Videos tagged “Bayes theorem”

Alejandro Baez  A Bayesian Approach to Clinical Decision Making
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Dr. Amado Alejandro Baez is the Emergency Medicine Program Director at the Jackson Memorial Hospital/ University of Miami Miller School of Medicine and has published extensively in Emergency Medicine, Trauma and Critical Care. He is a rock star  in fact, one of his research collaboratives is the ACDC project whose goal is to incorporate bayesian statistical modeling into clinical practice by using some of the most commonly used clinical scoring systems we use on a daily basis.... ROCK ON. In this lecture, Dr Baez discusses the application of Bayesian statistics to everyday clinical decisions and some of the work done by ACDC.
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Bayesian (inverse probability) inference in games : Part two
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the second of two sceencast lectures on how intelligent players reason about states and signals in a game ; the first is here https://vimeo.com/66710690 This lecture uses the two practise problems from class (one on breast cancer screening, the other on witness reports in a courtroom case) to develop a "language" of probability that is (1) easily understandable for ANY type or level of students  whether trained in statistics or not and (2) useful for students of game theory . Simple numerical examples using Gigerenzer style natural frequency/count reasoning are developed to explain a wide range of concepts connecting uncertainties about "states" and "signals" sensitivity, specificity, conditional probabilities, predictive probabilities, inverse probabilities, etc.
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The basics of inverse inference Part One: the game tree, truth tables, states and signals
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This is the first part of of two lectures on Bayesian inference, inverse probability inference...or...coherent rational inference, the way any intelligent rational player should think about TWO uncertainties: about some underlying state and about some diagnostic signal possibly related to or informative about that state . This first lecture introduces the basic problem of inference via a game tree and introduces the logicians "truth table" to help organise thinking about two interrelated unknowns  states and signals. The second lecture , here http://vimeo.com/66935222, takes these ideas and uses them to develop the language of probability for inference problems  in games against people or in games against nature , easily understandable for any type and level of student.
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Inverse Inference Practise Question: was Hinckley crazy?
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Practise question on inverse inference. Details of the question are over on strategicecon.com http://strategicecon.com/?p=420
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Strategic Reasoning involving Bayes Theorem in the Courtroom: Was he crazy or not?
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Video explanation for the following practice question on Bayes Theorem/Inverse inference: In 1982 Robert Hinckley went on trial for attempted murder of President Ronald Reagan. As the press reported: On March 30, 1981, in broad daylight, among a crowd of supporters and onlookers, Hinckley fired six bullets at Reagan in the space of three seconds, hitting Reagan, a police officer and a Secret Service agent, and seriously wounding Press Secretary James Brady. [Reagan was wounded but not killed. ] ....Hinckley's trial in 1982 ended in a notguilty verdict, by reason of insanity. The assassination attempt won him notoriety and media attention, and also led to legislation [during the next decade] limiting the use of the insanity plea in several states During Hinckley's trial the defense argued that Hinckley had a mental illness, schizophrenia. The prosecution argued that schizophrenia was rare, with only around 1 in 100 of the adult population suffering from schizohprenia. The defense lawyer didn't dispute this claim, but wanted to introduce as evidence a brain scan of Hinckley's that showed substantial brain atrophy ("atrophy" is a decrease in size or wasting away of a body part or tissue). The defense also presented evidence in the form of expert testimony that when people diagnosed as schizophrenics have brain scans, about 30% show signs of substantial brain atrophy, whereas when normal, nonschizophrenic people have the scan only about 2% show signs of substantial brain atrophy. The defense then argued that on the evidence it was 15 times more likely, that Hinckley suffered from schizophrenia compared to a normal person. C1 What would you, as an advisor to the jury, say about the defense lawyer's argument, quantitatively and qualitatively? In your answer use the Gigerenzer natural frequency method (table or graphical) to calculate and briefly explain how much more or less likely it is that Hinkley has schizophrenia after seeing all this evidence from the defense than before seeing it. Hint:Let S be the proposition that a person has schizophrenia and BA the proposition that a person has brain atrophy. Since either proposition can be true (1) or false (0) there are 4 logical possibities which you can represent in a truth table. Suppose we assess a prior probability that P(S=1)=0.01 meaning that without any other information our probability for some adult in the US having scizophrenia is the same as the proportion 1 in 100 of the adult population that suffers from schizohprenia. Suppose we accept expert testomony on conditionals, that P(BA=1S=1)=0.3 [when people diagnosed as schizophrenics have brain scans, about 30% show signs of substantial brain atrophy], whereas P(BA=1S=0)=0.02 [when normal, nonschizophrenic people have the scan only about 2% show signs of substantial brain atrophy]. C2 2 The defense lawyer's evidence is couched in "abouts", implying that the experts are far from certain about the proportions cited. As a prosecutor your researchers have found out that Hinckley had a history of drinking alcohol to excess, bordering on alcoholism. They also discovered that brain atrophy is common amongst alcoholics. Amongst "normal" (non schizophrenic) alcoholics, the chances of brain atrophy are estimated to be between 25% and as as high as 40% in some males but the combination of alcoholism and schizophrenia doesn't change the 30% figure for brain atrophy that the defense lawyer used. No one really knows the percentage of alcoholics who are schizophrenic. How do these changed bits of evidence alter the defense lawyers case? Explain your reasoning
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Example of Bayesian updating applied to avalanche forecasting
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This video uses a simple avalanche forecasting problem for a ski area to illustrate Bayes Rule, which is a method for updating a numerical probability based on new information. It is applied to preseason planning  helping to set the threshold precipitation for control; however, Baysian updating could be applied more frequently, e.g. on a day by day basis
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