伊利近山是一座相當特別的山，因為它比周圍的大廈還要矮。
在我有生之年，不知還要登上伊利近山多少次。
2010年3月27日星期六
2010年3月21日星期日
陽光下的新事
我常常跑這條路線：從勵德邨道與大坑道交界起步，沿大坑道往山上跑，在大坑道盡處轉上黃泥涌峽道，跑至最高點，然後折返。印象中，第一次跑這條路時正唸中三。廿多年來，沿路除了多了幾幢高廈、斜坡大規模修葺過以外，還有什麼大變化呢？怎麼也想不起…… 。
拿著部手機邊跑邊拍還是第一次，因為最近換了手機，之前用的都沒有拍攝功能。
很美麗的山脊線，山的另一面是香港仔：
以下照片拍得太陽下還有一個壓扁了的影像，也許是陽光穿透雲層時被折射，真不知這個現象有沒有特別的名稱，是否稱得上是海市蜃樓亦未可知：
以下照片看似平平無奇，但假如你夠細心，便會察覺太陽左邊山脊對上有一枚「幻日」﹝sun dog﹞。為了證實是幻日，我細察照片，將太陽及「疑似幻日」與周邊建築物作比對，並在地圖上定出拍照地點，再利用地圖上建築物的位置，分別定出太陽及「疑似幻日」當時的方向，量得兩條方向線的夾角為 22 度。沒有錯，當陽光穿過高雲時，光線受水平面向的六角形冰晶折射後的最少偏向角正是 22 度 ── 幻日距太陽的視角。當時看到的幻日確有如彩虹般的色譜，可惜拍下來卻不甚顯眼。
巨形的日晷：
拿著部手機邊跑邊拍還是第一次，因為最近換了手機，之前用的都沒有拍攝功能。
很美麗的山脊線，山的另一面是香港仔：
以下照片拍得太陽下還有一個壓扁了的影像，也許是陽光穿透雲層時被折射，真不知這個現象有沒有特別的名稱，是否稱得上是海市蜃樓亦未可知：
以下照片看似平平無奇，但假如你夠細心，便會察覺太陽左邊山脊對上有一枚「幻日」﹝sun dog﹞。為了證實是幻日，我細察照片，將太陽及「疑似幻日」與周邊建築物作比對，並在地圖上定出拍照地點，再利用地圖上建築物的位置，分別定出太陽及「疑似幻日」當時的方向，量得兩條方向線的夾角為 22 度。沒有錯，當陽光穿過高雲時，光線受水平面向的六角形冰晶折射後的最少偏向角正是 22 度 ── 幻日距太陽的視角。當時看到的幻日確有如彩虹般的色譜，可惜拍下來卻不甚顯眼。
巨形的日晷：
2010年3月11日星期四
Fooled by Rates and Ratios
In the book Fooled by Randomness, Nassim Nicholas Taleb wrote:
I recall that when I first came across with the subject of verification, I often mixed up rates and ratios. I later learned that false alarm ratio and false alarm rate are not the same, and hit rate and hit ratio are different. As in the above example, "rate of 5% false positive" means the false alarm rate is 5% (which is also equivalent to saying that the hit rate is 95%) whereas what the question asking is about the hit ratio (which complements the false alarm ratio).
What is more striking is that false alarm rate and false alarm ratio, both llustrates how frequent false alarm is encountered, can differ very much in number when the subject event is rare. In the given example, subject to the rate of occurrence of 1/1,000, a false alarm rate of 5% is in contrast with a false alarm ratio of over 98%!
The lesson to learn is that: when you are being told of the performance of a system by someone who throws out charts and numbers, beware of being tricked by small false alarm rate. It can be leveraged by the large number in the null-null quadrant of the contingency table to result in a large false alarm ratio.
The 2002 Nobel Prize in Economics was notable because one of the laureates Daniel Kahneman is not an economist but a psychologist. Kahneman, in collaboration with Amos Tversky, developed the Prospect Theory which is a psychologically realistic alternative to the classical Expected Utility Theory.
In their study, Kahneman and Tversky clarified the kinds of misperceptions of randomness that fuel many of the common fallacies and biases. What illustrated in the original posting of this subject is a fallacy that is commonly known as the base rate fallacy. In the legal regime, such a fallacy together with other fallacies, are collectively referred to as the prosecutor's fallacy.
I found in the behavioral literature at least forty damning examples of such acute biases, systematic departures from rational behavior widespread across professions and fields. Below is the account of a well-known test, and an embarrassing one for the medical profession. The following famous quiz was given to medical doctors (which I borrowed from the excellent Deborah Bennett's Randomness).
A test of a disease presents a rate of 5% false positives. The disease strikes 1/1,000 of the population. People are tested at random, regardless of whether they are suspected of having the disease. A patient's test is positive. What is the probability of the patient being stricken with the disease?
Most doctors answered 95%, simply taking into account the fact that the test has a 95% accuracy rate. The answer is the conditional probability that the patient is sick and the test shows it ─ close to 2%. Less than one in five professionals got it right.
I will simplify the answer (using the frequency approach). Assume no false negatives. Consider that out of 1,000 patients who are administered the test, one will be expected to be afflicted with the disease. Out of a population of the remaining 999 healthy patients, the test will identify about 50 with the disease (it is 95% accurate). The correct answer should be that the probability of being afflicted with the disease for someone selected at random who presented a positive test is the following ratio:
Number of afflicted persons / Number of true and false positives here 1 in 51.
Think of the number of times you will be given a medication that carries damaging side effects for a given disease you were told you had, when you may only have a 2% probability of being afflicted with it!
I recall that when I first came across with the subject of verification, I often mixed up rates and ratios. I later learned that false alarm ratio and false alarm rate are not the same, and hit rate and hit ratio are different. As in the above example, "rate of 5% false positive" means the false alarm rate is 5% (which is also equivalent to saying that the hit rate is 95%) whereas what the question asking is about the hit ratio (which complements the false alarm ratio).
What is more striking is that false alarm rate and false alarm ratio, both llustrates how frequent false alarm is encountered, can differ very much in number when the subject event is rare. In the given example, subject to the rate of occurrence of 1/1,000, a false alarm rate of 5% is in contrast with a false alarm ratio of over 98%!
The lesson to learn is that: when you are being told of the performance of a system by someone who throws out charts and numbers, beware of being tricked by small false alarm rate. It can be leveraged by the large number in the null-null quadrant of the contingency table to result in a large false alarm ratio.
The 2002 Nobel Prize in Economics was notable because one of the laureates Daniel Kahneman is not an economist but a psychologist. Kahneman, in collaboration with Amos Tversky, developed the Prospect Theory which is a psychologically realistic alternative to the classical Expected Utility Theory.
In their study, Kahneman and Tversky clarified the kinds of misperceptions of randomness that fuel many of the common fallacies and biases. What illustrated in the original posting of this subject is a fallacy that is commonly known as the base rate fallacy. In the legal regime, such a fallacy together with other fallacies, are collectively referred to as the prosecutor's fallacy.
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