Xians Og | an attempt at bloggin, nothing more
Time 2021-11-19 20:05:11Web Name: Xians Og | an attempt at bloggin, nothing more
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keywords: description:an attempt at bloggin, nothing more... Xians Og an attempt at bloggin, nothing more dice and sticksPosted in Books, Kids, R with tags Carl Friedrich Gauss, dice, optimisation, R, riddle, stick breaking process, The Riddler on November 19, 2021 by xi'anA quick weekend riddle from the Riddler about the probability of getting a sequence of increasing numbers from dice with an increasing number of faces, eg 4-, 6-, and 8-face dice. Which happens to be 1/4. By sheer calculation (à la Gauss) or simple enumération (à la R):
for(i in 1:4)for(j in (i+1):6)F=F+(8-j) F/4/6/8[1] 0.25
The less-express riddle is an optimisation problem related with stick breaking: given a stick of length one, propose a fraction a and win (1-a) if a Uniform x is less than one. Since the gain is a(1-a) the maximal average gain is associated with a=½. Now, if the remaining stick (1-a) can be divided when xa, what is the sequence of fractions one should use when the gain is the length of the remaining stick? With two attempts only, the optimal gain is still ¼. And a simulation experiment with three attempts again returns ¼.
Share:ShareLike this: Loading... finding our way in thedarkPosted in Books, pictures, Statistics with tags AMIS, approximate Bayesian inference, approximate MCMC, Bayesian Analysis, Bayesian synthetic likelihood, conditional density, k nearest neighour, knn estimator, random forests, storm on November 18, 2021 by xi'anThe paper Finding our Way in the Dark: Approximate MCMC for Approximate Bayesian Methods by Evgeny Levi and (my friend) Radu Craiu, recently got published in Bayesian Analysis. The central motivation for their work is that both ABC and synthetic likelihood are costly methods when the data is large and does not allow for smaller summaries. That is, when summaries S of smaller dimension cannot be directly simulated. The idea is to try to estimate
since this is the substitute for the likelihood used for ABC. (A related idea is to build an approximate and conditional [on θ] distribution on the distance, idea with which Doc. Stoehr and I played a wee bit without getting anything definitely interesting!) This is a one-dimensional object, hence non-parametric estimates could be considered For instance using k-nearest neighbour methods (which were already linked with ABC by Gérard Biau and co-authors.) A random forest could also be used (?). Or neural nets. The method still requires a full simulation of new datasets, so I wonder at the gain unless the replacement of the naïve indicator with h(θ) brings clear improvement to the approximation. Hence much fewer simulations. The ESS reduction is definitely improved, esp. since the CPU cost is higher. Could this be associated with the recourse to independent proposals?
In a sence, Bayesian synthetic likelihood does not convey the same appeal, since is a bit more of a tough cookie: approximating the mean and variance is multidimensional. (BSL is always more expensive!)
As a side remark, the authors use two chains in parallel to simplify convergence proofs, as we did a while ago with AMIS!
Share:ShareLike this: Loading... summit of thegodsPosted in Books, Kids, Mountains, pictures with tags anime, Baku Yumemakura, Everest, films, George Mallory, Jirô Taniguchi, Kodak, manga, Sandy Irvine, the summit of the gods on November 17, 2021 by xi'anHere are winners for some categories of the 2021 World Fantasy Awards:
Trouble the Saints by Alaya Dawn Johnson [novel]Riot Baby by Tochi Onyebuchi [novella]Where the Wild Ladies Are by Aoko Matsuda [collection]Somewhat surprisingly, not only I have not read these books, although Riot Baby is sitting in my Kindle, courtesy of Tor Books, but this is also the case for most winners of the past years. The first author I could recognise is K.J. Parker, in 2013, and the first book I had read is Murakamis Kafka on the Shore in 2006
Share:ShareLike this: Loading... BurninPosted in Books, Kids, pictures with tags climate change, COP 26, cover, Glasgow, global warming, Scotland, The New Yorker on November 15, 2021 by xi'anShare:ShareLike this: Loading... Older Entries Follow Xians Og on WordPress.com blogs links aboutamazon.com [support Og]amazon.fr [support Og]Andrew GelmanBayesian Choice (book)Bayesian Core (book)Bayesian Essentials with R (book)Error-statistics philosophyFreakonometricsIntroducing Monte Carlo Methods with R (book)Monte Carlo Statistical methods (book)R-bloggersStatsBlogsYe Norse Farce Shoppe ABCABC model choiceAlpsApproximate Bayesian computationarXivAustraliaBanffBayes factorBayesian AnalysisBayesian CoreBayesian inferenceBayesian model choiceBayesian statisticsbig databook reviewbook reviewsCanadaCHANCECIRMconferencecoronavirus epidemicsCOVID-19CRESTcross validatedEdinburghEnglandevidenceFranceGibbs samplingHamiltonian Monte CarloIcelandimportance samplingIndiaIntroducing Monte Carlo Methods with RISBAItaliaJapanjatpLe Mondelikelihood-free methodsLondonLuminymachine learningMarseillemathematical puzzleMCMCMCMC algorithmsMonte Carlo methodsMonte Carlo Statistical MethodsNaturenested samplingNormandyParisRRao-BlackwellisationRoyal Statistical SocietyScotlandseminarsimulated annealingsimulationslidessummary statisticssunrisesunsetThe GuardianThe New York TimesThe RiddlerThomas BayesUnited KingdomUniversity of OxfordUniversity of WarwickUniversité Paris DauphineUSAvacationsworkshop Recent entries dice and sticks finding our way in thedark summit of thegods 2021 World FantasyAwards Burnin on [not] makingtea AstroDeep in Paris [postdocposition] out-standing scientist worst colour scale? Xing glass bridges [ornot] Latest comments dice and sticks | R- on dice and sticksdice and sticks on dice and sticks667 per centimeter : on Burninecoquant on out-standing scientistXing glass bridges [ on Xing glass bridges [orno Og\s RSSRSS - PostsRSS - CommentsBlog at WordPress.com.
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