Experimental data in Particle and Nuclear physics, Particle Astrophysics and Radiation Protection Dosimetry are obtained from experimental facilities comprising a complex array of sensors, electronics and software. Computer simulation is used to study the measurement process. Probability Density Functions (PDFs) of measured physical parameters deviate from true PDFs due to resolution, bias, and efficiency effects. Good estimates of the true PDF are necessary for testing theoretical models, comparing results from different experiments, and combining results from various research endeavors. In the article, the histogram method is employed to estimate both the measured and true PDFs. The binning of histograms is determined using the K-means clustering algorithm. The true PDF is estimated through the maximization of the likelihood function with entropy regularization, utilizing a non-linear optimization algorithm specially designed for this purpose. The accuracy of the results is assessed using the Mean Integrated Square Error. To determine the optimal value for the regularization parameter, a bootstrap method is applied. Additionally, a mathematical model of the measurement system is formulated using system identification methods. This approach enhances the robustness and precision of the estimation process, providing a more reliable analysis of the system's characteristics.

翻译：在粒子物理与核物理、粒子天体物理以及辐射防护剂量学领域，实验数据来源于由复杂传感器阵列、电子设备和软件构成的实验设施。计算机仿真被用于研究测量过程。受分辨率、偏差及效率效应影响，测量物理参数的概率密度函数与真实概率密度函数存在偏差。对理论模型验证、不同实验结果比对以及多研究项目结果整合而言，获取真实概率密度函数的可靠估计至关重要。本文采用直方图方法估计实测与真实概率密度函数，通过K-means聚类算法确定直方图的分箱策略。利用专门设计的非线性优化算法，通过熵正则化下的似然函数最大化估计真实概率密度函数。采用均方积分误差评估结果准确性，并运用bootstrap方法确定正则化参数的最优值。此外，通过系统辨识方法建立测量系统的数学模型。该方法增强了估计过程的鲁棒性与精度，为系统特性分析提供了更可靠的数据支撑。