Tag: Statistics

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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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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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Authorship

Who wrote Beowulf?
Look for stylistic changes –
a single author?

Beowulf is one of the most well-known examples of Old English literature and debate has raged over whether the poem was written by a single author or combined from multiple sources. New research by Neidorf et al (2019) lends support to the single author theory.

Beowulf survives in a single manuscript that has been dated to around AD 1000. Using a statistical approach called stylometry the researchers analysed features of the writing, comparing the poem’s metre, word choices, letter combinations and sense pauses – small pauses between clauses and sentences. They found no evidence for any major stylistic shifts across the poem suggesting that Beowulf is the work of a single author.

Original research: http://dx.doi.org/10.1038/s41562-019-0570-1

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Weak spots in science

Weak spots in science:

Error, bias, misconduct.

Solutions proposed.

 

Modern science is not perfect, like any area it is subject to human errors, biases and instances of misconduct, accidental or otherwise. The underlying principles of science aim to avoid these problems, trying to achieve the golden ideal of accurate, impartial and trustworthy hypothesis testing. It is crucial then that these weak spots are recognised and addressed in order to avoid these potential pitfalls.

Jelte M. Wicherts (2017) has written a fascinating review of contemporary science, its weak spots and potential solutions. Problems discussed include p-hacking, post-hoc hypothesizing, outcome switching, selective reading and reporting, human error and various biases. Solutions such as increased transparency, data sharing and improved training are suggested. Whilst examples are taken from animal welfare research, the article is well worth a read for all scientists and anyone else interested in the scientific method.

Original research: http://dx.doi.org/10.3390/ani7120090

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Is ‘P’ suitable?

Refine and reduce

for animal welfare, but

is ‘P’ suitable?

 

Statistics and animal welfare might seem like unlikely bedfellows but a greater understanding of statistics may actually improve animal welfare. The 3Rs – Replacement, Reduction and Refinement – are critical for the ethical use of animals in experiments, but sometimes the animal species concerned cannot be replaced with a more ethical substitute. Refining procedures and reducing the numbers of animals tested should therefore be a fundamental consideration of any animal experiment.

Determining an appropriate sample size is often done using power analyses based around the P-value, but increasingly there is concern about the validity of this statistical term as a means of accepting or rejecting the experimental hypothesis. Instead, effect sizes and confidence intervals could be used to determine an experiment’s outcome and, in turn, minimum suitable sample size could be calculated using effect size precision. In this way statistics can be used to improve animal welfare by reducing the numbers of animals used. Sneddon et al, 2017.