## 1 Introduction  
By 2019, 523 million people have had a cardiovascular disease, and 18.6 million related deaths have been reported [1]. High blood pressure is a direct cause of death from cardiovascular disease (CVD) [2, 3]. Therefore, accurate blood pressure (BP) measurements are necessary for diagnosing hypertension. BP monitoring has become vital for people with CVD, particularly elderly people who are living alone. Rapid changes in BP in these patients can indicate an underlying severe illness. Furthermore, BP varies owing to intrinsic physiological changes for various reasons, such as food intake, environmental temperature, exercise, disease, and stress. Thus, the precision and uncertainty of BP measurements induced by physiological parameters [4] have been a constant concern for clinicians and practitioners [5, 6, 7]. However, using BP monitoring devices for estimating BP uncertainty is currently impossible. This necessitates a standard protocol for confidence intervals (CIs), representing the uncertainty of BP monitors [5, 8, 9]. Most BP monitors offer only single-point estimates without CIs [5, 8, 9]. Therefore, patients, nurses, and physicians may be unable to differentiate intrinsic variations owing to the estimate's statistical variation and physiological processes [7, 8, 9]. Machine learning (ML) algorithms are commonly used for BP estimation [5; 9; 10; 11; 12]. ML algorithms, including multiple linear regression (MLR) [13; 14], artificial neural networks (ANNs) [14; 15; 16], and support vector machine (SVM) [17; 18; 19] have been utilized for estimating BP [14; 20; 21; 22]. [PERSON] et al. [15] introduced a BP estimation method using photoplethysmography (PPG) signals using novel ANNs. [PERSON] et al. [23] proposed a new long short-term memory (LSTM) and convolutional neural network using cuffless BP estimation based on PPG and electrocardiogram (ECG) signals. Multichannel PPG was introduced using an SVM-ensemble-based continuous BP estimation in [19]. [PERSON] et al. [14] proposed a new method for estimating BP using a window-function-based piecewise neural network. This study evaluated a random-forest-based regression network, three-layer ANN-based regression network, and SVM model using PPG signals. Many studies on PPG-signal-based cuffless BP estimation have been conducted [13; 15; 21; 22; 23]. By contrast, studies on CIs estimation are limited. However, there have been studies on the uncertainty of estimating a few BP data based on conventional oscilloscope BP measurements [5; 6; 7; 8; 9]. The two most used methods for cuffless BP estimation were obtained using the extracted features and pulse transit time (PTT) from PPG signal pulses [14; 24; 25; 26]. The feature extraction method using PTT effectively estimates BP because PTT is closely correlated with BP [27]. According to this principle, arterial pressure can be determined by measuring pulse wave velocity (PWV) at pulse wave speed. This is because changes in PTT correspond to changes in PWV at a fixed distance and indicates a change in BP [26; 28; 29; 30]. Accordingly, this study proposed a new methodology for simultaneously estimating BP and CIs using cuffless BP measurement through a hybrid feature selection and decision based on the Gaussian process (GP). This study aimed to estimate BP and CIs, representing the uncertainty of cuffless BP estimation. Moreover, the GP can directly generate uncertainty estimates [31; 32; 33], such as providing a distribution of estimates rather than a single value. Another advantage of GP algorithms is that, similar to other kernel methods, they can be optimized precisely for given hyperparameter values [34]. Therefore, they perform well owing to the well-optimized parameter values, particularly with limited datasets [34]. However, the CIs automatically calculated by the GP algorithm are too wide to effectively represent the uncertainty. Therefore, CIs are estimated by applying the bootstrap method [8] using the results of the GP algorithm [31] to represent the uncertainty in the cuffless BP estimation.