Tag: Probability

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The Secretary Problem

Optimal stopping
for sexist scenarios –
an odd solution.

The Secretary Problem is the ‘fear of missing out’ in mathematical form. It encompasses the idea of deciding when to stop looking through a list of options when you can’t go back to a previously dismissed option and don’t know what future options might hold. It presents the scenario that you’re hiring a secretary and want to hire the very best. You consider each candidate in turn and must decide to hire or reject them immediately after their interview. You know how good they are and how good all those applicants before them were but you’ve no way of knowing how good the remaining applicants are – the best may be yet to come. When do you hire someone, when do you decide which is best?

It’s a problem involving optimal stopping theory – choosing when to take an action to maximise the expected reward and/or minimise the expected cost. When do you stop rejecting applicants to get the best secretary?

The shortest proof to the problem is the odds algorithm devised by F. Thomas Bruss in 2000. The proof equates to the idea that when hiring a secretary under the strict conditions of the problem, you should view a certain number of applicants and then hire the next applicant that scores higher than any of those. The number of applicants to reject first is defined by ~ n/e where n is the total number of applicants and e is the base of the natural logarithm. This proof of the problem is likely to select the single best applicant from the total pool of applicants around 37% of the time, regardless of how many applicants there are.

Curiously The Secretary Problem has been known by a number of different names, most of which involve men picking between women in some way: the marriage problem, the sultan’s dowry problem, the fussy suitor problem, the googol game, and the best choice problem.

Further reading:

Bruss, 2000, Sum the odds to one and stop – https://doi.org/10.1214%2Faop%2F1019160340

The Secretary Problem – https://en.wikipedia.org/wiki/Secretary_problem

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The Born Rule by Alicia Sometimes

wave functions are squared
amplitudes oscillating
predictions            likely

By Alicia Sometimes

The Born Rule — a formula for assigning outcome probabilities — is extremely complex for someone like me who hasn’t studied physics but I am intrigued in its history and its purpose.

Marc-Oliver Pleinert et al. (2020) test Born’s law using many-particle interferences. This article Mysterious Quantum Rule Reconstructed From Scratch by Philip Ball was inspiring and helped me navigate some intricacies of the Born Rule and put it in a wider context.

Original research: https://doi.org/10.1103/PhysRevResearch.2.012051

Alicia Sometimes is an Australian poet, writer and broadcaster. She has performed her spoken word and poetry at many venues, festivals and events around the world. Her poems have been in Best Australian Science Writing, Best Australian Poems and more. She is director and co-writer of the art/science planetarium shows, Elemental and Particle/Wave. She is currently a Science Gallery Melbourne ‘Leonardo’ (creative advisor). Her TedxUQ talk in 2019 was about the passion of combining art with science. You can catch up with her on Twitter @aliciasometimes and at her website www.aliciasometimes.com

Enjoyed Alicia’s sciku? Check out her other poems ‘Antimatter’ and ‘Axiogenesis‘.

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Whale strike

To avoid striking
whales, great creatures of the sea,
use the app. Impact!

Blue whales can be injured or killed in collisions with ships, particularly in regions where migration routes cross shipping lanes. Yet because they travel huge distances, predicting where whales will be at any given time is difficult. However, now research by Abrahms et al (2019) suggests that statistical modelling techniques may be able to help.

The researchers used satellite tracking data from 104 blue whales across 14 years along with daily information on three-dimensional oceanic habitats to model the whales’ daily distribution. By using an ensemble modelling approach they were able to produce daily, year-round predictions of blue whale habitat suitability in the Californian Current Ecosystem.

The statistical approach allows the researchers to quantify the spatial and temporal distribution of exposure to ship strike risk within shipping lanes in the Southern California Bight. The researchers plan on converting this approach into a downloadable app which would alert ships to the risks of whale collision and could recommend alternative shipping lanes or vessel slow-downs.

It’s a truly fascinating piece of research that seems likely to have a huge impact upon a real-world problem – research at its best.

The sciku also includes a line from Mr Scruff’s truly excellent track ‘Shanty Town’ from his ‘Keep It Unreal’ album released in 1999. The full line is ‘Whales! Great creatures of the sea! Please listen to me!’ It’s well worth checking out!

Original research: http://dx.doi.org/10.1111/ddi.12940

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Consequences

Curb carbon outputs

or face the consequences:

Falling stock prices.

 

We often hear about the environmental benefits of companies reducing their carbon outputs. Generally, however, little happens in business without consideration of the subsequent monetary impacts, and many companies have been slow to change their ways for little apparent financial incentive.

New research by Fang et al (2018) explores the impacts of companies not acting within the emission-intensive sector in North America. The researchers examined the risk factors of climate change on investment portfolios, both directly (e.g. physical risk to properties) and indirectly (e.g. as a result of stricter environmental regulations). They found that companies that don’t take steps to reduce their carbon output could be affected by stock price depreciation and asset devaluation within a decade. Such findings will hopefully prompt more action on curbing carbon emissions.

Original research: http://dx.doi.org/10.1080/20430795.2018.1522583

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With enough data by John Norwood

With enough data

A narrow majority

Becomes certainty

 

This sciku has to do with probability theory used in data science and machine learning. In a nutshell, the more data you have, the lower the uncertainty of your model and the smaller the bias needed to reliably predict an eventual outcome. This paper by Dolev et al (2010) geeks out on some of the technical details of purifying data and machine learning.

Original research: https://doi.org/10.1145/1953563.1953567

John Norwood is a Mechanical Engineer working with Carbon, Inc. to revolutionize how things are made. His interests include old houses, yoga, baking, cryptography, and bluegrass music. You can follow him on Twitter under the handle @pryoga

Enjoyed this sciku? Check out some of John’s other work: The answer is none, God may be defined, Rivers cut corners, and Squeamish ossifrage.