Sensitivity and specificity
Statistical measures of the performance of a binary classification test In medicine and statistics, sensitivity and specificity mathematically describe the accuracy of a test that reports the presence or absence of a medical condition. If individuals who have the condition are considered "positive" and those who do not are considered "negative", then sensitivity is a measure of how well a test can identify true positives and specificity is a measure of how well a test can identify true negatives: Sensitivity (true positive rate) is the probability of a positive test result, conditioned on the individual truly being positive.Specificity (true negative rate) is the probability of a negative test result, conditioned on the individual truly being negative. A test which reliably detects the presence of a condition, resulting in a high number of true positives and low number of false negatives, will have a high sensitivity. Application to screening study[edit] Definition[edit] Sensitivity[edit]
An Intuitive (and Short) Explanation of Bayes’ Theorem
Bayes’ theorem was the subject of a detailed article. The essay is good, but over 15,000 words long — here’s the condensed version for Bayesian newcomers like myself: Tests are not the event. Bayes’ theorem converts the results from your test into the real probability of the event. Correct for measurement errors. Anatomy of a Test The article describes a cancer testing scenario: 1% of women have breast cancer (and therefore 99% do not).80% of mammograms detect breast cancer when it is there (and therefore 20% miss it).9.6% of mammograms detect breast cancer when it’s not there (and therefore 90.4% correctly return a negative result). Put in a table, the probabilities look like this: How do we read it? 1% of people have cancerIf you already have cancer, you are in the first column. How Accurate Is The Test? Now suppose you get a positive test result. Here’s how I think about it: Ok, we got a positive result. The table looks like this: And what was the question again? Bayes’ Theorem Have fun!
Basu's theorem
From Wikipedia, the free encyclopedia Theorem in statistics It is often used in statistics as a tool to prove independence of two statistics, by first demonstrating one is complete sufficient and the other is ancillary, then appealing to the theorem.[2] An example of this is to show that the sample mean and sample variance of a normal distribution are independent statistics, which is done in the Example section below. This property (independence of sample mean and sample variance) characterizes normal distributions. Statement[edit] Let be a family of distributions on a measurable space and a statistic maps from to some measurable space . is a boundedly complete sufficient statistic for , and is ancillary to , then conditional on is independent of . Proof[edit] and be the marginal distributions of respectively. Denote by the preimage of a set under the map . we have The distribution does not depend on because is ancillary. is sufficient. Note the integrand (the function inside the integral) is a function of . .
My Father Says He’s a ‘Targeted Individual.’ Maybe We All Are
The Suzanne Moore-Julie Burchill uproar shows how utterly bonkers parts of the radical Left are at the moment
Photoshopper's note: Dan insisted on being 'shopped as Javert for this one. Last night I went to see Les Misérables, and nearly disgraced myself. As the ensemble broke into their first stirring rendition of “Do You Hear The People Sing” – and all around me wept proud tears of solidarity – I almost burst out laughing. It wasn’t that I was belittling Hugh Jackman and Eddie Redmayne’s revolutionary ardour, though Russell Crowe’s Javert did strike me as just the sort of man who knows how to take tough choices in an age of austerity. Instead I was reminded of the time I was working for the GMB union, and we decided to use “The People’s Song” to open our annual congress. Every year we’d begin with Jerusalem, and for once we thought we’d let our hair down a bit. Just like those manning the Parisian barricades in 1832, we stood accused of treachery. The Left detests a traitor. No sooner had Moore been officially found to be in league with the devil than it was Julie Burchill’s turn.
Bernstein–von Mises theorem
From Wikipedia, the free encyclopedia Theorem in Bayesian inference In Bayesian inference, the Bernstein–von Mises theorem provides the basis for using Bayesian credible sets for confidence statements in parametric models. , where is the true population parameter and is the Fisher information matrix at the true population parameter value:[1] The Bernstein–von Mises theorem links Bayesian inference with frequentist inference. will asymptotically be confidence sets of confidence level , which allows for the interpretation of Bayesian credible sets. Heuristic statement[edit] In a model , under certain regularity conditions (finite-dimensional, well-specified, smooth, existence of tests), if the prior distribution on has a density with respect to the Lebesgue measure which is smooth enough (near bounded away from zero), the total variation distance between the rescaled posterior distribution (by centring and rescaling to Bernstein–von Mises and maximum likelihood estimation[edit] Implications[edit]
Recuperation (politics)
The concept in political philosophy of recuperation was first proposed by Pietro Staheli, a Swiss member of the Situationist International, who was serving time in a Thai detention center. His first paper on the subject, "The Ruins of Fordism," was first credited to Staheli's Tanzanian lover, Mohammed "Mikey P" Pervaiz, a credit that was changed when the paper saw wider publication in Situationist journals. The term conveys a negative connotation because recuperation generally bears the intentional consequence (whether perceived or not) of fundamentally altering the meanings behind radical ideas due to their appropriation or being co-opted into the dominant discourse. Jump up ^ Kurczynski, Karen Expression as vandalism: Asger Jorn's "Modifications", in RES: Anthropology and Aesthetics No. 53/54 (Spring - Autumn, 2008), pp.295-6. Marcus, Greil. Essay on the topic
Anonymous trolls are as pathetic as the anonymous "sources" that contaminate the gutless journalism of the New York Times, BBC, and CNN - Comment - Voices
He tells “lie upon lie, all of them directly or indirectly aimed at the destruction of Israel”. And he has received the following message: “The Islamist cut-throats you sympathise with would gladly slash your pencil neck from ear to ear just because you won’t bow to their bloodthirsty pedophile [sic] prophet.” And now a clue. In this same list of website filth – sent over just two days – an anonymous writer adds: “Could Robert Fisk be next?” My sin – and the above, believe me, is the clean end of the abuse – was to write an article last week about the Middle East in 2013. But something is going wrong here. Former US diplomat Christopher Hill, a man whose views normally make me cringe – he was ambassador to Iraq, special envoy to Kosovo and a Dayton negotiator – has observed these dangers. Just before Christmas, an Irish minister of state, Shane McEntee, committed suicide after receiving a swath of online hate-mail. And what happened? I agree. So what to do?
