Toolbox for constructing the best histograms  

These tools provide the best histogram, kernel density estimation, Bayesian estimator, and Hidden Markov model, for a given series of event times. Paste or upload the event times, separated by a comma or a space. Your data will not leave your computer, because the computation is carried out on your computer. Matlab, Python, and R codes are also available for download below. The theory applied here for the purpose of optimizing the estimators can be found in the references.

1. You can paste your data here, or   or  


     (A) Histogram: L2 risk minimization [Reference 1].
(Related site)
     (B) Histogram: L2 risk minimization for non-Poisson spike trains [Reference 2].
     (C) Kernel density estimation: L2 risk minimization [Reference 3].
     (D) Kernel density estimation: L2 risk minimization [Reference 3], with [reflection boundary].
     (E) Bayesian rate estimation [Reference 4] [Reference 5]. (Estimating rate and irregularity)
     (F) Two-state Hidden Markov Model [Reference 6].

Version 3.3 : 2019/02/25  

Review article pertaining to the optimization principles and methods:
Shigeru Shinomoto (2010) Estimating the firing rate. in "Analysis of Parallel Spike Train Data" (eds. S. Gruen and S. Rotter) (Springer, New York).
For assistance, contact Shigeru Shinomoto, who directed this project. Individual programs were formulated by Hideaki Shimazaki, Takahiro Omi, Takeaki Shimokawa, and Yasuhiro Mochizuki. Revisions were made by Junpei Naito, Kazuki Nakamura, and Daisuke Endo.

Other analytical tools: SULAB: Single Unit LABoratory

------------------ Shigeru Shinomoto, Kyoto University, Japan. ----------------------------------------------------------