[{"id":412,"title":"Recasting through reweighting","sha":"8106c030eba22dd3a8d268940d5e42d8","user_id":null,"state":"published","body":"*Recasting* refers to reinterpreting the results of searches for new particles or standard model measurements in the context of different theoretical models\u0026nbsp;\\[[1](http://inspirehep.net/record/872781)\\]. The fundamental task is to replace the original hypothesis $p_0(x)$ with a new hypothesis $p_1(x)$, where $x$ is some observed quantity. The effect of the detector response and analysis cuts can be encoded in a *folding* operator $\\int\\,W(x|z)dz$ acting on the truth-level distribution $p(z)$. By keeping the  analysis fixed, $W(x|z)$ does not change, thus recasting amounts to:\r\n\\begin{equation}p_0(x)=\\int\\,p_0(z)W(x|z)dz\\hspace{.5cm}\\Longrightarrow\\hspace{.5cm}p_1(x)=\\int\\,p_1(z)W(x|z)dz\\end{equation}\r\n\r\nThere are two primary approaches:\r\n  * **folding**: Samples from $p_1(z)$ are run through a detector simulation and analysis chain to estimate $p_1(x)$\u0026nbsp;\\[[2](https://indico.cern.ch/event/567550/contributions/2638695/)\\]. This is common when $z$ is high-dimensional, $p_0(z)$ and $p_1(z)$ are very different, or $W(x|z)$ is sensitive to experimental details.\r\n  * **unfolding**: An alternate theory $p_1(z)$ is compared directly to an unfolded distribution $\\hat{p}(z)$ obtained from applying an approximate inverse operation to the observed data. Typically, unfolding is restricted to low-dimensional $x, z$ and Gaussian uncertainties.\r\n\r\nWe point out a third option\r\n   * **reweighting**: Reweight pre-folded events $(x_i,z_i)~\\sim\\,p_0(x,z)$ by the factor $r(z_i)=p_1(z_i)/p_0(z_i)$, as in\r\n\\begin{equation}p_1(x)=\\int p_1(z)W(x|z)dz=\\int\\,p_0(z)\\underbrace{\\frac{p_1(z)}{p_0(z)}}_{\\textrm{reweighting}}W(x|z)dz\\end{equation}\r\nThis approach does not require simulating new events or the approximations used in unfolding. Note, sample variance becomes a problem if $r(z_i)\\gg\\,1$.","created_at":"2017-10-14T14:16:18.901Z","updated_at":"2022-06-05T20:51:32.689Z","zenodo_id":1013926,"doi":"https://doi.org/10.5281/zenodo.1013926","subject":null,"tags":["physics","reinterpretation","lhc"],"vote_count":3,"view_count":1,"score":3.1,"deleted":false,"muted":false,"tweeted":true,"attachment_file_name":null,"attachment_content_type":null,"attachment_file_size":null,"attachment_updated_at":null}]