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：粒子物理、核物理、粒子天体物理及辐射防护剂量学中的实验数据来源于由复杂传感器阵列、电子学器件及软件构成的实验设施。测量过程通过计算机模拟进行研究。实测物理参数的概率密度函数（PDFs）因分辨率、偏差及效率效应而与真实PDFs存在偏差。准确估计真实PDF对于检验理论模型、比较不同实验结果以及整合各研究项目的成果至关重要。本文采用直方图方法估计实测与真实PDFs，并使用K-means聚类算法确定直方图分箱方案。通过专门设计的非线性优化算法，以熵正则化似然函数最大化方法估计真实PDF。采用均方积分误差评估结果精度，并应用Bootstrap方法确定正则化参数的最优值。此外，运用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手段。