bayes theorem
https://plus.maths.org/content/taxonomy/term/249
enMaths in a minute: Bayes' theorem
https://plus.maths.org/content/maths-minute-bayes-theorem
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Rachel Thomas </div>
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<p>It would be foolish to ignore evidence. Luckily Bayes' theorem shows us how to take it in into account.</p>
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Suppose that a particular type of cancer affects 1% of the population. There is a test for this cancer but it's not perfect: although the test gives a positive result for 90% of people who have the cancer, it also gives a positive result for 5% of the people who are cancer-free. You have just received a positive test result – what is the probability you have cancer?
</p><p><a href="https://plus.maths.org/content/maths-minute-bayes-theorem" target="_blank">read more</a></p>https://plus.maths.org/content/maths-minute-bayes-theorem#commentsbayes theoremconditional probabilityFP-belowMaths in a minutemedical statisticsMon, 25 Jan 2016 14:26:40 +0000Rachel6521 at https://plus.maths.org/contentUnderstanding uncertainty: ESP and Bayes
https://plus.maths.org/content/understanding-uncertainty-esp-and-bayes
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Kevin McConway </div>
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<p>In the previous article we looked at a psychological study which claims to provide evidence that certain types of extra-sensory perception exist, using a statistical method called significance testing. But do the results of the study really justify this conclusion?</p>
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<div align="center" style="margin:auto;width:400px; font-size:15; border: #9a7a9f 2px solid; padding:5px;">This article has been adapted from material on the <a href="http://understandinguncertainty.org/node/1286">Understanding Uncertainty website</a>.</div> <p><a href="https://plus.maths.org/content/understanding-uncertainty-esp-and-bayes" target="_blank">read more</a></p>https://plus.maths.org/content/understanding-uncertainty-esp-and-bayes#commentsbayes theoremconditional probabilityp-valueprobabilitypsychologysignificance teststatisticsunderstanding uncertaintyMon, 15 Oct 2012 15:48:39 +0000mf3445782 at https://plus.maths.org/contentThe logic of drug testing
https://plus.maths.org/content/logic-drug-testing
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John Haigh </div>
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<p>London 2012 vowed to be the cleanest Olympics ever, with more than 6,000 tests on athletes for performance enhancing drugs. But when an athlete does fail a drug test can we really conclude that they are cheating? John Haigh does the maths.</p>
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<p><em> London 2012 vowed to be the cleanest Olympics ever, with more than 6,000 tests on athletes for performance enhancing drugs. But when an athlete does fail a drug test can we really conclude that they are cheating? John Haigh does the maths. (You can also look at the <a href="https://plus.maths.org/content/logic-drug-testing#animation">animation below</a> to see the results illustrated.)</em></p><p><a href="https://plus.maths.org/content/logic-drug-testing" target="_blank">read more</a></p>https://plus.maths.org/content/logic-drug-testing#commentsbayes theoremconditional probabilityfalse positivemathematics in sportolympicsThu, 02 Aug 2012 10:23:50 +0000mf3445757 at https://plus.maths.org/contentUnderstanding uncertainty: how psychic was Paul?
https://plus.maths.org/content/understanding-uncertainty-how-psychic-paul-octopus
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David Spiegelhalter </div>
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<p>England's performance in the World Cup last summer was thankfully overshadowed by the attention given to Paul the octopus, who was reported as making an unbroken series of correct predictions of match winners. David Spiegelhalter looks at Paul's performance in an attempt to answer the question that (briefly) gripped the world: was Paul psychic?</p>
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<p> </p> <div style="text-align:center;margin-right: auto; margin-left: auto; width: 90%; font-size: 15px; border: 2px solid #9a7a9f; padding: 5px;">This article is adapted from material on the <a href="http://understandinguncertainty.org">Understanding Uncertainty website</a>.</div><p> </p><p><a href="https://plus.maths.org/content/understanding-uncertainty-how-psychic-paul-octopus" target="_blank">read more</a></p>https://plus.maths.org/content/understanding-uncertainty-how-psychic-paul-octopus#commentsbayes theoremCMSconditional probabilitymathematics in sportprobabilityunderstanding uncertaintyFri, 08 Oct 2010 10:47:02 +0000mf3445319 at https://plus.maths.org/contentOuter space: Thinking inside the box
https://plus.maths.org/content/os/issue55/outerspace/index
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John D. Barrow </div>
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<p>It's Monty Hall, only better!</p>
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<p>After my book <A href="http://www.rbooks.co.uk/product.aspx?id=1847920039"><i>100 Essential Things You Didn't Know You Didn't Know</i></a> was published I received lots of emails and letters asking about some of the mathematical applications and issues that appeared there. One topic was overwhelmingly the most common. Some people didn't understand it; others didn't believe it. Some puzzled correspondents were just interested readers, but at least one was a very famous professor of physics.<p><a href="https://plus.maths.org/content/os/issue55/outerspace/index" target="_blank">read more</a></p>https://plus.maths.org/content/os/issue55/outerspace/index#comments55bayes theoremouterspacethree door problemMon, 12 Jul 2010 16:17:37 +0000mf3445230 at https://plus.maths.org/contentIt's a match!
https://plus.maths.org/content/os/issue55/features/dnacourt/index
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Philip Dawid and Rachel Thomas </div>
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<p>"It's a match!" cries the CSI. At first glance it might seem that if the police have matched a suspect's DNA to evidence from the crime scene, then the case is closed. But some statistical thinking is required to understand exactly what a match is, and importantly, how juries should assess this as part of the evidence in a trial.</p>
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<p><br /><br /></p><p><a href="https://plus.maths.org/content/os/issue55/features/dnacourt/index" target="_blank">read more</a></p>https://plus.maths.org/content/os/issue55/features/dnacourt/index#comments55bayes theoremDNADNA evidencedna profilestatisticsStatistics in courtMon, 12 Jul 2010 11:28:32 +0000mf3445222 at https://plus.maths.org/contentSurvival odds: are all soldiers equal?
https://plus.maths.org/content/os/latestnews/jan-apr10/army/index
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<p>Being killed in a peacekeeping mission apparently depends on your nationality, at least if you're a soldier in the Spanish army. On the 1st of February 2010 the Colombian soldier John Felipe Romero serving in the Spanish army was killed in a terrorist attack in Afghanistan. It was then made public that so far 43% of the Spanish troops killed in attacks by local forces in Afghanistan and Lebanon have been foreigners. This is in striking contrast to the fact that foreign nationals make up only 7% of the Spanish army as a whole.</p>
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https://plus.maths.org/content/understanding-uncertainty
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Marianne Freiberger </div>
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What's the risk of passive smoking? Or climate change? How big is the terrorist threat? And should we trust league tables? These issues concern all of us, but it's not always easy to make sense of the barrage of media information. <b>David Spiegelhalter</b>, Winton Professor for the Public Understanding of Risk, gives <i>Plus</i> his take on uncertainty. </div>
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<p><i>What's the risk of passive smoking? Or climate change? How big is the terrorist threat? And should we trust league tables? These questions concern all of us, but it's not always easy to make sense of the barrage of media information. Maths and statistics are powerful tools in understanding risk and uncertainty, so it's no surprise that David Spiegelhalter, the new Winton Professor for the
Public Understanding of Risk, is based at the Centre for Mathematical Sciences at Cambridge University.<p><a href="https://plus.maths.org/content/understanding-uncertainty" target="_blank">read more</a></p>https://plus.maths.org/content/understanding-uncertainty#comments44bayes theoremBayesian modelCMSmathematics in the mediamedical statisticsmedicine and healthpublic understanding of mathematicsrisk analysisunderstanding uncertaintyFri, 31 Aug 2007 23:00:00 +0000plusadmin2314 at https://plus.maths.org/contentThe risk of death for sickle cell disease
https://plus.maths.org/content/risk-death-sickle-cell-disease
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A new Bayesian network helps predict the severity of the disease </div>
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<p>Sickle cell disease deforms red blood cells into a sickle-like shape.</p><p><a href="https://plus.maths.org/content/risk-death-sickle-cell-disease" target="_blank">read more</a></p>https://plus.maths.org/content/risk-death-sickle-cell-disease#commentsbayes theorembayesian networkmedicine and healthTue, 17 Jul 2007 23:00:00 +0000plusadmin2561 at https://plus.maths.org/contentThomas Bayes & Mr Zootpooper
https://plus.maths.org/content/thomas-bayes-mr-zootpooper
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Phil Wilson </div>
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The three door problem has become a staple mathematical mindbender, but even if you know the answer, do you really understand it? <b>Phil Wilson</b> lets his imagination run riot in this intergalactic application of Bayes' Theorem. </div>
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<p><i>It is the year 2057 and you are sitting in a vast auditorium beneath a night sky like nothing on Earth.<p><a href="https://plus.maths.org/content/thomas-bayes-mr-zootpooper" target="_blank">read more</a></p>https://plus.maths.org/content/thomas-bayes-mr-zootpooper#comments32bayes theoremconditional probabilitythree door problemMon, 01 Nov 2004 00:00:00 +0000plusadmin2257 at https://plus.maths.org/contentBeyond reasonable doubt
https://plus.maths.org/content/beyond-reasonable-doubt
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Helen Joyce </div>
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In 1999 solicitor Sally Clark was found guilty of murdering her two baby sons. Highly flawed statistical arguments may have been crucial in securing her conviction. As her second appeal approaches, <i>Plus</i> looks at the case and finds out how courts deal with statistics. </div>
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<p>Happier days - a family snapshot of Sally and Steve Clark when they were expecting Christopher</p><p><a href="https://plus.maths.org/content/beyond-reasonable-doubt" target="_blank">read more</a></p>https://plus.maths.org/content/beyond-reasonable-doubt#comments21bayes theoremconditional probabilitySat, 31 Aug 2002 23:00:00 +0000plusadmin2208 at https://plus.maths.org/contentRandom privacy
https://plus.maths.org/content/random-privacy
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<p>How old are you? How much do you earn?</p>
<p>What would you answer if asked asked these questions at website when you were buying your next TV or ordering groceries online? A lot of us would lie, and for a very good reason - to protect our privacy.</p><p><a href="https://plus.maths.org/content/random-privacy" target="_blank">read more</a></p>https://plus.maths.org/content/random-privacy#commentsbayes theoremdata analysisdata handlingprobability distributionSat, 31 Aug 2002 23:00:00 +0000plusadmin2742 at https://plus.maths.org/contentPrize specimens
https://plus.maths.org/content/prize-specimens
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Last October, two mathematicians won £1m when it was revealed that they were the first to solve the Eternity jigsaw puzzle. It had taken them six months and a generous helping of mathematical analysis. <b>Mark Wainwright</b> meets the pair and finds out how they did it. </div>
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<p>Alex Selby and Oliver Riordan, two mathematicians, with the help of a couple of computers, have shared a £1m prize by solving the "Eternity" puzzle. The puzzle was like an enormously difficult jigsaw. There were 209 pieces, all different, but all made from equilateral triangles and half-triangles, as in the example on the left.<p><a href="https://plus.maths.org/content/prize-specimens" target="_blank">read more</a></p>https://plus.maths.org/content/prize-specimens#comments13bayes theoremcomputer searcheternity gamegrid problemspacking problemsplane geometryprobabilitytilingMon, 01 Jan 2001 00:00:00 +0000plusadmin2175 at https://plus.maths.org/contentCars in the next lane really do go faster
https://plus.maths.org/content/cars-next-lane-really-do-go-faster
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Nick Bostrom </div>
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Yes, you were right to wish you were in the other lane during this morning's commute! <b>Nick Bostrom</b> tells why we're usually caught in the slow lane. </div>
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<p>When driving on the motorway, have you ever wondered about (and cursed) the fact that cars in the other lane seem to be getting ahead faster than you? You might be inclined to account for this by invoking Murphy's Law ("If anything can go wrong, it will", discovered by Edward A. Murphy, Jr, in 1949).<p><a href="https://plus.maths.org/content/cars-next-lane-really-do-go-faster" target="_blank">read more</a></p>https://plus.maths.org/content/cars-next-lane-really-do-go-faster#comments17anthropic principlebayes theoremconditional probabilitydata samplingdiffusionequilibriumestimationobservation selection effectthermodynamicsFri, 01 Dec 2000 00:00:00 +0000plusadmin2194 at https://plus.maths.org/contentYe banks and Bayes
https://plus.maths.org/content/ye-banks-and-bayes
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<p>Are you going to be a good customer for your bank? This might not worry you, but it certainly worries your bank! Banks would like to be able to predict both who their most profitable clients are likely to be, and which potential clients are most likely to be unreliable or a poor risk.</p>
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<p><a href="https://plus.maths.org/content/ye-banks-and-bayes" target="_blank">read more</a></p>https://plus.maths.org/content/ye-banks-and-bayes#commentsbayes theoremconditional probabilityprobabilityTue, 31 Aug 1999 23:00:00 +0000plusadmin2679 at https://plus.maths.org/content