I would think its biased, but that's just a hunch. I think that while this might get you an estimate that is expected to be closest to the right number, the maximum likelihood estimate would just be the highest number you've seen.
Could we use a Poisson distribution to estimate the total number?. By taking lambda= number of captured tanks per some unit of time, then finding the value where the cumulative probability is 'close enough' to 1?
That's a good question. Suppose we captured 3 tanks with numbers x1 < x2 < x3. First gap is: (x1-0-1) Second gap is: (x2-x1-1) Third gap is: (x3-x2-1) The -1 in each gap is because we don't count the tanks themselves when calculating the gaps. Add these gaps up and divide by the number of gaps and you find some nice cancellation to get an average gap of: (x3-3)/3. So in general the formula for average gap is: (m-k)/k
ROC analysis is always introduced as a technique developed in WWII to accurately detect enemy aircraft using radar. Yet, I could never find a fabricated or real-world example problem demonstrating how it would have been used this way. I think it would help make sense of the technique, just like this video has. If only someone could find a find/make something similar, that would be awesome!
Can we rephrase that tank counting estimation as a machine learning problem of regression, like with a predicted Y, actual Y, and a dataset, with partitioning into training, validation, and new unseen data? Can we make an actual dataset -- synthetic data if necessary -- and see empirically how well the tank counting estimation does on the predictions versus actuals? I know it's nice that WW2 was won that way, but it would be nice to see, side by side, the loss on each example which was not shown in your nice video. Can a better model be found using linear regression, or a weighted m and weighted adjustment factor, or a simple (or deep) neural network that has one unit to imitate linear regression as a NN using a kit like Tensorflow? Can that tank counting estimation technique also be used to count things that are unique individuals but which have no manufacturing serial numbers, like how many fish are in a pond? Has anyone published (or just blogged) using this model design on estimating real-world things besides tanks, like what was it actually useful on? Inquiring minds want to know!
@@prasenlonikar9753 Yes I agree with you, but even just seeing empirical evidence for the presenter's thesis would be a big step forward too. No ML is needed for that. We would just borrow some methodology from ML where we check the existing model on unseen data to see if it generalizes at all.
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'Intelligence Estimates' ... now that's ironic.
I just stumbled on the German tank problem recently and searched for youtube videos on it. This one had the most views but I'm surprised it's
Aw thanks!
Ritvik! This video's clearly so engaging and deserves way more views. Well done :)
A clearer version of the formula:
m + m/k - 1
where m/k is the average interval
Hmmm. So this estimator is clearly consistent. The more tanks you capture, the closer you get to the true parameter. Is it unbiased too?
I would think its biased, but that's just a hunch. I think that while this might get you an estimate that is expected to be closest to the right number, the maximum likelihood estimate would just be the highest number you've seen.
Good video, thanks
Could we use a Poisson distribution to estimate the total number?. By taking lambda= number of captured tanks per some unit of time, then finding the value where the cumulative probability is 'close enough' to 1?
Thank you so much for this insight. I am going to use this formula in Stock options trading
Nice ! Thanks
How is the average gap approach discussed in the video earlier equate to (m-k)/k?
That's a good question. Suppose we captured 3 tanks with numbers x1 < x2 < x3.
First gap is: (x1-0-1)
Second gap is: (x2-x1-1)
Third gap is: (x3-x2-1)
The -1 in each gap is because we don't count the tanks themselves when calculating the gaps.
Add these gaps up and divide by the number of gaps and you find some nice cancellation to get an average gap of:
(x3-3)/3.
So in general the formula for average gap is:
(m-k)/k
Thx for the response..I had the same question!
@@vps071 A clearer version of the formula:
m + m/k - 1
where m/k is the average interval
I guess using probability algorithm and key fact you can sometimes come up with a pretty accurate guesstimate... Cool !
(M-k)/k is the mean gap, is it advisable to find confidence interval of the gaps based on std deviation of various gaps
ROC analysis is always introduced as a technique developed in WWII to accurately detect enemy aircraft using radar. Yet, I could never find a fabricated or real-world example problem demonstrating how it would have been used this way. I think it would help make sense of the technique, just like this video has. If only someone could find a find/make something similar, that would be awesome!
This reminds me "Tank classic 1990"
This method may provide estimate of cummulative number of tanks produced. How did they account for the tanks destroyed out of those produced?
Good question. Maybe we can simulate a destruction rate of the tanks, and see for ourselves if it has an effect on the prediction quality.
Can we rephrase that tank counting estimation as a machine learning problem of regression, like with a predicted Y, actual Y, and a dataset, with partitioning into training, validation, and new unseen data?
Can we make an actual dataset -- synthetic data if necessary -- and see empirically how well the tank counting estimation does on the predictions versus actuals? I know it's nice that WW2 was won that way, but it would be nice to see, side by side, the loss on each example which was not shown in your nice video.
Can a better model be found using linear regression, or a weighted m and weighted adjustment factor, or a simple (or deep) neural network that has one unit to imitate linear regression as a NN using a kit like Tensorflow?
Can that tank counting estimation technique also be used to count things that are unique individuals but which have no manufacturing serial numbers, like how many fish are in a pond?
Has anyone published (or just blogged) using this model design on estimating real-world things besides tanks, like what was it actually useful on?
Inquiring minds want to know!
I'd like to try this. Make a ML or DL model for more accurate estimation
@@prasenlonikar9753 Yes I agree with you, but even just seeing empirical evidence for the presenter's thesis would be a big step forward too. No ML is needed for that. We would just borrow some methodology from ML where we check the existing model on unseen data to see if it generalizes at all.
interesting!