Implications from ASKAP Fast Radio Burst Statistics

Although there has recently been tremendous progress in studies of fast radio bursts (FRBs), the nature of their progenitors remains a mystery. We study the fluence and dispersion measure (DM) distributions of the ASKAP sample to better understand their energetics and statistics. We first consider a simplified model of a power-law volumetric rate per unit isotropic energy dN/dE ~ E^{-gamma} with a maximum energy E_max in a uniform Euclidean Universe. This provides analytic insights for what can be learnt from these distributions. We find that the observed cumulative DM distribution scales as N(>DM) ~ DM^{5-2*gamma} (for gamma > 1) until a maximum value DM_max above which bursts near E_max fall below the fluence threshold of a given telescope. Comparing this model with the observed fluence and DM distributions, we find a reasonable fit for gamma ~ 1.7 and E_max ~ 10^{33} erg/Hz. We then carry out a full Bayesian analysis based on a Schechter rate function with cosmological factor. We find roughly consistent results with our analytical approach, although with large errors on the inferred parameters due to the small sample size. The power-law index and the maximum energy are constrained to be gamma = 1.6 +/- 0.3 and log(E_max) [erg/Hz] = 34.1 +1.1 -0.7 (68% confidence), respectively. From the survey exposure time, we further infer a cumulative local volumetric rate of log N(E > 10^{32} erg/Hz) [Gpc^{-3} yr^{-1}] = 2.6 +/- 0.4 (68% confidence). The methods presented here will be useful for the much larger FRB samples expected in the near future to study their distributions, energetics, and rates.Comment: ApJ accepted. Expanded beyond the scope of the earlier version into 8 pages, 7 figures. Following referees' comments, we included a full Bayesian analysis based on a Schechter rate function with cosmological factor. The PDF of the inferred model parameters are presented by MCMC sampling in Figure 4 (the most important result). We also discussed the completeness of ASKAP sample in Section

Applications of inverse simulation to a nonlinear model of an underwater vehicle

Inverse simulation provides an important alternative to conventional simulation and to more formal mathematical techniques of model inversion. The application of inverse simulation methods to a nonlinear dynamic model of an unmanned underwater vehicle with actuator limits is found to give rise to a number of challenging problems. It is shown that this particular problem requires, in common with other applications that include hard nonlinearities in the model or discontinuities in the required trajectory, can best be approached using a search-based optimization algorithm for inverse simulation in place of the more conventional Newton- Raphson approach. Results show that meaningful inverse simulation results can be obtained but that multi-solution responses exist. Although the inverse solutions are not unique they are shown to generate the required trajectories when tested using conventional forward simulation methods

How to Host a Data Competition: Statistical Advice for Design and Analysis of a Data Competition

Data competitions rely on real-time leaderboards to rank competitor entries and stimulate algorithm improvement. While such competitions have become quite popular and prevalent, particularly in supervised learning formats, their implementations by the host are highly variable. Without careful planning, a supervised learning competition is vulnerable to overfitting, where the winning solutions are so closely tuned to the particular set of provided data that they cannot generalize to the underlying problem of interest to the host. This paper outlines some important considerations for strategically designing relevant and informative data sets to maximize the learning outcome from hosting a competition based on our experience. It also describes a post-competition analysis that enables robust and efficient assessment of the strengths and weaknesses of solutions from different competitors, as well as greater understanding of the regions of the input space that are well-solved. The post-competition analysis, which complements the leaderboard, uses exploratory data analysis and generalized linear models (GLMs). The GLMs not only expand the range of results we can explore, they also provide more detailed analysis of individual sub-questions including similarities and differences between algorithms across different types of scenarios, universally easy or hard regions of the input space, and different learning objectives. When coupled with a strategically planned data generation approach, the methods provide richer and more informative summaries to enhance the interpretation of results beyond just the rankings on the leaderboard. The methods are illustrated with a recently completed competition to evaluate algorithms capable of detecting, identifying, and locating radioactive materials in an urban environment.Comment: 36 page