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Estimating the chances of something that hasn’t happened yet

johndcook.com

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Re: Estimating the chances of something that hasn’t happened yet

#51

Post by Waterluvian »

comboy wrote: post #40
JoshuaDavid wrote: post #35

Earlier quoted context omitted.

Let's say there are 6 trials -- name them x1, x2, x3, y1, y2, y3. In the case of checking if x is faster than y 3 times, you're doing x1 In the case of checking if all three measurements of x are smaller than all three measurements of y, you're checking x1 In other words, the latter case is checking whether the slowest x of three trials is faster than the fastest y of three trials.

You're right. I actually edited before you replied. Should have deleted it or preferably think more before typing. But now it's forever.

I'm glad you kept it. The explanation was enlightening to me.

Re: Estimating the chances of something that hasn’t happened yet

#52

Post by J_cst »

rspeer wrote: post #21

If the author is reading this: When someone provides you a pro-bono translation, by all means credit them, but do not let them host it on their own site. Frequently, they are siphoning your PageRank. They will eventually replace the translation with monetized content of their choice. A good translation takes work! If you got a translation for free, why should you believe it's good, or that it has no ulterior motive?…

I am Italian and can confirm that the translation is perfectly fine. At the very beginning of the translation, in italics, the translator states that he follows Endeavour because on that blog he finds interesting articles about statistics and programming. After that he gives full credit to the author and back links the original post. To me there's nothing of suspicious or malicious.

Re: Estimating the chances of something that hasn’t happened yet

#53

Post by [deleted] »

jedberg wrote: post #34
ajkjk wrote: post #15

So basically the '3' comes entirely from the choice of a 95% confidence interval. If you want a 99% confidence interval it's instead the 'rule of 4.6', which doesn't roll off the tongue as well.

You could do the 'rule of 5' though and have a confidence of 99.3%, which is pretty close to 99.

[deleted]

Re: Estimating the chances of something that hasn’t happened yet

#54

Post by nkurz »

chowchowchow wrote: post #41
yummybear wrote: post #23

Earlier quoted context omitted.

In the same vein if the weather is good today, there is s large probability that it’s good tomorrow, but if it’s been good for 14 days there is an increasing probability of bad weather.

Why would this be true? What if we, by luck, had 14 days of good weather at the end of monsoon season? Your observation seems to be a function of the probabilities changing as the calendar date advances and not a historical run of good weather in the past.

Why would this be true?

It's not impossible, just location dependent. In some places, there actually is a clear cycle, where the weather alternates between good and bad on a weekly cycle. The Bay Area of California, where HN is headquartered, seems to be one of those places:

The Fog Cycle

Week by week from spring into August, the forces that produce the fog increase in intensity. The Pacific High moves farther north, closer to the latitude of San Francisco, sending out stronger winds; offshore the up-welling of cold bottom waters increases, condensing the winds’ moisture into thicker masses of fog; in the Central Valley, the northward-moving sun sends temperatures to the 100 degree mark and beyond. The hot air rises, sucking cool masses in great drafts through the only break in the Valley’s surrounding mountains, San Francisco Bay. With the ocean air comes the fog, evaporating gradually in the hot, dry air of the Valley, but sometimes penetrating at night as far as Sacramento and Stockton.

The fog seems to come and go in cycles. Until recent years, the conventional explanation for the fog’s behavior was a simple one: as the cool, fog-bearing ocean air is pulled over the coastal hills and across the Bay toward the hot Central Valley (that is, from a high-pressure to a low-pressure area), the nearest parts of the Valley begin to cool off after a few days, much as a draft from an open door lowers the temperature in a warm room.

The incoming cool, heavy sea air replaces the warm, rising land air, and temperatures in Sacramento and Stockton may drop from well above 100 degrees to the “cool” 90s. When the Valley cools sufficiently, the fog-producing machinery breaks down. Without the intense Valley heat to draw the sea air in through the Bay Region, the wind diminishes and no longer carries the fog inland. San Francisco, the Golden Gate, and the coastline are fog free.

Then the process starts all over again. Without the incoming wind and fog, the sun gradually reheats the Valley. The rising warm air again begins to attract the foggy marine air inland. The result is a fog cycle of about a week in length, producing roughly three or four days of fog over the Bay and three or four days of sun.

https://baynature.org/article/cutting-through-the-fog/

Re: Estimating the chances of something that hasn’t happened yet

#55

Post by exp1orer »

citilife wrote: post #29

I've seen a very similar problem to this referred to as "black swan events"[1]. The whole point is you can't actually compute it. You see the period, it's there. What he's doing here isn't science, it's a guess. As others have pointed it, it's rather rare that events happen with perfectly distributed probability (probably the opposite). For instance, the chance of being in an accident is much higher if an accident ju…

> it's better to say you don't know than guess wildly.

> although I don't have any statistics to back me up, I'd guess that most events happen in clusters

More seriously, yes, before you apply this rule you should think about whether "each event has the same probability of error" is appropriate for your situation.

Re: Estimating the chances of something that hasn’t happened yet

#56

Post by nitwit005 »

madrox wrote: post #14

What the author glosses over somewhat is the method of sampling. If you read the first 20 pages, find no typos, and use this rule to arrive at 15%, that could be way off. He's assuming the risk of typos are evenly distributed when there's a lot of reasons it may not be. For example, the first half of the book could've been more heavily proof-read than the latter half. It's not out of the question that editors get laz…

Doesn't the book example need to factor in the book length? If you read 20 pages, and it's 20 pages long, you should be 100% confident, but if you read 20 pages and it's 5000 pages long, your confidence should be near 0.

Re: Estimating the chances of something that hasn’t happened yet

#57

Post by neolefty »

jedberg wrote: post #34
ajkjk wrote: post #15

So basically the '3' comes entirely from the choice of a 95% confidence interval. If you want a 99% confidence interval it's instead the 'rule of 4.6', which doesn't roll off the tongue as well.

You could do the 'rule of 5' though and have a confidence of 99.3%, which is pretty close to 99.

If you're truly estimating, though, wouldn't you use a 50% confidence interval — which gives you the rule of 1 (chances of the thing being true are 1/n — if you've seen 20 pages without a typo, chances are 1/20 that there's a typo on a page, with 50% confidence)?

Re: Estimating the chances of something that hasn’t happened yet

#58

Post by rspeer »

J_cst wrote: post #52
rspeer wrote: post #21

If the author is reading this: When someone provides you a pro-bono translation, by all means credit them, but do not let them host it on their own site. Frequently, they are siphoning your PageRank. They will eventually replace the translation with monetized content of their choice. A good translation takes work! If you got a translation for free, why should you believe it's good, or that it has no ulterior motive?…

I am Italian and can confirm that the translation is perfectly fine. At the very beginning of the translation, in italics, the translator states that he follows Endeavour because on that blog he finds interesting articles about statistics and programming. After that he gives full credit to the author and back links the original post. To me there's nothing of suspicious or malicious.

I'm glad that this is a good example of a translation, and not a trick.

I still think that if a blog post author says "this is a translation of my post", the author should host it as a sibling page on their own server. That allows them to more reliably vouch for its content, and removes an avenue that can be used for trickery.

Re: Estimating the chances of something that hasn’t happened yet

#59

Post by whack »

In the example given, the author says that the odds of a given page having a typo is less than 3/20. Sure, but if we don't want a range, but an exact number? That sounds like a more interesting challenge to me.

Formal statement:

- You have observed N events, with 0 occurrences of X

- Someone wants to make a bet with you about the likelihood of X happening

- Once you've quoted a number, your counter-party then has the option of making an even bet about whether the actual likelihood is greater than or less than your prediction

Eg: If you predict 3/N using a 95% confidence interval, then 95% of the time, the actual likelihood will be less than 3/N. Your counterparty will then win the bet 95% of the time, simply by predicting it to be lower.

Your ideal strategy would be to quote a likelihood which is over/under 50% of the time, not 95%.

Ie, you want to pick E such that 50% of the time, it matches the observation you've made (no occurrences), and 50% of the time it does not.

E^N = 0.5

N log E = log 0.5

log E == log 0.5 / N

E = 0.5^(1/N)

For the example given, that comes out to 0.966. Ie, there's a 96.6% chance of no typos in a given page. Across 20 pages, this comes out to 0.966^20 => 50% chance of no typos. If your goal is to quote the single best estimate which can hold up well in a betting market, I believe this would be the ideal strategy

Re: Estimating the chances of something that hasn’t happened yet

#60

Post by mihaifm »

If you’re wondering where does the formula (1-p)^n come from, it’s a number often used in gambling (if I throw a die 7 times, what are the chances of getting at least a 3). The probability of an event having probability p happening after n trials is 1-(1-p)^n, and he’s using the inverse of that.

https://en.m.wikipedia.org/wiki/Binomial_distribution

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