use probability to quantify our
belief. Or perhaps more accurately, we use it to quantify our lack of
knowledge: in this case our lack of knowledge about how exactly the coin will
move. Since we are already using probability not just for "fundamental
randomness" but for quantifying lack of knowledge about the future, what's so
special about the future vs the past? It makes total sense to apply the same
reasoning to the past, even if we are talking about a specific instance.

~~~
rayiner
You're shifting the argument. Sure you should, in some cases,[1] use
probabilities to determine your belief about whether something happened or
not. That's precisely what the court says in the second paragraph. Your beef
was ostensibly with the wording of the first paragraph, but as I pointed out
that when talking about things that have happened in the past, the wording is
not incorrect.

[1] Of course you also shouldn't sometimes use probabilities. If we have
statistics saying that witnesses lie 15% of the time, is it helpful to present
expert testimony to the effect of "there is a 15% probability the witness is
lying?" Such evidence is not useful and also impinges on the fundamental right
of the jury to judge witness credibility.

~~~
jules
My only point is that whether something is in the past or in the future has
nothing to do with whether you can use probability. If you're consistent then
either you don't use probability at all to model lack of knowledge, or you use
it for both past and future. For example if you find it valid to say "when he
tosses that coin, it has 50% probability to land on heads and a 50%
probability to land on tails", then you should also find it valid to say "he
tossed that coin, and it now has a 50% probability to be on heads and 50%
probability to be on tails" if you did not yet see the coin. That's because in
both cases, the outcome was already determined (by the laws of physics,
disregarding quantum mechanics). The thing is that you just don't know which
way it will land or has landed because you lack perfect knowledge.

I don't have a problem with not using probability to model lack of knowledge,
but you have to apply that principle consistently (and whether it is ethically
desirable to use probability is an entirely different and even more difficult
question than whether or not it leads to accurate beliefs). That said, I do
prefer to use probability to model lack of knowledge, because what is the
alternative? Ad hoc gut feeling based reasoning?

------
Millennium
You know, I think I'm OK with this.

Sherlock Holmes was a detective, not a judge. What was appropriate for his
line of work isn't appropriate in the courtroom. Courts are not about what
MIGHT happen (or have happened); they are about what DID (or did not) happen.
Probability can be an excellent guide for further investigation into these
things, but it should be left to the investigators. If they can't find
anything harder than a set of odds, then judges have no place betting on them.

~~~
chimeracoder
> If they can't find anything harder than a set of odds, then judges have no
> place betting on them.

But this is how our entire legal system is set up. For criminal proceedings,
we have to find the defendant 'guilty beyond reasonable doubt'. What is
'reasonable doubt' if not a (theoretically) quantifiable or parameterizeable
representation of our belief that the defendant committed the criminal act?

We don't _explicitly_ quantify this threshold as, eg. a 95% chance, but that's
still the exact same process we require a jury to undergo, even if we don't
attach quantifiable numbers to the results.

The jury can never return a probability of 1 (in statistical terms, 'almost
certain'), or else the entire appeal system wouldn't exist.

~~~
Torgo
I believe that the purpose of randomize juries could be said to exist because
while there are parameters, no one person or entity knows all the parameters.

------
jheriko
this seems like a complete over simplification and naive analysis of the
situation - and the argument smells like a straw man and appeal to authority,
comparing it to sherlock holmes - who incidentally /is obviously wrong/. the
idea that 'whatever remains' is quantifiable and finite in the real world is a
stark contrast with reality - and actually the fact that a probability is
precisely 0 or 1 is very significant to its power in drawing conclusions. so
not only does forbidding probability not forbid sherlock holmes style 'logic'
but his logic is broken anyway in the vast majority of real world cases.

what the court says is common sense... its a shame it offends some academic
view... oh, no, wait, it really isn't.

~~~
jacques_chester
> _this seems like a complete over simplification and naive analysis of the
> situation_

The key phrase in the linked article:

> _and so I must now tell them that the entire philosophy behind their course
> has been declared illegal in the Court of Appeal. I hope they don't mind._

Is what reveals the misunderstanding. Judges don't "declare" things illegal,
they rule on matters of _what_ the law is. That the law _requires_ judgements
to be rendered in certain terms is not a statement of the legality of making
Bayesian arguments.

The law requires a _decision_. The conceptual basis of the common law is a
_promise_ that a court will _always_ render a clear and specific set of
rulings or orders, and that there will _always_ be an explanation of those
rulings or orders. Judges are not free to say to disputants that they are X%
likely to win their claim.

This is one of those places where Bayesian probability isn't a good fit. Fuzzy
logic -- so passé these days -- at least has an understood mechanism for
"defuzzifying" in a fashion which lawyers would find quite familiar.

It also overlooks that judges have many other places to introduce flexibility
and weighed judgement. For example, judges may assign blame in portions for
some crimes or torts; they may reject, moderate or modify some claims in
equity; they have leeway to combine multiple considerations and legislative
constraints in handing down criminal sentences and so on.

One thing that bugs me _tremendously_ about outsiders looking in at law is the
assumption that, since lawyers don't immediately and entirely embrace new idea
X, they are fusty old fools who are an impediment to the good. It's an
argument born of ignorance that lawyers are deliberately obtuse fools, or
judges out-of-touch theoreticians. Lawyers and judges touch on more problem
domains in more depth, with greater consequences, than pretty much every
academic and every software developer.

~~~
davorak
>> and so I must now tell them that the entire philosophy behind their course
has been declared illegal in the Court of Appeal. I hope they don't mind.

>Is what reveals the misunderstanding. Judges don't "declare" things illegal,
they rule on matters of what the law is. That the law requires judgements to
be rendered in certain terms is not a statement of the legality of making
Bayesian arguments.

The write seems to be assuming that the court case sets a president that make
it hard if not impossible to use Bayesian reasoning in the court room and sums
it up as "illegal".

> The law requires a decision. The conceptual basis of the common law is a
> promise that a court will always render a clear and specific set of rulings
> or orders, and that there will always be an explanation of those rulings or
> orders.

I thought this was a civil case and did not require "beyond a shadow of
doubt." but rather just high probability a term I have heard is that it
requires a preponderance of evidence. Bayesian statistics/reasoning is
supposed to help come to a conclusion with a high likely hood of being correct
which seems like the file state I want a judge to be in when ruling. What is
not good or counter productive about this state brought about by Bayesian
methods?

~~~
jacques_chester
The problem is that the law _requires_ a statement of cause in order to
apportion _responsibility_. It cannot abide uncertainty at the moment of
judgement. It is accepted that, because in civil cases, the consequences of
misjudgement are less severe, it is acceptable to relax the standard of
judgement to "balance of probabilities".

Note the case that was mentioned inline that this case was affirming: _Hotson
v East Berkshire Area Health Authority_ [1]. First of all, the linked poster
should be railing at _that_ decision, this one merely takes it as precedent.

In _Hotson_ there was a question about causality based on the given
probability of a child's recovery. Given that a child that fell out of a tree
was estimated to be 25% likely to recover, medical staff seemed to have taken
the view that the child was basically a hopeless case. Perhaps if they hadn't,
went the reasoning, the child might have done better because the staff would
have tried harder. In that were so, some responsibility could be apportioned
to the Health Authority, and not just to the child falling out of a tree.

The Lords ruled that the only thing that _certainly happened_ was the child
falling out of the tree. Counterfactuals based on probabilities couldn't be
admitted because there's no way to reliably nail the damn things down. Anybody
can come along with a different Bayesian network and give you a different
estimate. What _mattered_ , in the view of the Lords, was _what could be
verifiably said to have actually happened_.

A more-than-standard disclaimer:

I am not a lawyer. I was terrible at torts. Torts law is notorious tricky and
can vary very widely from country to country -- I studied in Australia and
these cases are in England. This post does not constitute legal advice. Hell,
it doesn't even make for good reading.

~~~
davorak
Interesting, thanks for the pointe

> What mattered, in the view of the Lords, was what could be verifiably said
> to have actually happened.

It would be interesting to see how "verifiably" and "actually happened" would
be refined to produce a judgement. I could imagine at least refinement towards
frequentist statistics, Bayesian methods, "I know it when I see it"(gut
feeling, other non-quantitative standard of obviousness).

~~~
jacques_chester
I would say that main things to remember about law in common law jurisdictions
are:

1\. The judge does not seek evidence, does not provide evidence, and does not
provide arguments. The presentation of fact and law is the job of the
plaintiff/respondent or prosecutor/defendant (depending on civil or criminal
law).

2\. The judge rules on what is introduced during court cases. Judges almost
always follow judgements that have been made previously -- precedent, also
called _stare decisis_ or "let the decision stand". In this case the precedent
identified was _Hotson_. A lower court judge who presumes to modify a higher
court's principles can expect that the higher court will accept an appeal on
matters of law.

3\. The legal system's purpose is to render certain, verifiable judgements.
Judgements can't be uncertain ("You are sentenced to a 95% chance of prison"
or "between 20,000 and 50,000 is awarded to the plaintiff for damages" is not
helpful), so as a step in the process of legal reasoning, information about
uncertainty is deliberately destroyed. This is called "balance of evidence" or
"preponderance of evidence" in civil trials, or "beyond reasonable doubt" in
criminal trials. It is deliberately imprecise, because all attempts to
introduce mechanical rules for evidentiary judgement have so far proved to be
even more gameable than the fuzzy statements.

The legal system is profoundly introspective. Lawyers will introduce matters
of legal interpretation in argument, these must be addressed. Appeals to
higher courts are usually only possible on questions of law, meaning that very
fine details of legal reasoning are constantly being teased out.

Judges must constantly weigh what the law _is_ , and they also at higher
levels frequently decide _how_ the law is determined to be what it is. Given
that subjects like jurisprudence and interpretation of laws can have massive
practical consequences, it's an area that receives great scrutiny.

I became interested in the methods of analysis and judgement because of
Australian constitutional law, where there are -- depending how you count --
between 4 and 6 basic schools of thought on how to interpret the Australian
Constitution.

------
tehwalrus
_"I teach the Bayesian approach to post-graduate students attending my
'Applied Bayesian Statistics' course at Cambridge, and so I must now tell them
that the entire philosophy behind their course has been declared illegal in
the Court of Appeal. I hope they don't mind."_

Classic. I was told (at same uni) that, in a case involving DNA evidence, I
could ask to be dismissed from a Jury, citing training in Bayesian statistics
(which was prohibited because reversing the scientific certainty to look at
false positives, in cases with weak circumstantial evidence, essentially kills
DNA evidence's usefulness. If someone was in the right city, you expect
hundreds of DNA matches out of millions of people, but if you can track them
to the right street at the right time, you would expect 0.001 matches, and
thus the evidence points to them much more strongly.)

~~~
jacques_chester
Everything you hear about law that was not conveyed to you by a lawyer, a law
lecturer or a judge is probably horseshit.

People _love_ to think they know some obscure wrinkle, some cool loophole,
some nifty curio about the law. But so many of the stories you hear are _just
stories_.

ps. a better way to get disqualified is to have studied law.

~~~
tehwalrus
indeed, this was my point. I didn't even contemplate trying it when I was
called for jury duty.

------
SEMW
See also: R v T (Footwear Mark Evidence)
<http://www.bailii.org/ew/cases/EWCA/Crim/2010/2439.html> (which is redacted
to hide the appellant's identity, giving the judgment a delightfully dystopian
feel).

There it was held that an expert witness shouldn't use Bayesian reasoning to
calculate probabilities to tell a jury " _outside the field of DNA (and
possibly other areas where there is a firm statistical base)_ ".

I _think_ that, by a 'firm statistical base', the court's getting at the sort
of situations where the right prior is a widely agreed on (such as DNA, where
the size of the DNA database is known), so there won't be much opportunity for
different expert witnesses to disagree on probabilities due to having
different priors. (N.B. IANAL)

This is still nonsense, IMHO. I can understand the court not wanting juries to
be overly swayed by a spuriously precise probability that might have been very
different if a different expert had been chosen. But there's no justification
for restricting the statistical methods that the expert uses to reach their
conclusion, however it's expressed to the jury.

Interestingly, that case shared one of the appeal judges from the case in TFA
(Lord Justice Beatson, then Mr Justice Beatson).

~~~
diminoten
I think the distinction being made here is the difference from using
statistical methods for determining overall guilt versus using statistical
methods for determining specific facts about the case.

We use statistics to say that someone was or was not at the scene of a crime
(DNA testing doesn't 100% guarantee that a persons' blood is actually a
match), for example. We don't make the leap that since they were there, "odds
are" they did it, however.

~~~
SEMW
The question in R v T that Bayes theorem was being applied to _was_ a
specific, factual one: whether a footprint could have been made by a
particular shoe.

------
DanBC
> * In upholding the first instance decision, the Court of Appeal reiterated
> the principle in cases where there are competing explanations for a
> particular loss that causation cannot be established only by a process of
> elimination such that the 'least unlikely' cause of a loss is identified. A
> claimant must demonstrate that the particular version of events that they
> rely upon is more likely to have happened than not, in order for the civil
> burden of proof to be satisfied.*

I'm not sure what the problem is.

"It could have been A, B, or C. It's really unlikely to have been A or B, and
thus it must be C" is obviously flawed, because for all we know it could have
been D, and even if it was C you need to show (on the balance of
probabilities) that C is the cause. Not just that C is more likely than A or
B.

~~~
jacques_chester
It's not the judge's role to independently nominate D. It's up to the lawyers
for the plaintiff and the respondent to present facts and make legal
arguments.

The judge's role is to weigh those legal arguments, and in (most) civil trials
to weigh the facts presented on the balance of probability, and to render a
decision.

If you require judges to run a Bayesian network over the entire universe for
each case, the legal system will get a wee bit slower.

~~~
Anderkent
_It's not the judge's role to independently nominate D._

But that is exactly why the judge can not assume all possibilities were
enumerated, and requires positive evidence for C, rather than negative
evidence for A and B.

~~~
jacques_chester
Judges, oddly enough, decide cases according to the rules of legal reasoning.
They cannot and won't introduce their own evidence. A judge that did so would
be rightly removed from the bench.

~~~
Anderkent
So you agree then? I did not say a judge should propose any evidence.

Perhaps it's easiest to explain with an example. Let's say the defence argues
for A, and prosecution argues for B. The prosecution shows that the
probability of A being true is 1%. The judge can _not_ take that as a B having
a probability of 99%, since it may be that C is true.

Thus the judge requires prosecution to show that B is 50%+ likely, not that A
is unlikely.

Does that make more sense?

------
flexie
This guy extrapolates wildly from the decision.

This is a question about whether or not a cigarette bud started a fire, not a
rejection of bayesian probability as such.

This guy should stick to teaching statistics, not law.

~~~
4ad
Did you bother reading the post at all? The inference in the ruling is based
on the rejection of Bayesian statistics.

~~~
flexie
Did you bother reading the ruling:
<http://www.bailii.org/ew/cases/EWCA/Civ/2013/15.html>

The ruling is not concerned with statistics as a mathematical discipline. The
"balance of probabilities" is a legal term.

Please read the court ruling, and then read the blogger's conclusion (summed
up sarcastically in his last sentence) and tell me if you think he's right :-)

~~~
alan_cx
'The "balance of probabilities" is a legal term.'

So is "reasonable doubt", but I am yet to see a perfect definition of it.
Indeed, in the UK a jury questioned its meaning, the judge got snottily
arrogant over it and ditched the case, but still not proper definition, either
from the critical judge or anywhere else in the legal system. Interesting to
me that the judge was so unable to answer the question, that he ditched a
whole trial.

I am amused by legal arrogance that thinks every one else should fully
understand all its weirdness and definitions. Especially having done some work
in a solicitors office where I was the arrogant one getting irritated with
most of the legal people not having even a basic understand of the computers
on their desks...

~~~
SEMW
> in the UK a jury questioned its meaning, the judge got snottily arrogant
> over it and ditched the case ... Interesting to me that the judge was so
> unable to answer the question, that he ditched a whole trial.

If you're talking about Huhne & Pryce, that's just wrong. The jury was
discharged because after 2 days of deliberations they told the judge that they
couldn't come to a verdict (which 10 of them agreed on).
<http://en.wikipedia.org/wiki/Hung_jury> .

I don't know where you got the idea that the judge got defensive because he
didn't know how to answer what reasonable doubt meant, but it's utter
nonsense. It's a very common question for juries to ask. The appeal courts
have debated several times what the best guidance is. The judge was following
the current guidance, which is tell the jury to treat it as ordinary english
words and refuse to give any more specific definition. If each judge gave
their own favourite interpretation of what 'beyond reasonable doubt' means
(e.g. p(false positive) < 5%, or whatever), then the standard of proof you'd
be tried under would depend on the judge, which would be obviously
unacceptable.

------
PaulHoule
If they make Bayesian analysis illegal only criminals will use Bayesian
analysis.

~~~
smoyer
If they make Bayesian analysis illegal, they've turned those using it into
criminals (by definition). Still a great comment!

------
jacques_chester
Please amend the title.

It is not correct.

The Court of Appeals has not "banned" Bayesian probability.

It does not have the power to do so.

------
pfortuny
The problem probably lies in the fact that you cannot prove something by
reduction to the absurd based on a probability distribution.

Because law requires positive proof (or it should) not just "this chain of
events is so unlikely under other assumptions that our assumptions must be
right". This is where Sherlock's quotation is misleading: he says "rule out
the IMPOSSIBLE", not the improbable.

The judge is right epistemologically. Bayesian statistics has only a
terminological issue.

------
drucken
The whole basis of law is elimination of "epistemic uncertainty" and threshold
of evidence for an event. If this is not possible, the case is not proved,
therefore case dimissed.

Sherlock Holme's statement is a statement of method, not statement of proof.

In other words, the law is far greater than Bayesian probability or any
method, including scientific, since the burden of proof is from the evidence
with the primary legal threshold of _"innocent until proven guilty"_.

~~~
Dylan16807
How many times in this comment page do people need to be reminded that the
burden of proof in civil cases is only 51%, not "beyond reasonable doubt" like
criminal cases.

------
jeremyjh
Poker players understand that a lack of knowledge of past events is exactly
the same as uncertainty about future events.

For example, if the first round of hold em has dealt two cards to each of 9
players, there are 18 cards out and you only know the state of two of them.
The odds that the flop will contain specific cards that help your hand are
calculated against the total number of unknown cards, regardless if the
unknowns are held by other players or still in the deck.

For example, you get a pair of 3s. There are two more threes in the deck, and
it is pretty likely that if the flop contains one of them that you will have
the best hand at the table at that point. For the first card turned up at the
flop, there is a 2/50 chance it will be a three, the next is 2/49, the next
2/48. It doesn't matter how many face-down cards have been dealt to your
opponents.

All the unknowns are still in the pool of possibilities, and it is no
different when you assess the evidence you have of any other type of event
that has already happen. Each bit of evidence means what means, and the
unknowns contribute to the pool of uncertainty.

------
jasonlingx
Why is this linkbait at the top of HN?

------
rayiner
If anyone finds this subject interesting: my evidence professor had a PhD in
statistics, and he's written about the application of probability to the law
of evidence extensively. See:
[http://papers.ssrn.com/sol3/cf_dev/AbsByAuth.cfm?per_id=5157...](http://papers.ssrn.com/sol3/cf_dev/AbsByAuth.cfm?per_id=51570)

------
mmcnickle
I not sure what the OP expects the court of appeal to do. They are tasked with
determining if there is cause for appeal; in this specific case whether the
original judge erred in law. They determined that he did not. They aren't
saying whether the judgement was right or wrong, rather that the judgement was
arrived at in a lawful manner.

------
misnome
As a frequentist I fully support this endeavour.

------
Colman
For anyone curious about how this would play out in the US, federal courts and
most state courts use the Daubert standard. TLDR: experts (including
statisticians) can testify if they're using fairly standard methods and there
are no significant gaps in the evidence-->analysis-->testimony chain.

<http://en.wikipedia.org/wiki/Daubert_standard>
[http://en.wikipedia.org/wiki/Daubert_v._Merrell_Dow_Pharmace...](http://en.wikipedia.org/wiki/Daubert_v._Merrell_Dow_Pharmaceuticals)

------
ekianjo
Accidents, murders, fires, etc... are all unlikely events by nature. Judging
whether one of them can have occurred based on probability does not prove
anything. The author post is wrong is the assumption that "an unlikely
event"="impossible". Probability does NOT ascertain certitude. There is always
an expression of confidence which is not equal to 100%, and therefore it seems
logical that a court does not take the probability of an event as a tangible
proof of what did or did not happen. Probability != science.

------
smoyer
What's the chance that the legal system would suddenly become coherent if we
replaced all lawyers (and therefore judges) with mathematicians?

~~~
jacques_chester
The law is highly coherent.

But it deals with the largest and messiest possible problem domain: everything
humans do.

~~~
danso
Well, "everything humans do" includes creating the law, so by that definition,
the law is highly incoherent.

And a close reading of the law reveals this. In fact, it is often by close
readings of the law (and precedent and every other historical quirk) on which
controversial and contested decisions are rendered

~~~
jacques_chester
> _Well, "everything humans do" includes creating the law, so by that
> definition, the law is highly incoherent._

Which meaning of incoherent are we taking here?

> _And a close reading of the law reveals this._

Do go on.

------
Draco6slayer
The opening Holmes quote is being used improperly. Holmes used that as
opening, then he went on to find further evidence to support that conclusion.
He did not rely on logic alone to determine the culprit, but rather went on to
find hard evidence.

------
zimbatm
It is well known that 70% of all statistics are wrong.

------
arcadeparade
Elizier Yodokowsky is going to be pissed.

------
hawkw
As a Bayesian rationalist, wut.

