- Patterns of Prediction: 100 posts
- Digital clock strikes 00:33:00
- Counting by palindromes starts a new K*
- Sequence of palindromes starts its last "patch"
before increasing in length
Historical backgroundBody mass index (BMI) is a value derived from the mass (weight) and height of a person. The BMI is defined as the body mass divided by the square of the body height, and is expressed in units of kg/sq.m, resulting from mass in kilograms and height in metres.
The BMI may be determined using a table or chart which displays BMI as a function of mass and height using contour lines or colours for different BMI categories, and which may use other units of measurement (converted to metric units for the calculation).
The BMI is a convenient rule of thumb used to broadly categorise a person as underweight, normal weight, overweight, or obese based on tissue mass (muscle, fat, and bone) and height. Commonly accepted BMI ranges are underweight (under 18.5 kg/sq.m), normal weight (18.5 to 25 kg/sq.m), overweight (25 to 30 kg/sq.m), and obese (over 30 kg/sq.m).
BMIs under 20 and over 25 have been associated with higher all-causes mortality, with the risk increasing with distance from the 20–25 range.
Limitations and "misuse"Wikipedia wrote:Adolphe Quetelet, a Belgian astronomer, mathematician, statistician, and sociologist, devised the basis of the BMI between 1830 and 1850 as he developed what he called "social physics".
The modern term "body mass index" (BMI) for the ratio of human body weight to squared height was coined in a paper published in the July 1972 edition of the Journal of Chronic Diseases by Ancel Keys and others. In this paper, Keys argued that what he termed the BMI was "...if not fully satisfactory, at least as good as any other relative weight index as an indicator of relative obesity".
Consideration of mathematical features of the BMI helps to show why it is unsuitable for application to individuals:Wikipedia wrote:The interest in an index that measures body fat came with observed increasing obesity in prosperous Western societies. Ancel Keys explicitly judged BMI as appropriate for population studies and inappropriate for individual evaluation. Nevertheless, due to its simplicity, it has come to be widely used for preliminary diagnoses. Additional metrics, such as waist circumference, can be more useful.
Measures of predictive capacity and relevant criticisms based on scientific studies are being reported. For instance:Wikipedia wrote:BMI of an individual is proportional to mass and inversely proportional to the height squared. So, if all body dimensions double, and mass scales naturally with height cubed, then BMI doubles instead of remaining the same. This results in taller people having a reported BMI that is uncharacteristically high, compared to their actual body fat levels. In comparison, the Ponderal index is based on the natural scaling of mass with height cubed.
However, many taller people are not just "scaled up short people", but tend to have narrower frames in proportion to their height. Carl Lavie has written: "The B.M.I. tables are excellent for identifying obesity and body fat in large populations, but they are far less reliable for determining fatness in individuals."
Body Image StigmaHealthline wrote: .
Is BMI a good indicator of health?
Despite concerns that BMI doesn’t accurately identify whether a person is healthy, most studies show that a person’s risk of chronic disease and premature death does increase with a BMI lower than 18.5 (“underweight”) or above 30.0 (“obese”).
For example, a 2017 retrospective study of 103,218 deaths found that those who had a BMI of 30.0 or greater (“obese”) had 1.5–2.7 times greater risk of death after a 30-year follow-up.
Another study showed that those in the “obese” BMI category had a 20% increased risk of death from all causes and heart disease, compared with those in the “normal” BMI category.
The researchers also found that those who were either in the “underweight” or “severely obese” and “extremely obese” categories died an average of 6.7 years and 3.7 years earlier, respectively, compared with those in the “normal” BMI category.
Other studies have shown that a BMI greater than 30.0 begins to significantly increase your risk of chronic health issues, such as type 2 diabetes, heart disease, breathing difficulties, kidney disease, non-alcoholic fatty liver disease, and mobility issues.
Furthermore, a 5–10% reduction in a person’s BMI has been associated with decreased rates of metabolic syndrome, heart disease, and type 2 diabetes.
Due to most research showing an increased chronic disease risk among people with obesity, many health professionals can use BMI as a general snapshot of a person’s risk. Still, it should not be the only diagnostic tool used.
Though BMI has been criticised for its oversimplification of health, most research supports its ability to estimate a person’s risk of chronic disease, particularly one’s risk of early death and metabolic syndrome.
/RogerEhealth.gov.au wrote: .
Determinants of heath, including weight status, involve complex interactions between multi-level factors including policy, community, socio-demographic, psychosocial, family and genetic influences. Awareness of weight stigma can help health professionals to provide care that recognises the complexity of these interacting factors and removes inadvertent blame from the individual for less desirable health outcomes. Among the general population, weight stigma is a recognised risk factor for adverse psychological and physical health issues, which can exacerbate unhealthy eating behaviours (such as binge eating) and weight gain (Yazdizadeh et al 2020).
There is evidence of perceived weight stigma felt by women receiving pregnancy care (regardless of their size) (Bombak et al 2016); (Incollingo Rodriguez et al 2019). This can be tied to the fact that high weight status has been linked to adverse pregnancy outcomes. High gestational weight gain has also been linked to increased vulnerability to weight stigmatisation (Incollingo Rodriguez et al 2019). Evidence from non-pregnant populations highlight the potential for stigma to reinforce an unhealthy weight gain cycle (Tomiyama 2014).
FootnoteRogerE wrote: ↑03 May 2021 03:24Consider a race of some sort in which there are 12 competitors. Before the race we don't know how it will turn out, but after the race is over we can assign the number 1 to the winner, 2 to the runner-up, 3 to third place-getter, and so on, down to 12 for the last competitor to finish. The correct sequence for the first three competitors is therefore (1, 2, 3).
Now suppose several people tried to predict the first three place-getters, in correct order:
• Prediction A actually selected (2, 3, 4). That is, the competitor predicted to place first actually placed second, the predicted second place-getter actually finished third, and the competitor predicted to place third actually finished fourth.
• Prediction B actually selected (3, 2, 1).
• Prediction C actually selected (1, 3, 10).
How should those three predictions be ranked, best to worst? How do you decide?
I thought about this problem, and came up with several different ways of comparing predictions, but I wasn't convinced that any of my methods was very satisfactory...
Altogether there are 12 x 11 x 10 = 1320 possible predictions of the first three place-getters. The very best prediction would be (1, 2, 3), and the very worst prediction would be (12, 11, 10). I wonder if there is a satisfactory/satisfying way to rank all 1320 possible predictions.
Of course, we could simply prescribe some rule(s), and say that those wishing to make competitive predictions will simply have to accept that their predictions will be ranked as prescribed. That would allow the best predictor to be identified, but it might still not be a satisfactory/satisfying ranking when viewed objectively...
A lesser objective might be to find a way to rank predictions that would allow some predictions to be ranked as "of equal merit" rather than insisting on a ranking that takes any two predictions and always ranks one as better than the other [a "linear ordering"]. But it still seems difficult to come up with a "partial ordering" which is satisfactory/satisfying. For instance, a rule which says "(1, 2, 3) is the best prediction, and all other possible predictions are equally bad" certainly manages to rank the possible predictions. However, it wouldn't satisfy the participants, especially not someone who predicted (1, 2, 4) when comparing with A, B or C above.
How would you rank (1, 2, 4) in comparison with (1, 3, 2)?
When it comes to the various topics in math (algebra, logic, calculus, etc), probability would be my worst.RogerE wrote: ↑07 May 2021 03:06Rank predictions of Race Results: a Proposed Formula cont.
Comparing some larger prediction lists
Here are a few sample prediction lists for the first six place-getters in a race:
How would you rank them (from most successful, down to least successful)?
.Prediction list A = (3, 2, 5, 1, 6, 4)
Prediction list B = (3, 4, 1, 2, 5, 6)
Prediction list C = (2, 3, 1, 5, 6, 4)
Prediction list D = (3, 1, 6, 2, 4, 5)
Prediction list E = (6, 1, 2, 4, 5, 3)
Prediction list F = (5, 6, 1, 2, 3, 4)
Prediction list G = (5, 2, 1, 4, 3, 6)
Let X < Y mean that prediction list X is less successful than prediction list Y.
That notation will give us a compact way of summarising the results.
Payoffs for prediction lists A–G
Using the formula proposed in the previous post, we find that
.A = (3, 2, 5, 1, 6, 4) has payoff P(A) = 53.93.
B = (3, 4, 1, 2, 5, 6) has payoff P(B) = 53.44
C = (2, 3, 1, 5, 6, 4) has payoff P(C) = 67.50
D = (3, 1, 6, 2, 4, 5) has payoff P(D) = 66.67
E = (5, 6, 1, 2, 3, 4) has payoff P(E) = 44.02
F = (6, 1, 2, 4, 5, 3) has payoff P(F) = 69.04
G = (5, 2, 1, 4, 3, 6) has payoff P(G) = 62.16
It turns out that A and B are very close in their level of success. Lists C, D, F, G are fairly close, but all are clearly better than A and B. List E is evidently inferior to the other five lists. The payoffs reflect how well the contestants selected to finish #1, #2, #3 actually performed.
Resultant ranking of prediction lists A–G
How does this compare with your intuitive ranking of those prediction lists?
I hope some of our readers will post a thoughtful comment or two.
Another delightful line:There is the persistent tale that 42 is Adams' tribute to the indefatigable paperback book, and is the average number of lines on an average page of an average paperback. Another common guess is that 42 refers to the number of laws in cricket, a recurring theme of the books.
A fine discussion for enthusiasts and admirers (and the source of the quotes above) isJohn Lloyd, Adams' collaborator on The Meaning of Liff and two Hitchhiker's fits, said that Adams has called 42 "the funniest of the two-digit numbers."
Apophenia /æpoʊˈfiːniə/ is the tendency to perceive meaningful connections between unrelated things.
The term (German: Apophänie) was coined by psychiatrist Klaus Conrad in his 1958 publication on the beginning stages of schizophrenia. He defined it as "unmotivated seeing of connections [accompanied by] a specific feeling of abnormal meaningfulness". He described the early stages of delusional thought as self-referential, over-interpretations of actual sensory perceptions, as opposed to hallucinations.
Apophenia has come to imply a human propensity to seek patterns in random information, such as gambling.
Here's a plot of the catalogue values (pooled data from four different catalogues) of the post-war Malaya coconut definitives against the quantity printed and the denomination, and for both explanatory variables, the response variable (catalogue price) has a few very high values and many low values.
Automated pattern recognition can be a powerful tool for analytical philately as well. For example, computer vision can be used to automatically detect and measure the shape, size and location of perfin holes:RogerE wrote: ↑30 Jan 2021 14:18Pattern Recognition
Pattern recognition is a topic relevant to this thread.
In fact, it is two topics, both relevant to this thread!
The Wikipedia article entitled Pattern recognition begins with the introductory noteSo, here I want to discuss Pattern recognition as a branch of engineering/computer science. The Wikipedia link just cited is the source of the quotations included here.This article is about pattern recognition as a branch of engineering. For the cognitive process, see Pattern recognition (psychology). For other uses, see Pattern recognition (disambiguation).
What is Automated Pattern Recognition?
Pattern recognition is the automated recognition of patterns and regularities in data.
It has applications in statistical data analysis, signal processing, image analysis, information retrieval, bioinformatics, data compression, computer graphics and machine learning.
Pattern recognition has its origins in statistics and engineering. Some modern approaches to pattern recognition include the use of machine learning, due to the increased availability of big data and a new abundance of processing power. However, these activities can be viewed as two facets of the same field of application, and together they have undergone substantial development over the past few decades.
A modern definition of pattern recognition is:
The field of pattern recognition is concerned with the automatic discovery of regularities in data through the use of computer algorithms and with the use of these regularities to take actions such as classifying the data into different categories. [Bishop, Christopher M. (2006). Pattern Recognition and Machine Learning. Springer]
Thus, in the conventional parsing notation in use in India, the predicted total is 72,00,000Wikipedia wrote:A lakh /læk, lɑːk/; abbreviated L; sometimes written lac, is a unit in the Indian numbering system equal to one hundred thousand (100,000; scientific notation: 10^5). In the Indian 2,2,3 convention of digit grouping, it is written as 1,00,000.
/RogerE["Score" comes] from Old Norse skor "mark, notch, incision; a rift in rock".
The connecting notion probably is counting large numbers (of sheep, etc.) with a notch in a stick for each 20. That way of counting, called vigesimalism, also exists in French. In Old French, "twenty" (vint) or a multiple of it could be used as a base, as in vint et doze("32"), dous vinz et diz ("50"). Vigesimalism was or is a feature of Welsh, Irish, Gaelic and Breton (as well as non-IE Basque), and it is speculated that the English and the French picked it up from the Celts.
Henrich coined the acronymHow does the culture we live in influence our psychology, motivation and decision making? Joe Henrich was a cultural anthropologist working in the Amazon when he first tried to find out...
He realised that his findings have big implications for psychological research, which tends to focus on students from Western backgrounds. In 2010, he introduced the "WEIRD" concept to describe the unusual psychology of the subjects in the majority of these studies.
Now professor of human evolutionary biology at Harvard University, he tells New Scientist about the origins of WEIRDness, its impact on history and its role in the modern world.
On the downsides of WIERDness, Henrich says:[Two cultural psychologists and I] noticed that in the behavioural sciences, and psychology in particular, about 96 per cent of study participants were from Western, Educated, Industrialised, Rich and Democratic societies — and that they were often psychological outliers in comparison with other populations.
WEIRD people tend to show greater trust in strangers and fairness towards anonymous others; think more analytically rather than holistically; make more use of intentions in moral judgements; are more concerned with personality, the self and the cultivation of personal attributes; they are more individualistic and less loyal to their group; and they are more likely to judge the behaviour of others as reflecting some enduring disposition rather than temporary situational factors.
A key summary statement from Henrich:In societies where there is a strong sense of kinship, like Fiji where I have done fieldwork, there is a sense of security, community, oneness — a kind of comfort that comes from the warm embrace of knowing you are at the centre of a tight web of relations who will always have your back. They aren't tied to you because you are a convenient contact or are currently smart or successful, they are tied to you in a deep way...
People living in tribal or clan-based societies also tend to see themselves as links in a chain connecting past to future, creating a sense of continuity that gives people a real sense of meaning and security.
.The picture of "human psychology" portrayed in the textbooks, and still in many journal articles, doesn't represent the psychology of Homo sapiens at all...
This bias hampers our efforts to understand the origins and nature of psychological processes and brain development. Much of what looks like reliably developing features of minds, with clear developmental trajectories over childhood, turns out to be the result of cultural products, like the institutions, values, technologies or languages individuals confront and must learn, internalise and navigate to make their way in the world. This applies not only to psychology and neuroscience... but also to aspects of human physiology, anatomy and health.
Users browsing this forum: No registered users and 1 guest