This (the ignoring of cost) seems like a flaw to Bayesian analysis, and makes me think there's probably some extension to it, which is being omitted here for simplicity, but which takes into account something like cost, value, or utility.

For example, the "cost" of a bayesian filter deciding to show a salesman a spam email is far lower than the "cost" of the same filter deciding to prevent them from seeing an email from a million-dollar sales lead.

So, while the calculation of probabilities should not take into account cost, it feels like the making decisions of based on those probabilities should take cost into account.

For example: the chances of our getting wiped out in the near future by a natural disaster. Yet, the potential consequences are dire, and the net costs per person of detection are low, or even negative. Therefore, we have a global near-earth-object detection network, a tsunami and quake detection network, fire watch towers, weather and climate monitors, disease tracking centers, and so on.

If this extension to Bayesian analysis exists, this seem a sensible place to link to it.

Does "sure" mean 100% confidence? If so, is this a correct statement?

Or would it be more correct to say: - we're extraordinarily confident that Newton's gravitation is close to correct, - we're extraordinarily confident that Einstein's gravitation is even closer, - we're mildly confident that we will find no closer theories, though one alternative to explaining dark matter would be modified gravitation, so we're considerably less confident than we would be if there were no known evidence suggesting inaccuracies in Einstein's gravitation, by a factor of P(Einstein|DarkMatter).

This UI could perhaps do with a flag meaning something like "this bit of writing is particularly meritorious, thought-inspiring, smile-creating: strive to retain in future edits if possible".

"you're allowed to increase P(BadDriver) a little bit,"

No, you're really not.

You're only allowed to replace P(BadDriver) with P(BadDriver|HadOneAccident).

If you have a second accident, you replace that in turn with P(BadDriver|HadOneAccident^HadASecondAccident), which if you are rational you might reexamine and update to P(BadDriver|HadTwoAccidents^HadQuiteALotOfNearMissesIfWeAreBeingHonest)

But my point is, when applying each new piece of evidence, you have to remember the conditions that caused you to get your current probability, or you end up with naive Bayes and after seeing a few new bookcases you believe in aliens.

From earlier pages, this will be harder than it initially appears.

Say that, on hearing there was a dagger, the king also ponders what other things an assassin might carry. Poisons, for sure - an assassin would have them like 6:1 odds at least, and a non-assassin would be surely no more than 0.02:1.

Listening devices, for spying and stuff. Probably 4:1 and 0.02:1 again.

Naive Bayesian analysis would say that doctors, with their knives and stethoscopes and drugs, would be carrying tools with odds of 9 * 6 * 4 : 1 = 216 : 1 if they were an assassin, and 0.02 * 0.02 * 0.3 = 0.00012 : 1 if they were not.

It's very easy to forget that "updated odds" are also "updated conditions". The king has not updated his odds of that person being an assassin; they have replaced their odds of "the person" being an assassin, with some new odds of "the person with the knife" being an assassin.

Subsequent odds need to be added in that light. The need to accurately track the decreasing weight of subsequent pieces of evidence feels like it is unlikely to be intuitively grasped by most.

Arguendo: more random non-common latin. Consider "For the sake of argument" or "Perhaps"

Be wary here.

We see on the next (log probability) that a plethora of small evidences sums to a very large number of bits.

In the bookcase aliens example, if you went to 312 houses and found that every one of them had a new bookcase, then by this approach, it's time to reexamine the aliens hypothesis.

In practice, it's just simply not. Aliens are still just as unlikely as they were previously. New bookcases are now more likely.

It's time to reexamine your 50:1 in favor of aliens estimate for a new bookcase. It's time to check whether there's a really good door-to-door bookcase salesman offering ridiculous deals in the area. Or whether there are new tax incentives for people with more bookcases. Or a zillion other far more likely things than the false dichotomy of "either each person bought bookcases independently with odds of 50:1 against, or it's bookcase aliens."

The corollary of Doyle's "Once you eliminate the impossible, whatever remains, no matter how improbable, must be the truth" is "make damn sure to eliminate all the probable stuff, before gallivanting into the weeds of the infeasible".

"Extreme credences" here should likely be "infinite credences".

Even so, previous page made the exact counterpoint:

While strong evidence may not change your view of things, things, extreme evidence absolutely should make you revisit your estimate of even an infinite credence level.

Is "-1 against" the same as "+1 for"?

Expressing the first practical example entirely in terms of negative numbers seems like a poor pedagogical choice.

Phrasing as "3 bits against" and then "a further 1 bit against" may help.

Adding that the blue ones are not a great pick if you want pearls may help people understand the direction of "against".

Is this a probability or an odd? What's a "chance"? In this list, "chance"s are expressed both as a fraction, and as a percentage, like some kind of hybrid probablodd. This feels like muddying the waters. When you're introducing a new concept like "probability and odds, while synonyms in lay speak, are different things in statistics", it's probably not good to conflate both with another lay synonym like "chance".