text: 101,74,1373942001519972353,561899047,Aki Vehtari,"New paper with Teemu Säilynoja and @paulbuerkner ""Graphical Test for Discrete Uniformity and its Applications in Goodness of Fit Evaluation and Multiple Sample Comparison"" <LINK> <LINK> We've recently had papers like simulation based calibration and new Rhat paper with rank plots, which involve looking at the uniformity of rank statistics. Thinking more, we realized that histograms are suboptimal and ECDF envelopes we used were based on continuous uniformity. The motivation was not uniformity testing for itself, but this paper belongs to a series of papers on improving diagnostics of diagnostics. The graphical aspect is also important to provide useful information about the shape of discrepancy away from the assumed uniformity. Histograms 1) loose information by binning, 2) the choice of bins affect the result, 3) the confidence band doesn't take into account the dependency. ECDF and ECDF difference plots don't have these problems and thus would be better. <LINK> The simultaneous confidence band for ECDF (and ECDF difference) doesn't have closed form solution and naive simulation based approach can be very slow. Aldor-Noiman et al proposed more efficient simulation based approach for continuous uniform case. In SBC and MCMC rank plots, the rank statistics are discrete. The rank statistics are also equivalent to probability integral transformation (PIT) using ECDF. We present how we can construct the confidence bands that are correct both in continuous and discrete case. <LINK> We propose a new optimization based approach for simultaneous confidence band which is much more efficient than Aldor-Noiman simulation approach. We also extend the apporach to comparing rank statistics of multiple samples such as arising from different Markov chains. <LINK> The code is available at <LINK> This is Teemu's first paper and I'm very happy with the outcome!",https://arxiv.org/abs/2103.10522,"Assessing goodness of fit to a given distribution plays an important role in computational statistics. The Probability integral transformation (PIT) can be used to convert the question of whether a given sample originates from a reference distribution into a problem of testing for uniformity. We present new simulation and optimization based methods to obtain simultaneous confidence bands for the whole empirical cumulative distribution function (ECDF) of the PIT values under the assumption of uniformity. Simultaneous confidence bands correspond to such confidence intervals at each point that jointly satisfy a desired coverage. These methods can also be applied in cases where the reference distribution is represented only by a finite sample. The confidence bands provide an intuitive ECDF-based graphical test for uniformity, which also provides useful information on the quality of the discrepancy. We further extend the simulation and optimization methods to determine simultaneous confidence bands for testing whether multiple samples come from the same underlying distribution. This multiple sample comparison test is especially useful in Markov chain Monte Carlo convergence diagnostics. We provide numerical experiments to assess the properties of the tests using both simulated and real world data and give recommendations on their practical application in computational statistics workflows. ","Graphical Test for Discrete Uniformity and its Applications in Goodness