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sadly we were only spending a weekend at my parents house and dad insisted correctly that it had to hang for a week by which time we had gone home so we didn t even get to taste it the jt takes a look at a more conventional approach which has brought long life and health to japan i m not sure there is any particular magic ingredient it s common sense that a population which eats modest portions of fresh fish and vegetables and generally walks and cycles moderate distances rather than sitting in a car is going to be healthy the only real vices are too much salt and pickles the latter of which leads to an abnormally high rate of stomach cancer it has to be said that having to chow down a bowl of plain steamed white rice with every meal leaves me if not exactly losing the will to live certainly losing the will to eat so it s not surprising that people are so thin it s rare i see someone here who would be considered overweight in the uk on our first visit to japan jules and i each lost about half a stone in a week we now keep our weight up with a weekend diet of baked potatoes and a regular circuit of several really good restaurants mostly western style if you count a proper indian curry as such round here our canteen is really excellent actually but there s a limit to how much rice and pickles i can face in a week posted by james annan at friday february 10 2006 0 comments email this blogthis share to x share to facebook share to pinterest tuesday february 07 2006 last chance saloon after huge strings of comments most of which can be found here here and here i m still not sure that i ve made much progress in explaining how bayesian probability works and how it differs from the frequentist view i ll have one last go before i give up a man picks an apple out of a barrel and gives it to me i weigh it on a set of moderately accurate scales which give a reading of 105 5g as previously this uncertainty is assumed to be gaussian with the quoted magnitude being 1 standard deviation what is the probability that the mass of the apple is less than 100g less than 105g to a frequentist these questions are simply ill posed and no answer is possible we don t know the distribution of apple masses in the barrel from which this one was sampled to a bayesian there are an infinite range of possible priors that could in principle be used to describe the initial uncertainty in the apple s mass one obvious choices would be to take it as a uniform distribution over a wide range eg 0 200g in that case the posterior pdf for the apple s mass is the gaussian distribution n 105 5 and the two probabilities requested are 16 and 50 respectively another plausible prior would be to use our prior knowledge of the apple being a common medium sized fruit and reckon that the overall distribution of apple masses is roughly gaussian of the form n 125 20 in that case the posterior pdf of the individual apple is marginally different from before at n 106 2 4 85 and the two probabilities are 10 and 40 for the apple being less than 100g and 105g respectively for each of those answers of course there is also a perfectly straightforward frequentist interpretation consider sampling apples from the u 0 200 distribution weighing each and of those whose weight is given at 105g the distribution has the n 105 5 shape and similarly for the gaussian prior so what s the difference the only difference is someone with a bayesian approach to probability will be prepared to actually pick a prior which might be one of the above or something else and give an answer someone who claims to take a frequentist approach to probability cannot do so and indeed if a frequentist experiment is actually performed in which apples are repeatedly sampled from the barrel and weighed on scales with 5g random error then the resulting distribution of those which are measured to be 105g will not coincide exactly with the bayesian s answer unless he got very lucky and actually guessed the distribution of apples in the barrel correctly note however that in my two examples above the answers are not really so different from each other unless the prior is something really pathological like each apple in the barrel is actually less than 100g then an apple which measures 105 5g is likely to be greater than 100g likely being the ipcc definition of about 60 90 so even though the bayesian won t be exactly correct he ll probably be near enough right for his answer to be a useful basis for decision making and note that even if you decide you need a better answer and try to take a more accurate measurement you still can t get round the fact that you always need to choose a prior which will affect the answer if only marginally in the real world you might need to make a decision shall i buy the apple or reject it as potentially undersized with the available data and no opportunity to improve your observation without a bayesian approach to probability you don t have the tools to address that question at all here endeth the lesson posted by james annan at tuesday february 07 2006 19 comments email this blogthis share to x share to facebook share to pinterest monday february 06 2006 how to measure the height of a building with the help of a barometer a small twist on an old tale it s not really related to the bayesian frequentist fuss but rather this it was the end of term and the three top students one each of engineering physics and maths had one practical exam left to determine which one got the overall prize the tutor took them to a clock tower and gave each one a barometer paper and pencil your task is to determine the height of the tower in the next 2 hours you should assume a priori that it is a typical example of its type which have heights uniformly distributed in the range 20 40m we ve examined the foundations and found that they are not safe for a building of more than 30m height obviously we are very worried unless we can rule out the possibility that it exceeds 30m at the 99 level or better we ll have to spend a million pounds reinforcing it can you tell us whether this is necessary he then walked off the students sat down on the front step to think the physicist and engineer started scribbling ideas the mathematician thought for a few seconds then went off to the pub for lunch 2 hours later they all assembled at the clock tower and the tutor asked for their answers the physicist says i observed the air pressure at the bottom of the tower climbed to the top and observed the air pressure again based on the pressure difference i estimate the height to be 25 2 5m which means there is a 2 3 chance of it exceeding 30m you d better do the reinforcements all uncertainties are assumed gaussian and quoted as 1 standard deviation the engineer says i climbed to the top of the tower and dropped the barometer timing the fall with the clock based on the time it took i estimate the height to be 27 2m which means there is a 7 chance of exceeding 30m you definitely have to reinforce it the mathematician says i estimate the tower s height to be 26 2 1 56m the chance of it exceeding 30m is less than 1 let s spend the money on renovating the bar instead the physicist and engineer are aghast but we ve both proved there is a substantial chance of disaster something must be done how did the mathematician calculate her answer and was her decision the correct one if she is right what did the others do wrong updated 6 02 well this wasn t really intended as a serious problem i m sure that you all realised that the mathematician combined the previous two estimates using bayes theorem note that the question as posed specifically defines the tower as a sample from a uniform distribution so it s a perfect well posed frequentist problem and the bayesian frequentist rambling in the comments is completely misplaced the vaguely amusing point i was making is that although the engineer and physicist did nothing wrong initially and both concluded that there was a significant 1 danger as soon as each of them hears the other one agree with their conclusion their position immediately becomes untenable their only fault is to not realise this as quickly as the mathematician did posted by james annan at monday february 06 2006 22 comments email this blogthis share to x share to facebook share to pinterest sunday february 05 2006 sutaabakkusu sutaabakkusu is japanese for starbucks and i m going to come out of the closet and admit that i am a fan boo hiss i hear my reader cry why are you supporting such an evil culturally imperialistic faceless multinational corporation as it stamps its ugly jackboot in the face of timeless japanese culture and beauty it s 100 no smoking that s why one of the more annoying features of everyday japan is the omnipresence of smokers the proportion of the male population who smoke is one of the highest in the world and there s no getting away from them i wouldn t care if they kept it to themselves but they don t until recently a lot of cafes and restaurants didn t even have a no smoking section so although you might go in spot a quiet smog free corner and sit down there you would always have the risk that 5 minutes later some old man would sit right next to you and start coughing and spluttering and blowing smoke over you and your food this cigarette of damocles hanging over us is hardly conducive to a relaxing meal even when a cafe had a no smoking section it was never anything more than a few tables barely visible through the haze about as much use as a no pissing end in a swimming pool and then after we d been here for a year or so the first starbucks opened in kamakura and it was 100 no smoking there are a few tables outside for the addicts and everyone flocked there for surprisingly enough the non smokers actually outnumber the smokers and even the smokers like to sit down in a nice clean environment every now and again you must have noticed how the smoking carriages on trains are always the last to fill up with smokers preferring to sit in a non smoking area and pop out for a smoke once or twice there was an article about the success of starbucks in the jt a couple of years ago ok here it is i remember thinking at the time that the author was astonishingly out of touch in the way he seemed to think that their growth was despite rather than substantially because of their no smoking policy perhaps in his sneering superiority he had never actually been to one maybe he is one of the addicts for whom clean air is an unwelcome assault on the senses maybe he is just a nutcase anyway the rest of japan is scrabbling to follow in starbucks footsteps with no smoking areas now springing up all over the place even the newly rebranded in house japanrailways becks cafes haunt of the haggard overworked salaryman now generally have large well segregated no smoking areas the small branch in ofuna station is 100 no smoking for at least part of the day our favourite restaurant is also fully no smoking it s the best indian restaurant in japan so be sure to try it out when you re in the area there are still plenty of smoky dives to be found but they are slowly dying out i d prefer it if they went no smoking themselves but as it is when i want a coffee or a snack i look out for the green and white sign recently a new and even better starbucks has opened in kamakura it might have happened some time ago it s in a part of town we rarely visit west of the centre in front of the city office it s a big bright airy building and even has a view into a garden so i can often be found there on a sunday morning worshipping the roasted bean at the church of st arbucks in fact i wrote most of this blog there who s for a green tea jelly frappuccino with whipped cream and caramel update 5 2 06 and i d just like to mention that british style pub the tavern in yokohama has just implemented a no smoking side too which is great news the owner said that far from chasing away customers it had proved a great success so far with the bar splitting the room into 2 sections it looks like the smoke free part should stay fairly clear the pub does good british style food so it will be much improved without someone puffing away right next to us i know i ll be more likely to pop in for a drink and a bite to eat thanks john posted by james annan at sunday february 05 2006 0 comments email this blogthis share to x share to facebook share to pinterest friday february 03 2006 woohoo our latest paper was just accepted by grl i think the contents may be of general interest so i ll be blogging about it some time soon when i m less tired and emotional those who are interested in the meantime will find it on my work web page posted by james annan at friday february 03 2006 12 comments email this blogthis share to x share to facebook share to pinterest thursday february 02 2006 probability prediction and verification v commotion in the comments well having posted what i thought was an interesting but essentially uncontentious discussion of bayesian and frequentist approaches to probability i was rather surprised to see the reaction in the comments i m going to pick primarily on wolfgang at first because he has given his opinions most explicitly which exposes the inconsistencies most clearly from what i can glean of their comments i think the others are displaying similarly inconsistent attitudes however he starts out in physics statements about probability makes sense in two cases i quantum theory ii systems where we do not know the initial state exactly in all cases we must be confident about the theory kinematics and dynamic otherwise the use of probability is misleading probability is not a good replacement for missing or wrong theories your example of the prime number illustrates this very well i could perhaps quibble over exactly what is meant by we do not know the initial state exactly but this looks like it is at least trying to be a fundamentally frequentist position fine if that s what he really wants but later on i pose the following problem in the comments to cip s post nb the electron neutrino is just some arbitrary poorly known particle i am assuming the wikipedia page is reasonably valid when it says its mass is thought to lie between 0 1ev and 2 5ev but note that even this statement is only meaningful in a bayesian worldview say you are trying to measure the mass of the electron neutrino one possible experiment costs 1 million and would work down to 0 5ev another possible experiment would cost 10 million but would work to 0 1ev you have other demands on the money do you consider there is any information in the above that can help you choose one experiment rather than the other do you consider that questions along the lines of how likely do i think it is that the mass of the neutrino is less that 0 5ev are even legitimate in the first place or do you simply reject that as an ill posed question if that is the case how do you actually make the decision in pract...
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