New Measure Of Uncertainty Research Articles

Belief Tsallis-Deng Structure Entropy and its uniform framework for analyzing multivariate time-series complexity based on evidence theory

In the framework of evidence theory, this paper proposes a new measure of uncertainty and introduces an entirely new unified framework for analyzing the complexity of multivariate time series. The theoretical foundation of this paper is random sets, viewing multivariate sequences as a new type of set variable, and using the belief theory framework to describe their behavior. Set variables are a natural extension of point variables, thus providing stronger universality in the analysis of multivariate time series. We tested our proposed new analytical framework on the logistic map and used the Tsallis-Deng Structure Entropy introduced in this paper to analyze the generated multivariate time series. Compared to the traditional Deng entropy, Tsallis-Deng Structure Entropy can adjust the sensitivity to time series complexity by tuning its structural parameter p. As the parameters of the logistic map change, the changes in Tsallis-Deng Structure Entropy show a high correlation with the Lyapunov exponent. In addition, we applied the proposed framework to analyze a multivariate epileptic EEG dataset. The results showed that using the novel evidence theory-based analysis framework for the 23-channel multivariate time series, the average classification accuracies of Deng entropy, Tsallis-Deng entropy, and Tsallis-Deng structural entropy for 24 epilepsy patients were 79 %, 74 %, and 82 %, respectively. In contrast, the average recognition accuracy using the traditional probabilistic framework based on multivariate embedding theory was 64 %. The evidence theory-based framework generally outperformed the multivariate embedding theory, with Tsallis-Deng structural entropy achieving the best performance. These results indicate that the proposed evidence theory-based framework not only avoids the dimensionality curse of the multivariate embedding theory but also better quantifies the complexity of multivariate time series from the same system and distinguishes different types of multivariate time series.

Sup-extropy: A measure of uncertainty

. In a recent development, a new measure of uncertainty, termed extropy, was introduced as the dual complement of Shannon entropy. This study proposes a modified extropy measure called sup-extropy. The proposed uncertainty measure is shown to be minimal value when the data follow a uniform distribution. Various fundamental properties of this measure are thoroughly examined. The joint and conditional versions of this measure are also presented. To illustrate its practical implications, highlights into its application in letter-catching experiments and information fusion analysis are provided.

A New Model Uncertainty Measure of Wave-Induced Motions and Loads on a Container Ship with Forward Speed

A new uncertainty quantifier is presented for linear transfer functions of wave-induced ship motions and loads obtained by various seakeeping codes. The numerical simulations are conducted for the high-speed Flokstra container ship in regular waves at various heading angles, and the results are compared with existing experimental data. The study employs five numerical codes that are based on three different seakeeping theories, namely strip theory, 3D frequency-domain method, and 3D time-domain method. Multiple measures are applied to quantify the uncertainty in the calculated transfer functions, such as frequency-independent model error, coefficient of determination, and the total difference. In addition, a new measure of uncertainty, termed modified total difference, is proposed for determining the uncertainty of individual seakeeping codes based on experimental data rather than the mean of results obtained by numerical codes. Results show that the uncertainty measures can identify differences between the codes. The predicted wave-induced loads have higher uncertainties compared to motions. The uncertainty assessment shows that none of the applied codes can produce accurate estimates for all wave-induced motions and loads at all heading angles at the same time.

Meaningful expression of uncertainty in measurement

The Guide to the expression of uncertainty in measurement (GUM) has been the enduring guide on measurement uncertainty for metrologists since its first publication in 1993. According to the GUM, a measurement should always be accompanied by a reasoned and defensible expression of uncertainty, and the primary such expression is the standard uncertainty. In this article, we distinguish between the use of an expression of uncertainty as information for the recipient of a measurement result and its use when propagating uncertainty about inputs to a measurement model in order to derive the uncertainty in a measurand. We propose a new measure of uncertainty, the characteristic uncertainty, and argue that it is more fit for these purposes than standard uncertainty. For the purpose of reporting a measurement result, we demonstrate that standard uncertainty does not have a meaningful interpretation for the recipient of a measurement result and can be infinite. These deficiencies are resolved by the characteristic uncertainty, which we therefore recommend for use in reporting. For similar reasons, we advocate the use of the median estimate as the measured value. For the purpose of propagating uncertainty in a measurement model, we propose simple propagation of the median and characteristic uncertainty and show through some examples that this characteristic uncertainty framework is simpler and at least as reliable and accurate as the propagation of estimate, standard uncertainty and effective degrees of freedom according to the GUM uncertainty framework.

New Measures of Uncertainty for Interval-Valued Data With Application to Attribute Reduction

Uncertainty measurement (UM) gives a brand-new perspective on attribute reduction in an information system (IS). Interval-valued data is a kind of very vital data in rough set theory (RST). Rough set model based on tolerance relations can be considered to deal with interval-valued data. However, these kinds of tolerance relations have deficiencies when they are used in fuzzy rough computation. This paper studies new UM for an interval-valued information system (IVIS) and considers its attribute reduction. Firstly, a novel fuzzy symmetry relation on the object set of an IVIS is established based on “The similarity between information values that is fed back to the attribute set”. Secondly, λ-information granules on the basis of a fuzzy symmetry relation are obtained. Then, four UMs for an IVIS are investigated. Next, numerical experiments and statistical tests are used to evaluate the performance of the proposed UMs. Moreover, attribute reduction in an IVIS is studied and the relevant algorithms are proposed. Finally, clustering analysis on the reduced IVIS is conducted. Experimental results indicate that the proposed algorithms are effective based on evaluation indicators of clustering performance. This paper provides a novel viewpoint for the establishment of fuzzy symmetry relation and attribute reduction algorithms.

New measures of uncertainty based on the granularity distribution of approximation sets

New measures of uncertainty based on the granularity distribution of approximation sets

Does policy uncertainty affect economic globalization? An empirical investigation

ABSTRACT This paper investigates the role of policy uncertainty on indices of economic globalization from 1996 to 2016 in the panel dataset of 142 countries. For this purpose, we use the nine measures of the Revisited KOF Economic Globalization Indices and two new measures of uncertainty: The World Uncertainty Index (WUI) and the Trade Policy Uncertainty Index (TPUI). The findings indicate that both the WUI and the TPUI are negatively associated with the overall index of economic globalization. The benchmark results remain consistent under various model specifications, econometric estimation techniques, and countries at different income levels.

The Determinants of Uncertainty in International Relations

Abstract Uncertainty about military power is widely considered an important determinant of international conflict, but research in international relations provides relatively little guidance about the origins of uncertainty. What factors influence the validity of actors’ assessments of military capabilities? When would one expect uncertainty about military capabilities to be particularly high, or especially low? We examine a series of factors capable of explaining the sources of uncertainty in international relations, positing that the uncertainty of assessments is a function of both characteristics of the state being assessed and the overall strategic environment. We test our theory using new measures of uncertainty that we derive from analyzing publicly available estimates of national military capabilities. Our findings offer a novel set of implications both for research that relies on uncertainty as a key cause of conflict and for policymakers faced with evaluating foreign military assessments.

Monetary Policy Uncertainty in China

In this paper, we study the measurement and the consequences of monetary policy uncertainty in China. We propose a new measure of uncertainty about the monetary policy of the People’s Bank of China (PBOC). The uncertainty index is extracted from the reporting about the PBOC’s monetary policy in international newspapers. We show that a shock to Chinese monetary policy uncertainty has significant effects on real economic activity, investment and asset prices in mainland China. Moreover, this shock has spillover effects on other Asian economies, leading to a fall in asset prices and GDP. Particularly, an increase in uncertainty leads to a drop in stock prices throughout the region. Hence, uncertainty about the PBOC’s monetary policy is an additional channel of transmission that coexists with the transmission of the PBOC monetary policy itself. Finally, we show that our index contains information over and above what is already incorporated in monetary policy uncertainty indices based on mainland newspapers.

Fiscal policy in the US: a new measure of uncertainty and its effects on the American economy

We use the dispersion of the Federal Budget Balance forecasts from Consensus Economics to construct a new measure of fiscal uncertainty; constant horizon forecasts are obtained through mixture distributions. The scheme we propose has several advantages over previous uncertainty measures. First (as opposed to recent proposals), it results in a forward-looking measure, which implies that any sudden development in terms of an (un)expected fiscal stance is immediately incorporated in the series. Second, the measure is by construction a real-time one. Third, being completely model-free, it is not contaminated (inflated) by model uncertainty. Fourth, our measure does not simply track uncertainty stemming from public consumption and investment, whereas it is comprehensive in also accounting both for the critical welfare component of public expenditure and for taxes. Fifth, as opposed to uncertainty indexes which can be interpreted only dynamically, our measure has an obvious intuitive point-wise interpretation. Interestingly, the inception of the Trump administration has led to unprecedented uncertainty shocks which have demonstrably put a non-negligible brake on the slow US recovery. More generally, we show that fiscal uncertainty shocks have clear recessionary effects. Furthermore, constraints on monetary policies during the ZLB have likely strengthened the recessionary effects of fiscal uncertainty shocks.

Monetary policy uncertainty in China

We propose a new measure of uncertainty about the monetary policy of the People’s Bank of China (PBOC). The uncertainty index is extracted from the reporting about the PBOC's monetary policy in international newspapers. A shock to Chinese monetary policy uncertainty has significant effects on economic activity in mainland China. An increase in monetary policy uncertainty leads to a strong fall in investment, GDP and prices. We also show that a monetary policy uncertainty shock originating in mainland China has strong spillover effects on other Asian economies, leading to a fall in asset prices and GDP. An increase in reporting about uncertainty in international newspapers leads to a drop in stock prices throughout the region. Hence, uncertainty about the PBOC's monetary policy is an additional channel of transmission that coexists with the transmission of PBOC monetary policy itself. Finally, we show that our index contains information over and above what is already incorporated in monetary policy uncertainty indices based on mainland newspapers.

Quantification of predicted uncertainty for a data-based model

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.

Does economic uncertainty affect domestic credits? an empirical investigation

Using the new measure of uncertainty (i.e., the World Uncertainty Index), this paper analyzes the effects of uncertainty on the level of domestic credits in a panel of 139 countries for the period from 1996 to 2017. The findings of the fixed-effects and the system Generalized Method of Moments (GMM) estimations show that a higher level of uncertainty decreases the level of domestic credits. Per capita income and money supply are positively related to the domestic credits, but the current account balance is negatively associated with domestic credit measures. After implementing various sensitivity analyses, i.e., to exclude the outliers and the countries in the different regions as well as to include various controls, the primary evidence remains robust.

Monetary policy uncertainty

We construct a new measure of uncertainty about Federal Reserve policy actions and their consequences, a monetary policy uncertainty (MPU) index. We evaluate the information content of our index and document the usefulness of our index in bridging periods of conventional and unconventional policy making. We also estimate the aggregate effects of shocks to MPU on output, credit spreads, and other variables. Finally, we investigate the transmission channels of MPU, finding that heightened MPU leads to protracted declines in firm investment through both real options and financial frictions channels.

Fiscal Policy in the US: A New Measure of Uncertainty and Its Recent Development

We use the dispersion of the Federal Budget Balance forecasts from Consensus Economics to produce a new measure of fiscal uncertainty; constant horizon forecasts are obtained through mixture distributions. The scheme we propose has several advantages over previous uncertainty measures. First (as opposed to recent proposals) it results in a forward-looking measure, which implies that any sudden development in (un)expected fiscal stance is immediately incorporated in the series. Second, the measure is by construction a real-time one. Third, being completely model-free it is not contaminated (inflated) by model uncertainty. Fourth, it is comprehensive in accounting both for the critical welfare component of public expenditures and for taxes, i.e. it does not simply track uncertainty stemming from public consumption and investment. Fifth, as opposed to uncertainty indexes which can be interpreted only dynamically, our measure has an obvious intuitive point-wise interpretation. Interestingly, the inception of the Trump administration has led to unprecedented uncertainty shocks which are shown to have put a non-negligible brake on the US slow recovery. On a more general level, we show that fiscal uncertainty shocks have clear recessionary effects. Furthermore, constraints on monetary policies during the ZLB have likely caused the recessionary effects of fiscal uncertainty shocks to be stronger.

Term structure dynamics in a monetary economy with learning

This paper investigates a continuous-time monetary asset-pricing model of the term structure of nominal interest rates. In a pure exchange economy with incomplete information, investors cannot observe the expected growth rates of both exogenous real output and money supply. Therefore, they apply dynamic Bayesian inference. The model obtains explicit solutions for equilibrium prices of consumption goods and nominal bonds, and the stochastic process of an investor’s beliefs. The dependence of term premia on beliefs allows the model to introduce a GARCH property, which interacts with the volatility of the macro variables. In particular, the volatility of excess returns is inversely related to noise in the macro variables, suggesting that their imprecise information does not increase fluctuations in interest rates. Using beliefs as the factor of uncertainties in economic states, the model also shows that there is a negative correlation between the new measure of uncertainty and the velocity of money, consistent with Friedman’s explanation that demand for money for precautionary motives has a negative impact on the velocity.

New measures of uncertainty for an interval-valued information system

An information system as a database that represents relationships between objects and attributes is an important mathematical model. An interval-valued information system is a generalized model of single-valued information systems. As important evaluation tools in the field of machine learning, measures of uncertainty can quantify the dependence and similarity between two targets. However, the existing measures of uncertainty for interval-valued information systems have not been thoroughly researched. This paper is devoted to the study of new measures of uncertainty for an interval-valued information system. Information structures are first introduced in a given interval-valued information system. Then, the dependence between two information structures is depicted. Next, new measures of uncertainty for an interval-valued information system are investigated by using the information structures. As an application of the proposed measures, the rough entropy of a rough set is proposed by means of information granulation. Finally, a numerical experiment on the Face recognition dataset is presented to demonstrate the feasibility of the proposed measures, and a statistical effectiveness analysis is conducted. The results are helpful for understanding the essence of uncertainty in interval-valued information systems.

Policy Uncertainty and the Demand for Money in Australia: an Asymmetry Analysis

Previous research has considered the impacts of both monetary and output uncertainty on the demand for money in Australia using a linear model and found that while output volatility has significantly positive effects, money supply volatility does not. Furthermore, the predictive power of the linear model was very low. In this paper, we use a nonlinear model and a new measure of uncertainty known as policy uncertainty and show that this new measure has significantly long‐run asymmetric effects on the demand for money in Australia. Due to the nonlinear adjustment of policy uncertainty measure, the new nonlinear model has a very high predictive power. The adjustedR2moves from 0.30 in the linear model to 0.80 in the nonlinear model.

A quantile-based generalized dynamic cumulative measure of entropy

ABSTRACTThe cumulative residual entropy (CRE), introduced by Rao et al. (2004), is a new measure of uncertainty and viewed as a dynamic measure of uncertainty. Asadi and Zohrevand (2007) proposed a dynamic form of the CRE, namely dynamic CRE. Recently, Kumar and Taneja (2011) introduced a generalized dynamic CRE based on the Varma entropy introduced by Varma (1966) and called it dynamic CRE of order α and type β. In the present article, we introduce a quantile version of the dynamic CRE of order α and type β and study its properties. For this measure, we obtain some characterization results, aging classes properties, and stochastic comparisons.

Monetary Policy Uncertainty

We construct new measures of uncertainty about Federal Reserve policy actions and their consequences - monetary policy uncertainty (MPU) indexes. We show that, under a variety of VAR identification schemes, positive shocks to uncertainty about monetary policy robustly raise credit spreads and reduce output. The effects are of comparable magnitude to those of conventional monetary policy shocks. We evaluate the usefulness of our MPU indexes, and examine the influence of Fed communication. Our analysis suggests that policy rate normalization that is accompanied by reduced uncertainty can help neutralize the contractionary effects of the rate increases themselves.