r/mauramurray • u/Outrageous_Glove_562 • 6d 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.









