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：粒子与核物理、粒子天体物理以及辐射防护剂量学中的实验数据，均来源于包含复杂传感器阵列、电子设备与软件系统的实验装置。计算机模拟被用于研究测量过程。由于分辨率、偏差及效率效应的影响，被测物理参数的概率密度函数（PDF）会偏离真实PDF。获取真实PDF的准确估计对于检验理论模型、比较不同实验的结果以及整合各类研究工作的成果至关重要。本文采用直方图方法对测量PDF与真实PDF进行估计。直方图的分箱方案通过K-means聚类算法确定。真实PDF的估计通过最大化经过熵正则化的似然函数实现，该过程采用专门设计的非线性优化算法完成。结果的准确性通过均方积分误差进行评估。为确定正则化参数的最优值，采用了自助法。此外，利用系统辨识方法建立了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确性，为系统特性提供了更可靠的分析。