In many problems related to reliability and survival analysis, the evaluation of uncertainty and information associated with system lifetimes must be performed conditional on the current age (survival condition) of the system. >The aim of this thesis is to study, analyze, and organize the existing knowledge on generalizations of dynamic cumulative information measures and their applications in reliability and model selection. To this end, we first extract the basic definitions of cumulative information measures (including cumulative residual entropy, cumulative residual Fisher information, and past-based versions) and review their analytical relationships with hazard rate and mean residual lifetime functions. Then, the theoretical properties of these measures are compared in specific models (equilibrium and proportional hazards). Next, nonparametric estimation methods (particularly kernel-based estimators) and Monte Carlo simulation results for various distributions are collected and evaluated. Finally, the practical application of dynamic cumulative information measures in selecting competing lifetime distributions (with emphasis on real reliability data) is described, and their performance is compared with classical criteria such as AIC and BIC.

  Accurate prediction of mortality risk in patients undergoing hematopoietic stem cell tra  lantation (HSCT) plays a vital role in clinical decision-making. Although ensemble machine learning models have been widely employed in recent years to improve the accuracy of these predictions, most previous studies have modeled clinical outcomes as simple binary events, disregarding the time-to-event structure and censoring information. Furthermore, systematic and statistically rigorous comparisons of different ensemble strategies in this field remain limited. The primary objective of this study was to develop and evaluate an ensemble framework that integrates survival analysis, including the Kaplan–Meier method and Cox regression, with machine learning models, and to compare three ensemble strategies—simple averaging, weighted averaging, and stacking—using appropriate statistical tests.This study was conducted using the publicly available IN13-01 dataset from the Center for International Blood and Marrow Tra  lant Research (CIBMTR), comprising 1,673 patients who underwent HSCT. To prevent information leakage, 19 variables associated with post-tra  lant outcomes were excluded. A Cox proportional hazards regression model was fitted using ten clinical variables, and the resulting risk score, together with four interaction features, was added to the set of predictors used by the machine learning models, including logistic regression, random forest, and gradient boosting. Finally, the three ensemble strategies were evaluated on an independent test set comprising 25% of the data using the area under the receiver operating characteristic curve (AUC), F1-score, accuracy, sensitivity, and specificity. Pairwise comparisons of model performance were conducted using DeLong’s test.The Kaplan–Meier analysis indicated that conditioning regimen intensity, tra  lant type, performance status, age, and tra  lant period were significantly associated with overall survival (p < 0.01, HR = 1.147). In the multivariable Cox model, age (p < 0.001, HR = 0.827) and performance status (p < 0.001, HR = 0.827) were identified as the strongest independent predictors, and the model achieved a concordance index of C-index = 0.611. Furthermore, the Cox risk score was identified as the most important feature in the machine learning models, with a permutation importance of 86%, substantially exceeding that of the other features.Among the ensemble strategies, stacking achieved the highest performance, with an AUC of 0.6913, and demonstrated a reported statistically significant improvement over logistic regression (DeLong’s test, p = 0.17). However, the difference in performance between stacking and the best-performing base model, random forest (AUC = 0.689), was not statistically significant (p = 0.726).Overall, the findings of this study suggest that integrating survival analysis information with machine learning models through a Cox risk score is an effective approach for jointly leveraging time-to-event information and clinical characteristics to predict mortality risk. Nevertheless, increasing the complexity of ensemble strategies, from simple averaging to stacking, does not necessarily result in a statistically significant improvement over the best-performing base model. Therefore, the evaluation and selection of ensemble models should be based not only on numerical comparisons of performance metrics but also on appropriate statistical significance tests.

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A time series is a set of data recorded over time. For example, we can refer to the time series of the price of a share in the stock market, the amount of rain in an area, etc. One of the most important goals of time series analysis is to predict its future values. Several statistical methods for predicting time series, such as the method of using time series analysis models of Autoregressive integrated moving average model and Seasonal autoregressive integrated moving average model, wavelet analysis methods have been in-troduced. Along with statistical methods, neural networks are also a powerful tool for predicting time series, due to the ability of neural networks to model relationships and complex patterns in data, predicting time series using it has attracted the attention of researchers in various fields and is a research topic. It has become popular. The use of convolutional neural networks to predict time series is known as an e?ective method for analyzing and predicting repetitive patterns in time data. These networks are designed to recognize di?erent patterns in temporal data and can make accurate predictions for future data values using these patterns. Long Short Term Memory (LSTM) Recurrent Neural Networks and Gate Recurrent Neural Networks (GRU) are two types of neural networks used for time series forecasting. LSTM and GRU networks are useful for time series forecasting due to their ability to retain memory over time. These networks, using a memory unit, keep the previous information and make the next prediction according to this information. In this thesis, time series forecasting with convolutional neural network and LSTM and GRU neural networks is investigated. The performance of these networks in prediction accuracy is compared. Also, their performance is compared with statistical methods such as SARIMA.Key ords. Forecasting time series, Neural networks, Recurrent neural networks, Long short-term memory, Gated recurrent unit, Convolutional neural networks.