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When it comes to Machine Learning, the successful application seem to be very well known. For example, Neural Networks have been successfully used to create Self Driving Cars and Game Playing Algorithms (e.g. Go, Chess).

When we think of classical statistical models such as regression model, it seems more difficult to think of equally well known and successful applications of such models.

I understand that this might be in part because Machine Learning might get more news/media attention and the problems in which Machine Learning tends to be applied in are in some ways easier to quantify success - e.g. does this neural network beat the world champion?. I also understand that Machine Learning itself is heavily rooted in statistics, e.g. PAC learnability.

But in terms of the classical statistical models such as regression, have their been any successful applications of these models on a similar scale to the successful applications of machine learning?

Thanks!

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    $\begingroup$ There are countless examples in medical science that are on a bigger scale and more valuable to humanity than self driving cars and board games. For example all clinical trials. $\endgroup$
    – Oliver882
    Aug 12 at 7:58
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    $\begingroup$ All three answers posted so far (2022-08-12) give examples from distant past, long before Machine Learning was invented. It would be interesting to see current success stories. Re: clinical trials: This is a tautology. Clinical trials are required to use statistics. I wonder whether the situation would be different if ethics committees included Machine Learning experts. $\endgroup$
    – Igor F.
    Aug 12 at 14:17
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    $\begingroup$ (-1) "It seems more difficult to think of equally well known and successful applications of such models" appears to reflect no research at all. Crack open any statistical textbook written in the last century for examples. Maybe one could discuss the degree to which statistical applications are "well known," but that would not be on topic here on CV. $\endgroup$
    – whuber
    Aug 12 at 15:16
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    $\begingroup$ For a perspective that's perhaps more nuanced that the question implies: Why games may not be the best benchmark for AI. Self-driving cars are more of a hypothetical success since we actually don't have them. $\endgroup$
    – dipetkov
    Aug 12 at 17:08
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    $\begingroup$ The contributions of machine learning are so miniscule when compared to the enormous contributions of statistics to scientific progress that one is tempted to think this could be a trick question. $\endgroup$ Aug 12 at 23:41

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The whole history of statistics is full of them. For example, $t$-tests were born in Guinness brewery as means of optimizing their processes:

T-Distribution, also known as Student's t-distribution, gets its name from William Sealy Gosset who first published it in English in 1908 in the scientific journal Biometrika using his pseudonym "Student" because his employer preferred staff to use pen names when publishing scientific papers instead of their real name, so he used the name "Student" to hide his identity. Gosset worked at the Guinness Brewery in Dublin, Ireland, and was interested in the problems of small samples – for example, the chemical properties of barley with small sample sizes.

Linear regression was discovered by Carl Friedrich Gauss to predict planetary movement in astronomy.

As about Poisson distribution...

A further practical application of this distribution was made by Ladislaus Bortkiewicz in 1898 when he was given the task of investigating the number of soldiers in the Prussian army killed accidentally by horse kicks;: 23-25  this experiment introduced the Poisson distribution to the field of reliability engineering.

Pierre-Simon Laplace applied Bayes theorem to estimate the mass of Saturn in the 1800s and his result was off just by 0.05%.

Everything in statistics was discovered for solving practical problems and they gained popularity because of proving useful.

Yes, it's not self-driving cars, but I doubt would have self-driving cars today if Gauss didn't do his research on the least squares in the 1800s. Every machine learning textbook mentions the Bayes theorem which was first studied by Thomas Bayes in the late 1700s. The examples are countless.

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The German Tank Problem is a statistical approach to estimating a population size given a sample. The goal is to estimate the total number of items $N$, given a random sample of the population which has observable serial numbers from $1$ to $N$.

The problem is so named for its real-life application, in which Allied intelligence agencies wanted to estimate the number of German tanks being produced during World War II. By observing the serial numbers on a limited number of destroyed tanks, statisticians were able to infer the total number of tanks in the population with remarkable accuracy. Post-war analysis revealed that the statistical estimates were often superior to the estimates generated from conventional intelligence methods.

Other statistics developed during wartime include the Receiver Operator Characteristic (ROC) curve, which is a means of evaluating a classifier. WWII radar operators would have to classify radar blips as either enemy planes, or false alarms like birds or weather. The development of the ROC curve allowed a principled means of evaluating the performance of an individual radar operator, indicating whether they could correctly and reliably identify enemy aircraft, or if they would require further training. The ROC curve is used in many fields from medicine to meteorology to evaluate the performance of a classification method.

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  • $\begingroup$ Particularly with this now being a community wiki, it might be best to post these as two distinct answers, one about the tanks and one about ROC curves for radar. $\endgroup$
    – Dave
    Aug 12 at 7:56
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To add some medical examples to the excellent cases already cited by others:

Richard Doll established the link between smoking and lung cancer. Although a medical doctor, the link was established using epidemiological techniques.

Florence Nightingale, the Lady of the Lamp. The common perception is that she spent nights in hospitals during the Crimean War tending to wounded soldiers. In fact, she spent her time compiling statistics that demonstrated that vastly more of deaths were caused by injury and disease rather than direct enemy action on the battle field. One of the drawings she used to illustrate her point still bears her name: the Nightingale plot. She was the first female member of the Royal Statistical Society.

John Snow identified the source of the Broad Street cholera outbreak in 1854.

The first generally recognised modern clincal trial was conducted by James Lind, a Royal Navy surgeon, who in 1747 established that lack of vitamin C was the cause of scurvy. As a result of his work, the Royal Navy began to issue a daily ration of lemons to its sailors, therby giving rise to the use of the (not very flattering in some quarters) soubriquet of "Limey" for Britons.

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Success stories of statistics are everywhere. The reason that you don't see newspaper articles about statistical success stories is not because they rarely happen; it's because they happen so often that it's not considered news.

Some examples of successful applications of statistics are:

  • Every successful scientific study involving a large number of individuals or measurements
  • Every time an organization makes a good decision based on a large amount of data
  • Every time an instrument is correctly calibrated or tested by taking a large number of measurements
  • Every time someone makes a successful prediction about the future based on a large number of things that happened in the past

And there are millions of examples of each of these.

If you want to find a statistical success story in the news, look at any news article about any great achievement. Statistics plays a role in everything.

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  • $\begingroup$ This is a good answer apart from the last paragraph, which is obviously not true. $\endgroup$
    – Oliver882
    Aug 19 at 21:30
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When we think of classical statistical models such as regression model, it seems more difficult to think of equally well known and successful applications of such models.

But in terms of the classical statistical models such as regression, have their been any successful applications of these models on a similar scale to the successful applications of machine learning?

Although there are many unsuccessful or wrong applications in science, I would say that science is for a large part a demonstration of successful applications.

To answer the question why classical models aren't often in the news, let's divide statistics in the inference and algorithmic viewpoints (Efron & Hastie, 2021) or, similarly, the prediction and explanation viewpoints (Yarkoni & Westfall, 2017). Then, your machine learning examples all belong in the prediction category. I think these obtain so much attention because they offer the basis for automated systems. Even more so, they offer automated models which companies can use to earn money with, so they are incentivized to spend money on selling the models. Conversely, successful applications of inference often do not mention the model; only the outcome.

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