Statistical methods and algorithm play important roles in the analysis of experimental data. Our group has special interests in this area. Through our experience in various experiments (Daya Bay, MicroBooNE, DUNE ...), we come up many techniques, which are summarized here.
The determination of Neutrino Mass Ordering (or Neutrino Mass Hierarchy) is an important question to be addressed in the neutrino physics. From the statistical point of view, it is a simple vs. simple hypothesis testing instead of a nested hypothesis testing. We advocate using Bayesian approaches to express experimental sensitivities and results. Some details can be found in this paper.
In a counting experiment, the likelihood-ratio test statistics in a simple vs. simple hypothesis testing approaches to a normal distribution at large statistics. This mean and variance of this normal distribution is connected and can be categorized by the value of the test statistics of Asimov data set. We propose to utilize this feature with the standard CLs method to present searches of new physics. More details of this method can be found in this paper.
Wiener filter is a common technique used in the digital signal processing. We extend this idea to the problem of data unfolding and propose the Wiener SVD method. Compared to the standard SVD method, the Wiener SVD simplifies the procedure avoiding the scan of regularization strength (tau). The mean squared error (MSE, the summation of bias squared and the variance squared) of the Wiener SVD is generally better than that of standard SVD method. More details can be found in this paper.
We realized that a linear combination of the standard Neyman and Pearson chisquares (CNP) lead to a better approximation of the Poisson chisquare in a counting experiment. CNP chisquare is directly compatible with the covariance matrix formalism, which may have computational advantages in certain scenarios. More details can be found in this paper.
The goal of TPC signal processing is to reconstruct the distribution of ionization electrons arriving at wire planes from the digitized TPC waveform. Build upon the earlier work, we introduced the "2D deconvolution" method, which significantly improved the quality of reconstructed ionization electron distributions.
In a section of the MicroBooNE LArTPC detector, the wire bias voltages were distorted. The result of this distortion is that two type of signals (bipolar and unipolar shapes) can show up on the same channel. Compared to the standard signal processing problem where the dimension of unknowns (ionization electron distributions) is the same as the dimension of measurements (TPC waveform), the number of unknowns is twice of the that of measurements in this case. We solved this problem by implementing the compressed sensing technique. More details can be found in this paper.
Most recently, by introducing the deep neutral network to the signal region of interest detection, the performance of the TPC signal processing is enhanced, especially for the so-called prolonged TPC signals.
Wire-Cell is a novel tomographic event reconstruction method, which is being developed aiming to solve the long-standing problem of automated 3D neutrino event reconstruction in LArTPC. The principle of Wire-Cell strictly follows the principle of LArTPC, that is, the same amount of ionization electrons are observed by all the wire-planes. Using both time and charge information, 3D image of the event topologies are firstly obtained. Further reconstruction steps including the clustering, tracking, and particle identifications (PID) are then directly applied to the 3D image. The application of Wire-Cell 3D image reconstruction on MicroBooNE can be found in this paper.
We developed a novel many-to-many TPC-charge/PMT-light matching algorithm, which aims at matching all scintillation light signals with all ionization charge signals. This technique is crucial in achieving the high-performance generic neutrino detection in MicroBooNE.
In a single-phase LArTPC with wire readouts, the fundamental data are multiple 2D projection measurements. We constructed a fitting procedure to determine the 3D track trajectory and its associated dQ/dx (four unknown variables for a 3D point: 3 for position and 1 for dQ/dx). The fitting procedure consists of two parts i) determination of track trajectory and ii) determination of dQ/dx, so that each part can utilize the linear algebra to ensure the stability of the fit. This technique is crucial in achieving good particle identification for any track direction. More details can be found in MicroBooNE high-performance generic neutrino detection technote .