Quantification of predicted uncertainty for a data-based model

Chai, Jangbom,Kim, Taeyun Korean Nuclear Society 2021 Nuclear Engineering and Technology Vol.53 No.3

A data-based model, such as an AAKR model is widely used for monitoring the drifts of sensors in nuclear power plants. However, since a training dataset and a test dataset for a data-based model cannot be constructed with the data from all the possible states, the model uncertainty cannot be good enough to represent the uncertainty of estimations. In fact, the errors of estimation grow much bigger if the incoming data come from inexperienced states. To overcome this limitation of the model uncertainty, a new measure of uncertainty for a data-based model is developed and the predicted uncertainty is introduced. The predicted uncertainty is defined in every estimation according to the incoming data. In this paper, the AAKR model is used as a data-based model. The predicted uncertainty is similar in magnitude to the model uncertainty when the estimation is made for the incoming data from the experienced states but it goes bigger otherwise. The characteristics of the predicted model uncertainty are studied and the usefulness is demonstrated with the pressure signals measured in the flow-loop system. It is expected that the predicted uncertainty can quite reduce the false alarm by using the variable threshold instead of the fixed threshold.

Option-Implied Preferences with Model Uncertainty

Byung Jin Kang,Tong Suk Kim,Hyo Seob Lee 한국재무학회 2010 한국재무학회 학술대회 Vol.2010 No.05

This paper constructs an equilibrium model of option-implied preferences with model uncertainty. Our theoretical model shows that an investor with model uncertainty has a higher level of risk aversion than an investor without model uncertainty, which is helpful in explaining the equity premium puzzle. Using the detection-error probabil- ity, we estimate the option-implied uncertainty aversion. Empirical ¯ndings show that the estimated option-implied risk aversion with model uncertainty is larger than that without model uncertainty. With the higher level of uncertainty aversion, the empirical uncertainty premium shows the steeper smirk pattern across the wealth, which looks very similar to the smirk pattern of the implied volatility of S&P 500 index options.

Private Equity Valuation under Model Uncertainty

Yuxiang BIAN 한국유통과학회 2022 The Journal of Asian Finance, Economics and Busine Vol.9 No.1

The study incorporates model uncertainty into the private equity (PE) valuation model (SWY model) (Sorensen et al., 2014) to evaluate how model uncertainty distorts the leverage and valuations of PE funds. This study applies a continuous-time model to PE project valuation, modeling the LPs’ goal as multiplier preferences provided by Anderson et al. (2003), and assuming that LPs’ aversion to model uncertainty causes endogenous belief distortions with entropy as a measure of model discrepancies. Concerns regarding model uncertainty, according to the theoretical model, have an unclear effect on LPs’ risk attitude and GPs’ decision, which is based on the value of the PE asset. It also demonstrates that model uncertainty lowers the certainty-equivalent valuation of the LPs. Finally, we compare the outcomes of the Full-spanning risk model with the Non-spanned risk model, and they match the intuitive economic reasoning. The most important implication is that model uncertainty will have negative effects on the LPs’ certainty-equivalent valuation but has ambiguous effects on the portfolio allocation choice of liquid wealth. Our works contribute to two literature streams. The first is the literature that models the PE funds. The second is the literature introduces model uncertainty into standard finance models.

모델 불확실성을 고려한 항공기 러그 구조물의 피로 수명 예측

임종빈 한국항공우주학회 2011 한국항공우주학회 학술발표회 논문집 Vol.2011 No.11

공학에서 입력 값에 의한 응답을 계산할 때, 입력과 응답의 상관관계를 표현 하는 다양한 모델들을 이용한다. 이러한 모델들은 일반적으로 실험 데이터를 기반으로 생성되며 같은 현상에 대해서도 다른 모델들이 존재한다. 같은 현상에 대해서 다양한 모델이 존재할 때, 어떤 모델을 선택하여 주어진 문제를 해결할 지는 경험이 있는 전문가의 선택에 의해서 결정되는 경우가 많다. 이 때 특정 모델을 선택함으로써 발생되는 불확실성을 모델 불확실성이라 한다. 본 논문에서는 모델 불확실성을 고려하여 항공기 러그 구조물의 피로수명을 예측하는 방법을 제시하였다. 모델 불확실성으로써는 S-N 선도 모델을 설정하였으며, 불확실성에 의한 구조물의 피로 수명에 대한 평균과 표준편차를 구하였다. 계산된 피로 수명의 평균과 표준편차를 이용하여 피로수명에 대한 구조물의 확률론적 신뢰구간을 설정하였다. There are many models to express a relationship between input and output in engineering fields. In general, a model among models that represent a same phenomenon is selected by an expert to solve a engineering problem. When a model is selected there is model uncertainty because the selected model is not the best model but a better model. In this paper, the fatigue life of a aircraft lug is estimated considering model uncertainty. As a model uncertainty two S-N curve models are considered. The mean and standard deviation of the estimated fatigue life of the aircraft lug is calculated due to the model uncertainty. Consequently, the reliable bounds of estimated fatigue life are suggested for the aircraft lug.

Uncertainty estimation of the SURR model parameters and input data for the Imjin River basin using the GLUE method

Bae, Deg-Hyo,Trinh, Ha Linh,Nguyen, Hoang Minh Elsevier 2018 JOURNAL OF HYDRO-ENVIRONMENT RESEARCH Vol.20 No.-

<P>This study investigated the flow simulation uncertainty caused by the model parameters and input data for the Imjin River basin using the generalized likelihood uncertainty estimation (GLUE) method and the Sejong University rainfall-runoff (SURR) model for four events during 2007, 2008, 2009 and 2010. Based on the nonsystematic errors caused by the rainfall interpolation process, the input uncertainty was estimated and compared with the model parameter uncertainty for the regions with different data information situations. The reasons for the high or low uncertainty of the model parameters and input were also analyzed. Two indices were used to examine the uncertainty of the streamflow simulation: the ratio of the number of observations falling inside the uncertainty interval (p - factor) and the width of the uncertainty interval (r - factor). The results indicated that the uncertainty of the streamflow simulation of the northern area (Gunnam station) was significantly higher than that of the southern areas (Jeonkok and Jeogseong stations) for both model parameter and input uncertainty. In the southern areas, the parameter uncertainty was higher than the input uncertainty. However, the northern area exhibited the opposite trend, with the former being lower than the latter. Additionally, the uncertainty was also shown in the time of the hydrograph. The uncertainty at the peak flow was higher than that at the beginning or the end of each event.</P>

Copula 모형을 이용한 에너지 가격과 경제적 불확실성 사이의 의존관계 분석

김부권,최기홍,윤성민 한국환경경제학회 2020 자원·환경경제연구 Vol.29 No.2

본 연구는 에너지(석유, 천연가스, 석탄) 가격과 경제적(실물 및 금융) 불확실성 사이의 의존성 구조를 분석하였다. Copula 모형을 이용해 얻은 의존구조 분석 결과를 요약하면 다음과 같다. 첫째, 에너지 가격과 실물ㆍ금융 불확실성 조합의 적합한 모형을 살펴보면, 원유가격과 실물ㆍ금융 불확실성 조합은 BB7 copula 모형, 천연가스 가격과 실물ㆍ금융 불확실성 조합은 Joe copula 모형, 석탄 가격과 실물ㆍ금융 불확실성 조합은 Clayton copula 모형이 각각 가장 적합한 모형으로 선정되었다. 둘째, 전체적인 의존성 구조를 살펴보면, 원유가격, 천연가스 가격, 석탄 가격과 실물 불확실성은 양(+)의 의존성을 보였다. 그렇지만 금융 불확실성과 원유가격은 양(+)의 의존성을 갖지만, 천연가스 가격과 석탄 가격은 금융 불확성과 음(-)의 의존성을 가지는 것으로 나타났다. 전체적으로 보면, 에너지원 중 원유가격이 실물ㆍ금융 불확실성과 가장 높은 의존성을 가지는 것으로 나타났다. 셋째, 극단적인 사건을 나타내는 꼬리 의존성을 분석한 결과, 실물 불확실성과 원유, 천연가스 가격은 위 꼬리 의존성만 보이는 비대칭 관계를 가지는 것으로 나타났으며, 금융 불확실성과 원유가격은 위 꼬리 의존성만 보이는 비대칭 관계를 가지는 것으로 나타났다. 즉, 비대칭 관계를 갖는 에너지 가격은 부정적인 극단사건이 발생하는 경우 불확실성 변수와 강한 의존관계가 있는 것으로 나타났다. 반면, 경제적 불확실성과 석탄 가격은 꼬리 의존성이 없는 것으로 나타났다. This study analyzes the dependence structure between energy (crude oil, natural gas, coal) prices and economic (real and financial) uncertainty. Summary of the results of the dependence structure between energy prices and economic uncertainty analysis is as follows. First, the results of model selection show that the BB7 copula model for the pair of crude oil price and economic uncertainty, the Joe copula model for the pair of natural gas price and economic uncertainty, and the Clayton copula model for the pair of coal price and economic uncertainty were chosen. Second, looking at the dependency structure, it showed that the pair of energy (crude oil, natural gas, coal) prices and real market uncertainty show positive dependence. Whereas, the only pair of financial market uncertainty-crude oil price shows positive dependency. In particular, crude oil price was found to have the greatest dependence on economic uncertainty. Third, looking at the results of tail dependency, the pair of real market uncertainty-crude oil price and pair of real market uncertainty-natural gas price have an asymmetric relationship with the upper tail dependency. It can be seen that the only pair of financial market uncertainty-crude oil represents asymmetric relationships with the upper tail dependencies. In other words, combinations with asymmetric relationships have shown strong dependence when negative extreme events occur. On the other hand, tail dependence between economic uncertainty and coal price be not found.

확률적 시뮬레이션을 이용한 모델 기반 강화학습

주하람(Haram Joo),김준오(Juno Kim),이상완(Sang Wan Lee) 한국지능시스템학회 2018 한국지능시스템학회논문지 Vol.28 No.5

본 논문은 상태천이에 불확실성이 있는 동적 환경에서도 안정적인 학습이 가능한 model-based 강화학습 전략을 제안한다. 기존의 강화학습 알고리즘은 보상의 기대치 최대화에 초점을 둔 model-free 방식으로 환경의 불확실성을 경험적으로 습득하므로 적응 속도가 느리다. 이에 비해 환경 모델을 학습하는 model- based 방식은 아직 경험하지 못한 상황에 대한 시뮬레이션 결과를 보상의 기대치 학습에 적용함으로써 환경변화에 빠른 적응이 가능하다. 본 연구에서는 환경의 상태천이에 대한 확률 모델을 온라인 학습하고, 학습된 모델을 이용하여 확률적으로 시나리오를 시뮬레이션하며, 이를 바탕으로 보상의 기대치를 최대화하는 전략을 찾아내는 model-based 강화학습 방식을 구현하였다. OpenAI의 FrozenLake 시뮬레이터를 이용하여 불확실성을 내포한 동적 환경을 구현하였으며, 제안한 모델과 기존 방법의 성능을 다양한 측면에서 비교하였다. 제안된 모델은 상태천이의 불확실성과 환경변화의 불안정성이 모두 존재하는 극한 상황 속에서도 변화에 강인한 전략 탐색의 기틀을 제공한다. This paper proposes a model-based reinforcement learning strategy that enables stable learning even in a dynamic environment containing state transition uncertainty. The existing reinforcement learning algorithm is a model-free method that focuses on maximizing the expectation of the reward, and the adaptation speed is slow because it empirically learns the uncertainty of the environment. In contrast, the model-based method that learns the environmental model can adapt quickly to changes in the environment by applying the simulation results to the expectation reward. In this paper, we propose a model-based reinforcement learning method that finds a strategy that maximizes the expectation of reward based on the on-line learning of the probability transition model of the environment, simulates the scenario probabilistically using the learned model. We implemented the dynamic environment containing uncertainty using FrozenLake simulator of OpenAI and compared the performance of the proposed model with the existing method in various aspects. The proposed model provides a framework for strategy exploration even in extreme situations where both uncertainty of state transition and instability of environmental change exist.

딥러닝 기반 시계열 분석 모델의 불확실성 정량화 비교 연구

윤영인(Young-In Yoon),정혜영(Hye-Young Jeong) 한국자료분석학회 2024 Journal of the Korean Data Analysis Society Vol.26 No.1

인공지능의 발전으로 머신러닝과 딥러닝 모델이 다양한 산업에서 적용되어 좋은 성능을 보이고 있으며 최근 금융시장에서도 적용되는 사례가 증가하고 있다. 그러나 딥러닝 모델은 예측 결과가 나오게 된 과정과 해석을 파악하기에 어려움이 있다. 이는 결과에 대한 해석이 특히 중요시 되는 금융에 딥러닝 모델을 적용하는데 어려움이 있어 신뢰할 수 있는 모델에 대한 필요성이 대두되고 있다. 신뢰할 수 있는 모델이란 모델에 Dropout과 같은 변화에도 일관된 예측을 보이는 안정적인 모델로 모델의 불확실성을 통해 파악할 수 있다. 본 연구는 딥러닝 모델의 불확실성을 확인하여 신뢰할 수 있는 모델의 기준을 보이고 모델의 불확실성을 통해 이상 탐지하는 모델을 파악하고자 한다. 실험에서 전통적인 통계 모델 ARIMA(Auto Regressive Integrated Moving Average)와 시계열 데이터에 주로 쓰이는 딥러닝 모델인 CNN(Convolutional Neural Network), LSTM(Long Short Term Memory), MLP(Multi-Layer Perceptron), 및 CNN-LSTM 모델을 적용하였고 MC(Monte Carlo) Dropout을 통해 베이지안 관점에서 불확실성을 측정하였다. 실험 결과 다양한 패턴의 시계열 데이터에 대해 통계 모델보다 여러 딥러닝 모델이 성능이 좋음을 확인하였고 성능이 가장 우수하지는 않아도 불확실성이 적어 안정적인 모델이 LSTM 계열임을 확인하였다. 이를 통해 불확실성이 모델의 정확도와 함께 모델 선택 시 고려되어야 할 요소임을 확인하였고 불확실성이 큰 모델이 이상 탐지하므로 CNN 계열의 모델이 적합함을 확인하였다. With the advancement of artificial intelligence, machine learning, and deep learning, their applications in various industries, particularly finance, have increased. However, interpreting predictions from deep learning models poses challenges, especially in finance where result interpretation is important. This study aims to determine the uncertainty of stable deep learning models, despite changes in the model like dropout, to establish standards for reliable models and identify those detecting anomal data through model uncertainty. In the experiment, the traditional statistical model ARIMA and deep learning models mainly used for time series analysis, CNN, LSTM, MLP, and CNN-LSTM. Uncertainty was measured from a Bayesian perspective using MC Dropout. The experimental results confirmed that deep learning models performed better than statistical models for various patterns of time series data. It was observed that, even if the performance was not the best, LSTM based models exhibited low uncertainty, indicating stability. Consequently, this study highlights the importance of considering uncertainty along with accuracy in model selection. Moreover, it was confirmed that models with higher uncertainty are suitable for anomaly detection, making CNN based models particularly fitting for this purpose.

The Explicit Treatment of Model Uncertainties in the Presence of Aleatory and Epistemic Parameter Uncertainties in Risk and Reliability Analysis

Ahn, Kwang-ll,Yang, Joon-Eon Korean Nuclear Society 2003 Nuclear Engineering and Technology Vol.35 No.1

In the risk and reliability analysis of complex technological systems, the primary concern of formal uncertainty analysis is to understand why uncertainties arise, and to evaluate how they impact the results of the analysis. In recent times, many of the uncertainty analyses have focused on parameters of the risk and reliability analysis models, whose values are uncertain in an aleatory or an epistemic way. As the field of parametric uncertainty analysis matures, however, more attention is being paid to the explicit treatment of uncertainties that are addressed in the predictive model itself as well as the accuracy of the predictive model. The essential steps for evaluating impacts of these model uncertainties in the presence of parameter uncertainties are to determine rigorously various sources of uncertainties to be addressed in an underlying model itself and in turn model parameters, based on our state-of-knowledge and relevant evidence. Answering clearly the question of how to characterize and treat explicitly the forgoing different sources of uncertainty is particularly important for practical aspects such as risk and reliability optimization of systems as well as more transparent risk information and decision-making under various uncertainties. The main purpose of this paper is to provide practical guidance for quantitatively treating various model uncertainties that would often be encountered in the risk and reliability modeling process of complex technological systems.

Uncertainty assessment of future projections on water resources according to climate downscaling and hydrological models

Lee, Moon-Hwan,Bae, Deg-Hyo IWA Publishing 2018 Journal of hydroinformatics Vol.20 No.3

<P>Quantifying the uncertainty of future projection is important to assess the reliable climate change impact. In this sense, this study is aimed at investigating the uncertainty sources of various water variables (seasonal dam inflow, 1-day maximum dam inflow, and 30-day minimum dam inflow) according to downscaling methods and hydrological modeling. Five regional climate models (RCMs), five statistical post-processing methods and two hydrological models were applied for the uncertainty analysis. The changes for seasonal dam inflow are 0.1, 58.8, 5.1, and 1.1 mm for the SWAT model and 2.1, 76.1, −8.5, and −2.9 mm for the VIC model in spring, summer, autumn, and winter, respectively. The effects of the hydrological model is smaller than that of RCM for future projections of the seasonal dam inflow. The changes of annual 1-day maximum dam inflow vary according to the selection of RCM whereas the changes of annual 30-day minimum dam inflow are sensitive to the selection of hydrological model. The RCM is the dominant source of uncertainty of all seasonal dam inflow (except for winter) and high flow, whereas the hydrological model is the dominant source of uncertainty in winter dam inflow and low flow. Considering these results, the appropriate multi-model ensemble chain according to target variable will be necessary for reliable climate change impact assessment.</P>