In the grand HN tradition of being triggered by a word in the post and going off on a not-quite-but-basically-totally-tangential rant:
There’s (at least) three areas here that are footguns with these kinds of calculations:
1) 95% is usually a lot wider than people think - people take 95% as “I’m pretty sure it’s this,” whereas it’s really closer to “it’d be really surprising if it were not this” - by and large people keep their mental error bars too close.
2) probability is rarely truly uncorrelated - call this the “Mortgage Derivatives” maxim. In the family example, rent is very likely to be correlated with food costs - so, if rent is high, food costs are also likely to be high. This skews the distribution - modeling with an unweighted uniform distribution will lead to you being surprised at how improbable the actual outcome was.
3) In general normal distributions are rarer than people think - they tend to require some kind of constraining factor on the values to enforce. We see them a bunch in nature because there tends to be negative feedback loops all over the place, but once you leave the relatively tidy garden of Mother Nature for the chaos of human affairs, normal distributions get pretty abnormal.
I like this as a tool, and I like the implementation, I’ve just seen a lot of people pick up statistics for the first time and lose a finger.
jrowen 6 hours ago [-]
This jives with my general reaction to the post, which was that the added complexity and difficulty of reasoning about the ranges actually made me feel less confident in the result of their example calculation. I liked the $50 result, you can tack on a plus or minus range but generally feel like you're about breakeven. On the other hand, "95% sure the real balance will fall into the -$60 to +$220 range" feels like it's creating a false sense of having more concrete information when you've really just added compounding uncertainties at every step (if we don't know that each one is definitely 95%, or the true min/max, we're just adding more guesses to be potentially wrong about). That's why I don't like the Drake equation, every step is just compounding wild-ass guesses, is it really producing a useful number?
kqr 5 hours ago [-]
It is producing a useful number. As more truly independent terms are added, error grows with the square root while the point estimation grows linearly. In the aggregate, the error makes up less of the point estimation.
This is the reason Fermi estimation works. You can test people on it, and almost universally they get more accurate with this method.
If you got less certain of the result in the example, that's probably a good thing. People are default overconfident with their estimated error bars.
pests 3 hours ago [-]
> People are default overconfident with their estimated error bars.
You say this but yet roughly in a top level comment mentions people keep their error bars too close.
kqr 35 minutes ago [-]
Sorry, my comment was phrased confusingly.
Being overconfident with error bars means placing them too close to the point estimation, i.e. the error bars are too narrow.
bigfudge 2 hours ago [-]
They are meaning the same thing. The original comment pointed out that people’s qualitative description and mental model of the 95% interval means they are overconfident… they think 95 means ‘pretty sure I’m right’ rather than ‘it would be surprising to be wrong’
btilly 9 hours ago [-]
I strongly agree with this, and particularly point 1. If you ask people to provide estimated ranges for answers that they are 90% confident in, people on average produce roughly 30% confidence intervals instead. Over 90% of people don't even get to 70% confidence intervals.
I don't think estimation errors regarding things outside of someone's area of familiarity say much.
You could ask a much "easier"" question from the same topic area and still get terrible answers: "What percentage of blue whales are blue?" Or just "Are blue whales blue?"
Estimating something often encountered but uncounted seems like a better test. Like how many cars pass in front of my house every day. I could apply arithmetic, soft logic and intuition to that. But that would be a difficult question to grade, given it has no universal answer.
kqr 5 hours ago [-]
I have no familiarity with blue whales but I would guess they're 1--5 times the mass of lorries, which I guess weigh like 10--20 cars which I in turn estimate at 1.2--2 tonnes, so primitively 12--200 tonnes for a normal blue whale. This also aligns with it being at least twice as large as an elephant, something I estimate at 5 tonnes.
The question asks for the heaviest, which I think cannot be more than three times the normal weight, and probably no less than 1.3. That lands me at 15--600 tonnes using primitive arithmetic. The calculator in OP suggests 40--320.
The real value is apparently 170, but that doesn't really matter. The process of arriving at an interval that is as wide as necessary but no wider is the point.
Estimation is a skill that can be trained. It is a generic skill that does not rely on domain knowledge beyond some common sense.
dotaenjoyer 3 hours ago [-]
[dead]
yen223 7 hours ago [-]
I guess people didn't realise they are allowed to, and in fact are expected to, put very wide ranges for things they are not certain about.
pertdist 7 hours ago [-]
I did a project with non-technical stakeholders modeling likely completion dates for a big GANTT chart. Business stakeholders wanted probabilistic task completion times because some of the tasks were new and impractical to quantify with fixed times.
Stakeholders really liked specifying work times as t_i ~ PERT(min, mode, max) because it mimics their thinking and handles typical real-world asymmetrical distributions.
[Background: PERT is just a re-parameterized beta distribution that's more user-friendly and intuitive https://rpubs.com/Kraj86186/985700]
kqr 31 minutes ago [-]
This looks like a much more sophisticated version of PERT than I have seen used. When people around me have claimed to use PERT, they have just added together all the small numbers, all the middle numbers, and all the big numbers. That results in a distribution that is too extreme in both lower and upper bound.
baq 2 hours ago [-]
arguably this is how it should always be done, fixed durations for any tasks are little more than wishful thinking.
youainti 10 hours ago [-]
> I’ve just seen a lot of people pick up statistics for the first time and lose a finger.
I love this. I've never though of statistics like a power tool or firearm, but the analogy fits really well.
900K 1.5M # tonnes of rice per year NK gets from Russia
* 1K # kg in a tone
* 1.2K 1.4K # calories per kg of rice
/ 1.9K 2.5K # daily caloric intake
/ 25M 28M # population of NK
/ 365 # years of food this buys
/ 1% # as a percentage
kqr 5 hours ago [-]
Oh, this is very similar to what I have with Precel, less syntax. Thanks for sharing!
NunoSempere 9 hours ago [-]
Another tool in this spirit is <https://carlo.app/>, which allows you to do this kind of calculation on google sheets.
notpushkin 7 hours ago [-]
Would be a nice touch if Squiggle supported the `a~b` syntax :^)
antman 9 hours ago [-]
I tried the unsure calc and the android app and they seem to produce different results?
NunoSempere 9 hours ago [-]
The android app fits lognormals, and 90% rather than 95% confidence intervals. I think they are a more parsimonious distribution for doing these kinds of estimates. One hint might be that, per the central limit theorem, sums of independent variables will tend to normals, which means that products will tend to be lognormals, and for the decompositions quick estimates are most useful, multiplications are more common
ralferoo 42 minutes ago [-]
On the whole it seems like a nice idea, but there's a couple of weird things, such as:
> Note: If you're curious why there is a negative number (-5) in the histogram, that's just an inevitable downside of the simplicity of the Unsure Calculator. Without further knowledge, the calculator cannot know that a negative number is impossible (in other words, you can't have -5 civilizations, for example).
The input to this was "1.5~3 x 0.9~1.0 x 0.1~0.4 x 0.1~1.0 x 0.1~1.0 x 0.1~0.2 x 304~10000" - every single range was positive, so regardless of what this represents, it should be impossible to get a negative result.
I guess this is a consequence of "I am not sure about the exact number here, but I am 95% sure it's somewhere in this range" so it's actually considering values outside of the specified range. In this case, 10% either side of all the ranges is positive except the large "304~10000".
Trying with a simpler example: "1~2 x 1~2" produces "1.3~3.4" as a result, even though "1~4" seems more intuitive. I assume this is because the confidence of 1 or 4 is now only 90% if 1~2 was at 95%, but it still feels off.
I wonder if the 95% thing actually makes sense, but I'm not especially good at stats, certainly not enough to be sure how viable this kind of calculator is with a tighter range. But just personally, I'd expect "1~2" to mean "I'm obviously not 100% sure, or else I wouldn't be using this calculator, but for this experiment assume that the range is definitely within 1~2, I just don't know where exactly".
kqr 29 minutes ago [-]
The calculator in Emacs has support for what it is you request, which it calls "interval forms". Interval form arithmetic simply means executing the operations in parallel on both ends of the interval.
It also has support for "error forms" which is close to what the calculator in OP uses. That takes a little more sophistication than just performing operations on the lower and upper number in parallel. In particular, the given points don't represent actual endpoints on a distribution, but rather low and high probability events. Things more or less likely than those can happen, it's just rare.
> I'm not especially good at stats
It shows! All the things you complain about make perfect sense given a little more background knowledge.
dejongh 15 minutes ago [-]
Cool. It would be great to extend with a confidence operator. Something like:
Without default confidence:
0~9
With confidence:
0%100~9%95
We are sure it is 0 or more and we are %95 certain it is 9 or less.
Would that work?
kqr 5 hours ago [-]
I have made a similar tool but for the command line[1] with similar but slightly more ambitious motivation[2].
I really like that more people are thinking in these terms. Reasoning about sources of variation is a capability not all people are trained in or develop, but it is increasingly important.[3]
I think arbitrary distribution choice is dangerous. You're bound to end up using lots of quantities that are integers, or positive only (for example). "Confidence" will be very difficult to interpret.
Does it support constraints on solutions? E.g. A = 3~10, B = 4 - A, B > 0
I want to ask about adjacent projects - user interface libraries that provide input elements for providing ranges and approximate values. I'm starting my search around https://www.inkandswitch.com/ and https://malleable.systems/catalog/ but I think our collective memory has seen more examples.
elia_42 49 minutes ago [-]
Interesting. I like the notation and the histogram that comes out with the output. I also like the practical examples you gave (e.g. the application of the calculator to business and marketing cases). I will try it out with simple estimates in my marketing campaigns.
dmos62 2 hours ago [-]
Love it! I too have been toying with reasoning about uncertainty. I took a much less creative approach though and just ran a bunch of geometric brownian motion simulations for my personal finances [0]. My approach has some similarity to yours, though much less general. It displays the (un)certainty over time (using percentile curves), which was my main interest. Also, man, the UI, presentation, explanations: you did a great job, pretty inspiring.
”Without further knowledge, the calculator cannot know that a negative number is impossible (in other words, you can't have -5 civilizations, for example).”
Not true. If there are no negative terms, the equation cannot have negative values.
kqr 25 minutes ago [-]
The calculator cannot know whether there are no negative terms. For example, if people's net worth is distributed 0.2–400, there's likely a significant chunk of people who are, on the whole, in debt. These will be represented as a negative term, even though their distribution was characterised by positive numbers.
burning_hamster 25 minutes ago [-]
The range notation indicates 95% confidence intervals, not the minima and maxima. If the lower bounds are close enough to zero (and the interval is large enough), then there may some residual probability mass associated with negative values of the variable.
ttoinou 11 hours ago [-]
Would be nice to retransform the output into an interval / gaussian distribution
Note: If you're curious why there is a negative number (-5) in the histogram, that's just an inevitable downside of the simplicity of the Unsure Calculator. Without further knowledge, the calculator cannot know that a negative number is impossible
Drake Equation or equation multiplying probabilities can also be seen in log space, where the uncertainty is on the scale of each probability, and the final probability is the product of exponential of the log probabilities. And we wouldnt have this negative issue
hatthew 11 hours ago [-]
The default example `100 / 4~6` gives the output `17~25`
ttoinou 1 hours ago [-]
Amazing, thank you !
gregschlom 11 hours ago [-]
The ASCII art (well technically ANSI art) histogram is neat. Cool hack to get something done quickly. I'd have spent 5x the time trying various chart libraries and giving up.
smartmic 3 hours ago [-]
Here [1] is a nice implementation written in Awk. A bit rough around the edges, but could be easily extended.
On a similar note, I like the crude hand-drawn illustrations a lot. Fits the "napkin" theme.
krick 11 hours ago [-]
It sounds like a gimmick at first, but looks surprisingly useful. I'd surely install it if it was available as an app to use alongside my usual calculator, and while I cannot quite recall a situation when I needed it, it seems very plausible that I'll start finding use cases once I have it bound to some hotkey on my keyboard.
This is neat! If you enjoy the write up, you might be interested in the paper “Dissolving the Fermi Paradox” which goes even more on-depth into actually multiplying the probability density functions instead of the common point estimates. It has the somewhat surprising result that we may just be alone.
https://qalculate.github.io can do this also for as long as I've used it (only a couple years to be fair). I've got it on my phone, my laptop, even my server with apt install qalc. Super convenient, supports everything from unit conversion to uncertainty tracking
The histogram is neat, I don't think qalc has that. On the other hand, it took 8 seconds to calculate the default (exceedingly trivial) example. Is that JavaScript, or is the server currently very busy?
usgroup 59 minutes ago [-]
I think the SWI Prolog clpBNR package is the most complete interval arithmetic system. It also supports arbitrary constraints.
I assume this is a montecarlo approach? (Not to start a flamewar, at least for us data scientists :) ).
kccqzy 14 hours ago [-]
Yes it is.
porridgeraisin 13 hours ago [-]
Can you explain how? I'm an (aspiring)
kccqzy 13 hours ago [-]
I didn't peruse the source code. I just read the linked article in its entirety and it says
> The computation is quite slow. In order to stay as flexible as possible, I'm using the Monte Carlo method. Which means the calculator is running about 250K AST-based computations for every calculation you put forth.
So therefore I conclude Monte Carlo is being used.
constantcrying 12 hours ago [-]
Line 19 to 21 should be the Monte-Carlo sampling algorithm. The implementation is maybe a bit unintuitive but apparently he creates a function from the expression in the calculator, calling that function gives a random value from that function.
hawthorns 11 hours ago [-]
It's dead simple. Here is the simplified version that returns the quantiles for '100 / 2 ~ 4'.
import numpy as np
def monte_carlo(formula, iterations=100000):
res = [formula() for _ in range(iterations)]
return np.percentile(res, [0, 2.5, \*range(10, 100, 10),
97.5, 100])
def uncertain_division():
return 100 / np.random.uniform(2, 4)
monte_carlo(uncertain_division, iterations=100000)
marcodiego 11 hours ago [-]
I put "1 / (-1~1)" and expected something around - to + infinty. It instead gave me -35~35.
I really don't known how good it is.
NunoSempere 9 hours ago [-]
I'm guessing this is not an error. If you divide 1/normal(0,1), the full distribution would range from -inf to inf, but the 95% output doesn't have to.
SamBam 8 hours ago [-]
I don't quite understand, probably because my math isn't good enough.
If you're treating -1~1 as a normal distribution, then it's centered on 0. If you're working out the answer using a Monte Carlo simulation, then you're going to be testing out different values from that distribution, right? And aren't you going to be more likely to test values closer to 0? So surely the most likely outputs should be far from 0, right?
When I look at the histogram it creates, it varies by run, but the most common output seems generally closest to zero (and sometimes is exactly zero). Wouldn't that mean that it's most frequently picking values closest to -1 or 1 denoninator?
pyfon 8 hours ago [-]
Only 1 percent of values would end up being 100+ on a uniform distribution.
For normal it is higher but maybe not much more so.
etbebl 6 hours ago [-]
OK, but do we necessarily just care about the central 95% range of the output? This calculation has the weird property that values in the tails of the input correspond to values in the middle of the output, and vice versa. If you follow the intuition that the range you specify in the input corresponds to the values you expect to see, the corresponding outputs would really include -inf and inf.
Now I'm realizing that this doesn't actually work, and even in more typical calculations the input values that produce the central 95% of the output are not necessarily drawn from the 95% CIs of the inputs. Which is fine and makes sense, but this example makes it very obvious how arbitrary it is to just drop the lowermost and uppermost 2.5%s rather than choosing any other 95/5 partition of the probability mass.
lswainemoore 7 hours ago [-]
That may be true, but if you look at the distribution it puts out for this, it definitely smells funny. It looks like a very steep normal distribution, centered at 0 (ish). Seems like it should have two peaks? But maybe those are just getting compressed into one because of resolution of buckets?
This is awesome. I used Causal years ago to do something similar, with perhaps slightly more complex modelling, and it was great. Unfortunately the product was targeted at high paying enterprise customers and seems to have pivoted into finance now, I've been looking for something similar ever since. This probably solves at least, err... 40~60% of my needs ;)
nritchie 10 hours ago [-]
Here (https://uncertainty.nist.gov/) is another similar Monte Carlo-style calculator designed by the statisticians at NIST. It is intended for propagating uncertainties in measurements and can handle various different assumed input distributions.
your_challenger 5 hours ago [-]
Very cool. This can also be used for LLM cost estimation. Basically any cost estimation I suppose. I use cloudflare workers a lot and have a few workers running for a variable amount of time. This could be useful to calculate a ball park figure of my infra cost. Thank you!
kccqzy 14 hours ago [-]
I actually stumbled upon this a while ago from social media and the web version has a somewhat annoying latency, so I wrote my own version in Python. It uses numpy so it's faster. https://gist.github.com/kccqzy/d3fa7cdb064e03b16acfbefb76645... Thank you filiph for this brilliant idea!
13 hours ago [-]
omoikane 11 hours ago [-]
If I am reading this right, a range is expressed as a distance between the minimum and maximum values, and in the Monte Carlo part a number is generated from a uniform distribution within that range[1].
But if I just ask the calculator "1~2" (i.e. just a range without any operators), the histogram shows what looks like a normal distribution centered around 1.5[2].
Shouldn't the histogram be flat if the distribution is uniform?
> Range is always a normal distribution, with the lower number being two standard deviations below the mean, and the upper number two standard deviations above. Nothing fancier is possible, in terms of input probability distributions.
nkron 5 hours ago [-]
Really cool! On iOS there's a noticeable delay when clicking the buttons and clicking the backspace button quickly zooms the page so it's very hard to use. Would love it in mobile friendly form!
constantcrying 12 hours ago [-]
An alternative approach is using fuzzy-numbers. If evaluated with interval arithmetic you can do very long calculations involving uncertain numbers very fast and with strong mathematical guarantees.
It would especially outperform the Monte-Carlo approach drastically.
sixo 11 hours ago [-]
This assumes the inputs are uniform distributions, or perhaps normals depending on what exactly fuzzy numbers mean. M-C is not so limited.
constantcrying 11 hours ago [-]
No. It assumes the numbers aren't random at all.
Although fuzzy-number can be used to model many different kinds of uncertainties.
This is more limited. I just tested and for one example, exponentiation seems not to be supported.
vortico 10 hours ago [-]
Cool! Some random requests to consider: Could the range x~y be uniform instead of 2 std dev normal (95.4%ile)? Sometimes the range of quantities is known. 95%ile is probably fine as a default though.
Also, could a symbolic JS package be used instead of Monte-Carlo? This would improve speed and precision, especially for many variables (high dimensions).
Could the result be shown in a line plot instead of ASCII bar chart?
I was looking for this. Seen it (or a similar tool) ages ago.
Want to use it every 3 months or so to pretend that we know what we can squeeze in the roadmap for the quarter.
12 hours ago [-]
ashu1461 9 hours ago [-]
So is it 250k calculations for every approximation window ? So i guess it will only be able to calculate upto 3-4 approximations comfortably ?
Any reason why we kept it 250k and now a lower number like 10k
alexmolas 13 hours ago [-]
is this the same as error propagation? I used to do a lot of that during my physics degree
constantcrying 12 hours ago [-]
It doesn't propagate uncertainty through the computation, but rather treats the expression as a single random variable.
lorenzowood 7 hours ago [-]
See also Guesstimate https://getguesstimate.com. Strengths include treating label and data as a unit, a space for examining the reasoning for a result, and the ability to replace an estimated distribution with sample data => you can build a model and then refine it over time. I'm amazed Excel and Google Sheets still haven't incorporated these things, years later.
montag 6 hours ago [-]
Thank you, I would have mentioned this myself, but forgot the name of it.
shubhamintech 3 hours ago [-]
love it! gonna use this instead of calculating my own extremes now
alex-moon 10 hours ago [-]
> The UI is ugly, to say the least.
I actually quite like it. Really clean, easy to see all the important elements. Lovely clear legible monospace serif font.
throwanem 14 hours ago [-]
I love this! As a tool for helping folks with a good base in arithmetic develop statistical intuition, I can't think offhand of what I've seen that's better.
rao-v 14 hours ago [-]
This is terrific and it’s tempting to turn into a little python package. +1 for notation to say it’s ~20,2 to mean 18~22
po1nt 2 hours ago [-]
I love it! Now I need it in every calculator
croisillon 12 hours ago [-]
i like it and i skimmed the post but i don't understand why the default example 100 / 4~6 has a median of 20? there is no way of knowing why the range is between 4 and 6
constantcrying 12 hours ago [-]
The chance of 4~6 being less than 5 is 50%, the chance of it being greater is also 50%. The median of 100/4~6 has to be 100/5.
>there is no way of knowing why the range is between 4 and 6
??? There is. It is the ~ symbol.
perching_aix 12 hours ago [-]
how do you mean?
vessenes 12 hours ago [-]
cool! are all ranges considered poisson distributions?
re 12 hours ago [-]
No:
> Range is always a normal distribution, with the lower number being two standard deviations below the mean, and the upper number two standard deviations above. Nothing fancier is possible, in terms of input probability distributions.
chris_wot 10 hours ago [-]
There's an amazing scene in "This is Spinal Tap" where Nigel Tufnel had been brainstorming a scene where Stonehenge would be lowered from above onto the stage during their performance, and he does some back of the envelope calculations which he gives to the set designer. Unfortunately, he mixes the symbol for feet with the symbol for inches. Leading to the following:
In the grand HN tradition of being triggered by a word in the post and going off on a not-quite-but-basically-totally-tangential rant:
There’s (at least) three areas here that are footguns with these kinds of calculations:
1) 95% is usually a lot wider than people think - people take 95% as “I’m pretty sure it’s this,” whereas it’s really closer to “it’d be really surprising if it were not this” - by and large people keep their mental error bars too close.
2) probability is rarely truly uncorrelated - call this the “Mortgage Derivatives” maxim. In the family example, rent is very likely to be correlated with food costs - so, if rent is high, food costs are also likely to be high. This skews the distribution - modeling with an unweighted uniform distribution will lead to you being surprised at how improbable the actual outcome was.
3) In general normal distributions are rarer than people think - they tend to require some kind of constraining factor on the values to enforce. We see them a bunch in nature because there tends to be negative feedback loops all over the place, but once you leave the relatively tidy garden of Mother Nature for the chaos of human affairs, normal distributions get pretty abnormal.
I like this as a tool, and I like the implementation, I’ve just seen a lot of people pick up statistics for the first time and lose a finger.
This is the reason Fermi estimation works. You can test people on it, and almost universally they get more accurate with this method.
If you got less certain of the result in the example, that's probably a good thing. People are default overconfident with their estimated error bars.
You say this but yet roughly in a top level comment mentions people keep their error bars too close.
Being overconfident with error bars means placing them too close to the point estimation, i.e. the error bars are too narrow.
You can test yourself at https://blog.codinghorror.com/how-good-an-estimator-are-you/.
> Heaviest blue whale ever recorded
I don't think estimation errors regarding things outside of someone's area of familiarity say much.
You could ask a much "easier"" question from the same topic area and still get terrible answers: "What percentage of blue whales are blue?" Or just "Are blue whales blue?"
Estimating something often encountered but uncounted seems like a better test. Like how many cars pass in front of my house every day. I could apply arithmetic, soft logic and intuition to that. But that would be a difficult question to grade, given it has no universal answer.
The question asks for the heaviest, which I think cannot be more than three times the normal weight, and probably no less than 1.3. That lands me at 15--600 tonnes using primitive arithmetic. The calculator in OP suggests 40--320.
The real value is apparently 170, but that doesn't really matter. The process of arriving at an interval that is as wide as necessary but no wider is the point.
Estimation is a skill that can be trained. It is a generic skill that does not rely on domain knowledge beyond some common sense.
Stakeholders really liked specifying work times as t_i ~ PERT(min, mode, max) because it mimics their thinking and handles typical real-world asymmetrical distributions.
[Background: PERT is just a re-parameterized beta distribution that's more user-friendly and intuitive https://rpubs.com/Kraj86186/985700]
I love this. I've never though of statistics like a power tool or firearm, but the analogy fits really well.
- for command line, fermi: https://git.nunosempere.com/NunoSempere/fermi
- for android, a distribution calculator: https://f-droid.org/en/packages/com.nunosempere.distribution...
People might also be interested in https://www.squiggle-language.com/, which is a more complex version (or possibly <https://git.nunosempere.com/personal/squiggle.c>, which is a faster but much more verbose version in C)
```
5M 12M # number of people living in Chicago
beta 1 200 # fraction of people that have a piano
30 180 # minutes it takes to tune a piano, including travel time
/ 48 52 # weeks a year that piano tuners work for
/ 5 6 # days a week in which piano tuners work
/ 6 8 # hours a day in which piano tuners work
/ 60 # minutes to an hour
```
multiplication is implied as the default operation, fits are lognormal.
900K 1.5M # tonnes of rice per year NK gets from Russia
* 1K # kg in a tone
* 1.2K 1.4K # calories per kg of rice
/ 1.9K 2.5K # daily caloric intake
/ 25M 28M # population of NK
/ 365 # years of food this buys
/ 1% # as a percentage
> Note: If you're curious why there is a negative number (-5) in the histogram, that's just an inevitable downside of the simplicity of the Unsure Calculator. Without further knowledge, the calculator cannot know that a negative number is impossible (in other words, you can't have -5 civilizations, for example).
The input to this was "1.5~3 x 0.9~1.0 x 0.1~0.4 x 0.1~1.0 x 0.1~1.0 x 0.1~0.2 x 304~10000" - every single range was positive, so regardless of what this represents, it should be impossible to get a negative result.
I guess this is a consequence of "I am not sure about the exact number here, but I am 95% sure it's somewhere in this range" so it's actually considering values outside of the specified range. In this case, 10% either side of all the ranges is positive except the large "304~10000".
Trying with a simpler example: "1~2 x 1~2" produces "1.3~3.4" as a result, even though "1~4" seems more intuitive. I assume this is because the confidence of 1 or 4 is now only 90% if 1~2 was at 95%, but it still feels off.
I wonder if the 95% thing actually makes sense, but I'm not especially good at stats, certainly not enough to be sure how viable this kind of calculator is with a tighter range. But just personally, I'd expect "1~2" to mean "I'm obviously not 100% sure, or else I wouldn't be using this calculator, but for this experiment assume that the range is definitely within 1~2, I just don't know where exactly".
It also has support for "error forms" which is close to what the calculator in OP uses. That takes a little more sophistication than just performing operations on the lower and upper number in parallel. In particular, the given points don't represent actual endpoints on a distribution, but rather low and high probability events. Things more or less likely than those can happen, it's just rare.
> I'm not especially good at stats
It shows! All the things you complain about make perfect sense given a little more background knowledge.
Without default confidence: 0~9
With confidence: 0%100~9%95
We are sure it is 0 or more and we are %95 certain it is 9 or less.
Would that work?
I really like that more people are thinking in these terms. Reasoning about sources of variation is a capability not all people are trained in or develop, but it is increasingly important.[3]
[1]: https://git.sr.ht/~kqr/precel
[2]: https://entropicthoughts.com/precel-like-excel-for-uncertain...
[3]: https://entropicthoughts.com/statistical-literacy
https://en.wikipedia.org/wiki/Interval_arithmetic
I think arbitrary distribution choice is dangerous. You're bound to end up using lots of quantities that are integers, or positive only (for example). "Confidence" will be very difficult to interpret.
Does it support constraints on solutions? E.g. A = 3~10, B = 4 - A, B > 0
I want to ask about adjacent projects - user interface libraries that provide input elements for providing ranges and approximate values. I'm starting my search around https://www.inkandswitch.com/ and https://malleable.systems/catalog/ but I think our collective memory has seen more examples.
[0] https://dmos62.github.io/personal-financial-growth-simulator...
Not true. If there are no negative terms, the equation cannot have negative values.
[1] https://github.com/stefanhengl/histogram
Consider https://f-droid.org/en/packages/com.nunosempere.distribution...
> 0.4.0
> BRAKING: x~y (read: range from x to y) now means "flat distribution from x to y". Every value between x and y is as likely to be emitted.
> For normal distribution, you can now use x+-d, which puts the mean at x, and the 95% (2 sigma) bounds at distance d from x.
https://github.com/filiph/unsure/blob/master/CHANGELOG.md#04...
https://arxiv.org/abs/1806.02404
The histogram is neat, I don't think qalc has that. On the other hand, it took 8 seconds to calculate the default (exceedingly trivial) example. Is that JavaScript, or is the server currently very busy?
https://github.com/ridgeworks/clpBNR
https://github.com/filiph/unsure/blob/master/lib/src/calcula...
I assume this is a montecarlo approach? (Not to start a flamewar, at least for us data scientists :) ).
> The computation is quite slow. In order to stay as flexible as possible, I'm using the Monte Carlo method. Which means the calculator is running about 250K AST-based computations for every calculation you put forth.
So therefore I conclude Monte Carlo is being used.
I really don't known how good it is.
If you're treating -1~1 as a normal distribution, then it's centered on 0. If you're working out the answer using a Monte Carlo simulation, then you're going to be testing out different values from that distribution, right? And aren't you going to be more likely to test values closer to 0? So surely the most likely outputs should be far from 0, right?
When I look at the histogram it creates, it varies by run, but the most common output seems generally closest to zero (and sometimes is exactly zero). Wouldn't that mean that it's most frequently picking values closest to -1 or 1 denoninator?
For normal it is higher but maybe not much more so.
Now I'm realizing that this doesn't actually work, and even in more typical calculations the input values that produce the central 95% of the output are not necessarily drawn from the 95% CIs of the inputs. Which is fine and makes sense, but this example makes it very obvious how arbitrary it is to just drop the lowermost and uppermost 2.5%s rather than choosing any other 95/5 partition of the probability mass.
But if I just ask the calculator "1~2" (i.e. just a range without any operators), the histogram shows what looks like a normal distribution centered around 1.5[2].
Shouldn't the histogram be flat if the distribution is uniform?
[1] https://github.com/filiph/unsure/blob/123712482b7053974cbef9...
[2] https://filiph.github.io/unsure/#f=1~2
> Range is always a normal distribution, with the lower number being two standard deviations below the mean, and the upper number two standard deviations above. Nothing fancier is possible, in terms of input probability distributions.
It would especially outperform the Monte-Carlo approach drastically.
Although fuzzy-number can be used to model many different kinds of uncertainties.
It seems to break for ranges including 0 though
100 / -1~1 = -3550~3500
I think the most correct answer here is -inf~inf
Someone also turned it into the https://github.com/rethinkpriorities/squigglepy python library
Want to use it every 3 months or so to pretend that we know what we can squeeze in the roadmap for the quarter.
Any reason why we kept it 250k and now a lower number like 10k
I actually quite like it. Really clean, easy to see all the important elements. Lovely clear legible monospace serif font.
>there is no way of knowing why the range is between 4 and 6
??? There is. It is the ~ symbol.
> Range is always a normal distribution, with the lower number being two standard deviations below the mean, and the upper number two standard deviations above. Nothing fancier is possible, in terms of input probability distributions.
https://www.youtube.com/watch?v=Pyh1Va_mYWI
Means "100 divided by some number between 4 and 6"