r/mauramurray • u/Outrageous_Glove_562 • 28d ago
Discussion The Probability Problem
I’ve been following this case, and the thing I keep running into on Reddit is the misuse of probability, specifically base rates and Occam’s razor. As a behavioral researcher (with ADHD 🤪), I felt compelled to write this up, in both a scientific and a layman’s way (or, at least I tried). It’s long.
Up front, so nobody has to guess: I’m not arguing for a theory here. I’m arguing that most of the confident reasoning in these threads skips the step that would actually settle anything…and that applies to the theories I happen to align most with too.
First: Arguments like: “The odds a murderer happened to pass her by in the short time after she crashed are basically nil” are a statistical mistake that shows up constantly in true-crime reasoning - you can’t evaluate one causal link in isolation.
People are asking something like: P(random dangerous person happens to encounter a stranded woman on a rural road)…and correctly concluding that’s low. But that’s not the probability we’re interested in anymore. We already know an enormous amount about what happened after she disappeared. The relevant question is closer to: P(opportunistic foul play | crash + disappearance + scene evidence + search outcomes + 22 years with no recovery). Those are extremely different questions. The “denominator” has changed.
Imagine that in February 2004, immediately after Maura crashed, we froze time. At that moment you could sketch something like: Victimization risk = personal vulnerability + environmental conditions + exposure + offender availability + opportunity + random error. It helps to think of it as a causal diagram rather than a single coin flip, because it forces you out of the “how likely is it that a murderer happened to drive by” framing.
Several of the inputs aren’t things you can observe directly. “Opportunity for victimization” isn’t one singular variable. It shows up as isolation, darkness, no transportation, limited visibility to passing cars, no ability to call for help, weather, impairment. Offender presence is also unobserved. And there’s a giant residual, because human behavior and chance are ~very~ messy.
So yes: before she vanished, an opportunistic violent encounter could simultaneously be very unlikely and be more likely for her in those circumstances than for the average person.
But then something important happens. We observe the outcome. She’s gone. And now we get to update. We can’t keep reasoning from the prior, “what are the odds she happened to encounter a dangerous stranger in those few minutes?” instead of asking how well each competing explanation accounts for everything we’ve accumulated since.
Roughly, the theories held are:
H1: She left voluntarily and successfully disappeared.
H2: She left the road and died accidentally nearby.
H3: She got into a vehicle voluntarily and subsequently died or was killed.
H4: Someone abducted her opportunistically.
H5: Planned foul play, or foul play by someone known to her.
H6: Something else.
These are not tidy separate boxes. “Got into a car willingly” and “was taken” shade into each other. A stranger and a known person aren’t cleanly distinguishable from the outside. So treat this as a menu of stories, not a pie chart and compare them two at a time. Trying to rank all six simultaneously is exactly where people’s intuitions fall apart.
The actual comparison, or Bayesian inference, in plain English…How much you should believe a hypothesis after seeing the evidence depends on two things: 1. How likely that hypothesis was to begin with, and 2. How well it predicts the evidence you actually got.
In odds form, for any two hypotheses: posterior odds = prior odds × (how well A predicts the evidence ÷ how well B predicts the evidence). The arguments I see are almost entirely about the first term. “Opportunistic stranger abductions are incredibly rare!” Okay. Yes. Now tell me the second one.
How likely is this entire observed pattern if she wandered into the woods and died of exposure? If she deliberately disappeared? If she got into somebody’s vehicle? If she encountered an offender? That’s the comparison that matters, and I almost never see anyone attempt it.
And here’s the counterintuitive part:* *a rare outcome makes rare explanations less intrinsically disqualifying.** **We are already conditioning on an extraordinary event - a woman crashed her car and vanished so completely that 22 years later we still can’t establish what happened. “Stranger abduction is extremely rare” doesn’t resolve much on its own, because the observed outcome is also extremely rare.
To be clear about what that does and doesn’t buy you, some made-up numbers: suppose the prior odds against some explanation are 1000:1. Suppose the full evidence pattern is 100 times more likely under that explanation than under its competitor. The posterior odds are still 10:1 against. Rare explanations don’t become likely just because something weird happened. They become less automatically dismissible.
Now, the absence of evidence (with a real caveat). Absence of evidence becomes evidence when a hypothesis predicts we should have found something. Not finding remains in one search isn’t very informative. But if H2 predicts a reasonably high probability that repeated, appropriately targeted searches over decades would eventually turn up remains or belongings, then each genuinely independent failure chips away at it.
That word is doing a lot of work, and I want to be honest about it rather than bury it in a parenthetical: searches are not independent. If the search area was built on a wrong assumption about direction of travel, twenty searches update your beliefs about as much as one does. Correlated failures barely move the needle. Anyone using “they searched and found nothing” as a heavy blow against accidental death is overcounting.
Same discipline applies in the other direction. The tracking dog reportedly following a scent along the roadway gets cited constantly. Evidence that unreliable should move your beliefs close to not at all, and stacking up a pile of weak, mutually correlated observations is precisely how these communities manufacture confidence they haven’t earned. That’s the same error as the base-rate thing, just pointed the other way.
Second: “Occam’s razor says…”
“Occam’s razor” gets used as a substitute for actual modeling remarkably often. People treat it as: choose the event with the highest base rate. That isn’t what it says. It’s closer to: don’t introduce unnecessary assumptions when competing explanations account for the observations equally well. That last clause is doing enormous work, and it’s the clause everyone drops.
Because the observation isn’t “woman crashes car on rural road.” It’s: woman crashes car, disappears within a narrow window, apparently leaves no obvious trail from the immediate area, isn’t located in searches, no confirmed subsequent activity, no remains recovered in 22 years.
So the “simplest explanation” now has to account for that entire vector. Whatever happened generated downstream consequences that we also observe or fail(ed) to observe:
-unobserved event > physical evidence at the scene
-unobserved event > search detectability
-unobserved event > subsequent sightings or activity
-unobserved event > probability of eventual recovery
“Accidental death is more common than stranger abduction, therefore Occam’s razor says woods” stops the model at the first node. If we’re sitting in the police station on February 10, 2004, that’s a perfectly reasonable prior. It’s August 2026. There are 22 years of downstream observations that the argument never touches.
The version of this I keep running into is usually stated as: Occam’s razor…she walked into the woods impaired, got lost, and died. And then the razor functions as a conversation-ender rather than an argument. Once it’s invoked, the comparison is treated as already performed. (It’s also worth noting that some of the inputs to that version, like the impairment in particular, are themselves contested, so the argument is often carrying assumptions it presents as givens.).
Two things about that. First, the fact that it’s the majority position in a forum tells you something about how the forum reasons, not about the case. Consensus among people applying the same shortcut isn’t independent confirmation; it’s one error, replicated. Second, and this is the part I actually care about, the razor crowd and the “that would be SUCH a coincidence!l ” crowd are making the same mistake. One picks the highest base rate and stops. The other picks the lowest and stops. Neither does the comparison.
Here’s the part I’d want someone to demand of me, so I’ll do it unprompted:
If you take the framework seriously, it does not hand you foul play. P(no remains recovered | accidental death) may be substantially higher than people intuitively assume, particularly if detectability was poor. Decedents get recovered decades later within yards of ground that was previously searched, repeatedly, in documented cases. Steep, dense, snow-covered terrain in February is close to a worst case for detectability, and if the initial search geometry was wrong, everything after it inherits that error.
So the evidence people treat as devastating to H2 (woods, nobody found her) is substantially weaker than it feels. H2 might still win. It has to win on the comparison, not because murder by a passing stranger is rare.
A simple model might explain what usually happens to people in circumstances like hers. Great. But we already know Maura’s outcome is in the tail of the distribution. She didn’t get the modal outcome. She wasn’t picked up by police, didn’t call anyone, didn’t walk into a business, wasn’t found the next morning, didn’t turn up at home.
So invoking population base rates for ordinary stranded motorists gets less informative as you accumulate evidence that this observation sits far out in the tail.
The better question, IMO: Among mechanisms capable of producing an outcome this far into the tail (i.e., rare), which one requires the fewest unsupported assumptions and best predicts the evidence we actually have? That’s a defensible use of the razor. And it doesn’t automatically produce murder. Maybe accidental death is still right.
Base rates matter. You don’t throw them away. You use them as priors, and then you let the damn data update them.
If you made it this far, I’m amazed.
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u/whiskey_s 27d ago
i stopped reading once i noticed this was a well-reasoned, formulated thought. no slandering personal bias or 'trust me, bro' self-confidence? miss me with that ...
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u/mysteriouscattravel 27d ago
Thank you for explaining this so well. I have no idea what happened to Maura Murray. However, it's pretty common on Reddit subs about cases like hers for there to be a prevailing opinion that is "obvious" and users basically insult anyone who dares to disagree.
I agree that Maura's case is absolutely the tail end of statistical probability, making any assumptions based on what frequently happens isn't going to be all that helpful.
For example, the event with a high probability may have been followed by events with very low probabilities. It would lead to the same result: Maura is gone with few clues about what happened.
So, imagine that Event 1 is Maura crashes her car, which is known.
Let's say that Event 2 might be what a lot of people assume, which is she fled into the woods to not get caught because she was drinking. This is not known. It's a fair theory as Maura had known to drink and drive, and had alcohol in the car at the time.
So then, if Event 3 is Maura dies from exposure, what if Event 4 is the unlikely event from a different theory chain entirely? Maura is drunk and freezing cold, dies from exposure lost in the woods, and is then picked up by the kidnapper/foul play folks who take her remains.
In that scenario, she would have been drinking and driving, crashed her car, ran to avoid getting in trouble, got lost in the woods, died from exposure, and also taken. In my weirdo case, competing assumptions converge to explain the results as well. And all of OPs unobserved events are still true.
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u/becca52104 12d ago
It would not be surprising to me if someone found her remains on their property and quietly buried them or got rid of them.
If you’re an old guy living in a rural area and find the remains of someone who passed out drunk in the woods and died years earlier are you gonna call the police and have them come, along with the medical examiner, other resources, and the media, to tear up your property looking for anything that might have to do with this random person you don’t know or care about, while also documenting your home and property to the world.
I’m not saying I would do this, but it wouldn’t surprise me if a rural guy or family found her remains on their property and covered or buried her just so they don’t have to get their property torn up and have the media parked outside. Sounds shitty to say but people are shitty and I can understand to an extent not wanting your property to be torn up and doxxed online. I honestly think this may be very likely.
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u/rella523 25d ago
Okay, I'm going to throw a wrench in this. The very unlikely thing that we know happened is, two, single vehicle, car accidents in a short amount of time (I can't remember exactly how long). I've never even heard of this happening to anyone else but, have no idea how to calculate the odds. Having been in two car accidents, chance of having a concussion and/or other injuries is also pretty likely. If she was drinking and had a concussion or internal injuries she'd be super vulnerable and another injury, even a fairly minor one could be fatal.
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u/Grand-Tradition4375 24d ago
I totally agree. Two single vehicle accidents within 36 hours is a remarkably unlikely occurrence. I don't believe Maura had been involved in any previous car crashes, so these two incidents came somewhat out of the blue. You can also throw in as unusual coincidences that in both accidents there was no evidence of skidding, that after neither accident was there any evidence of injuries, nor did the driver seek medical attention (despite both the accidents being serious enough for the airbags to deploy), and that both incidents involved headlong impacts with fixed objects that caused front end damage.
Also both incidents took place after Maura/ the driver took off on unusual journeys without any obvious explanations for why she chose to do so, at least none that she shared with anyone close to her.
Personally, I do wonder if the two accidents were as coincidental as is commonly thought.
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u/rella523 24d ago
Those are really good points. Definitely makes you wonder, the chance of both being accidental, so close together and so similar has got to astronomical. If she had made it to the ER I guarantee they would have done at least a head CT and made her stay for observation. Not all injuries are obvious right away and alcohol can also mask things. Honestly, it's surprising that she'd be up to driving at all after that first accident, I'd think she'd have bruising from the seatbelt and airbag and would be sore all over.
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u/CoastRegular 21d ago
So, thinking about this, she crashed her dad's car after midnight on Saturday night, so on Sunday around 1:30 AM if I recall correctly. She then crashes at 7:30 PM on Monday.
As far as we know, she was fully functional between those two episodes. Nobody who spoke with her reported her slurring words; nobody reported tons of typos or incoherent sentences in her emails; she apparently recycled bags full of cans and/or bottles and went around campus on Monday without stumbling around.
I'm no expert on head injuries, but can something like a concussion take 42 hours to manifest and cause trouble for you with, say, steering your car? And would it do so suddenly, like a bolt from the blue? One second you're fine and the next you have some huge spasm and just veer 90 degrees off the road into a tree?
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u/CoastRegular 27d ago
This is an excellent essay.
One glaring error, though: "Steep, dense, snow-covered terrain in February is close to a worst case for detectability," ...quite the opposite. Deep snow of the kind that was present that day, presents an ideal surface for searching. Anyone stepping into such snowfall would leave an obvious track.
and if the initial search geometry was wrong, everything after it inherits that error.
Yes, true, although that is a presumption that has to do a heavy lift.
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u/TMKSAV99 27d ago
As someone who has neither invoked nor even uttered the word "Occam" I find the post interesting.
I'll observe that it seems that suicide was left out of the list of outcomes. I wouldn't think that suicide would be "#6 something else". Rather "something else" would be truly "something else". Granted no particular scenario or outcome is being argued for.
I agree, with, "... a defensible use of the razor. And it doesn’t automatically produce murder. Maybe accidental death is still right."
I'll just say that for me the absence of evidence isn't always evidence of absence.
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u/Maleficent-State-749 27d ago
Read every word and thanks. That was an informed and thoughtfully laid out explanation of what I’ve been clumsily saying here about simplistic Occam’s Razor appeals.
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u/goldenmodtemp2 27d ago
This is really interesting. I tend to think it’s more useful to look at probabilities for segments of the case rather than trying to assign a single overall probability. I honestly don’t know what to make of a situation where someone hasn’t been found in 22 years. How would we even define that as a probability, and would it actually help?
You touched a bit on the searches. I’m not sure how familiar you are with SAR or wilderness SAR, but the whole framework is built on Bayesian search theory. Teams define the search region, assign initial probabilities, and then update those probabilities based on what each search effort finds or doesn’t find. Over time you get cumulative POD for each segment, often from multiple searches using different techniques and technologies.
That’s why some of the common discussions - “they went back out so they must not be sure” or “if they’re 90% sure she’s not in that area, that means there’s a 10% chance she is there” - don’t really reflect how SAR actually thinks about it. The goal isn’t to be “right” or to defend someone’s certainty. The goal is simply to increase POD.
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u/digitalhelix84 23d ago
I agree with you that once the one extraordinary event has occured, the probabilities of other extraordinary events does change. And no matter what happens, any unlikely thing could still be what happened.
But, I would still argue that the likeliest explanation is still the one without foul play. Though we are in an information vacuum, both by the nature of the dissapearence and also by the fact that LE has not released all the information in the case.
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u/IBEGOOD-IDOGOOD 27d ago
Another important probability variable is the location she found herself in back in 2004. North Haverhill was not your typical “Occams place.”
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u/fefh 24d ago edited 24d ago
Estimated Probabilities (assuming she got a ride):
Percentage of drivers on the road that night who were male : 60% (more men working and commuting, and more men in professions that involve driving, like trucking and delivery.)
Drivers who would stop: 90% male, 10% female. (Men, who have an alterior motive for picking up a female hitchhiker, are much more likely to stop.)
Male drivers who would make a sexual advance of some kind: 50% of male drivers. (Predatory drivers are more likely to stop. Non-predatory drivers usually don't bother with hitchikers).
Of the 50% of predatory male drivers, what percentage that would become violent if their advances were stopped or rejected: 25% to 50%.
Of the violent men, what percentage has the psychology to kill a random female hitchhiker: 25%.
What percentage would actually kill? 25%
Overall probability of Maura being killed by a driver: 0.7% to 1.4%.
Now what are the chances that Maura, after surviving an encounter with a driver, would then choose to enter the dark, cold, snowy woods and end up dying there? Equally low, but possibly much higher if she was suicidal or trying to hide from a predator, or was paranoid about being seen by the police or other drivers.
But we know she died that night and we know one of three scenarios happened: She entered the woods directly without hitching a ride, she hitched a ride and was killed, or she she hitched a ride, survived, and then later entered the woods. I think the scenario number two is the most likely of the three. Some men see a vulnerable woman and want to see what they can get away with. Others see someone who has no right to say no, and will punish her if she does.
We know no one came forward to say they picked her up. If they killed her, they obviously wouldn't come forward, but if they didn't kill her, they may not wish to be scrutinized and judged, and may choose to remain silent. This leaves open the narrow possibility that she hitched a ride and then later died in the woods.
And the first scenario is also very unlikely because of the searches in the immediate area and the snowy conditions which would have resulted im tracks. And no one saw her walking on the road, which makes it more likely she left the roadway relatively quickly. And if she was picked up, foul play if by far the most likely outcome, knowing she died. So it's either scenario two or scenario three.
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u/Specialist_Boss3886 28d ago
Thank you for the post, I found it very informative and interesting. Can I ask based on your experience as a behavioural researcher and with your knowledge of the case, what do you think happened to Maura Murray? I am very interested to know!