Balanced-BiEGCN: A Bidirectional EvolveGCN with a Class-Balanced Learning Network for Dynamic Anomaly Detection in Bitcoin

In a research study, population data are often not available, so the population parameter is unknown. Meanwhile, knowledge about the population parameter is needed to know the characteristics of the studied population. Therefore, it is needed to estimate the parameter of the population which can be estimated by sample data. There are several methods of parameter estimation which are generally classified into classical and Bayesian method. This research studied the Bayesian parameter estimation method to determine the parameters of the exponentially distributed survival data associated with the reliability measure of the estimates under symmetric and asymmetric loss functions for complete sample data in a closed form. The symmetric loss functions used in this research are Squared Error Loss Function (SELF) and Minimum Expected Loss Function (MELF). The asymmetric loss functions used are the General Entropy Loss Function (GELF) and Linex Loss Function (LLF). Performance of some loss functions used in this research are then compared through numerical simulation to select the best loss function in determining the parameter estimation of the exponentially distributed survival data. We also studied which loss function is best for underestimation and overestimation modeling. Based on simulation results, the Bayes estimates using MELF is the best method to estimate population parameters of the exponentially distributed survival data for the overestimation modeling, while LLF is the best for the underestimation modeling. We provided direct application in a case study of fluorescence lamp survival data. The results show that the best method to estimate the parameter of the standard fluorescence life data is using LLF for underestimation with and MELF for overestimation with .

This paper examines behavioural aspects of the West Texas Intermediate (WTI) oil 1-month futures from 1995 to 2012. We consider that oil futures are formed based on an underlying generalised loss function with an unknown shape parameter that provides information regarding preferences. Even without observing fundamentals of WTI oil futures we can assess whether preferences lean towards a symmetric or asymmetric loss function. Our empirical evidence is robust across information sets and shows that overall loss preferences of WTI 1-month oil futures are rather optimistic and thus the underlying loss function is asymmetric. This implies that if one disregards this asymmetry the WTI oil futures should not be viewed as rational. We further provide statistical tests that allow deviations from a symmetric loss function. As part of a sensitivity analysis, and given the long span of our sample, we perform a novel analysis for detecting breakdowns in our series over time. Based on this analysis we re-examine the shape parameters of the loss function for WTI oil month futures for sub-periods. Interestingly, preferences of WTI 1-month oil futures have shifted towards optimism post 2008 period, marking the collapse of Lehman Brothers.

Recent theoretical and empirical work has cast doubt on the hypotheses of a linear Phillips curve and a symmetric quadratic loss function underlying traditional thinking on monetary policy. This paper analyzes the Barro-Gordon optimal monetary policy problem under alternative loss functionsincluding an asymmetric loss function corresponding to the "opportunistic approach" to disinflationwhen the Phillips curve is convex. Numerical simulations are used to compare the implications of the alternative loss functions for equilibrium levels of inflation and unemployment. For parameter estimates relevant to the United States, the symmetric loss function dominates the asymmetric alternative.

PurposeThe step-stress accelerated test is the most appropriate statistical method to obtain information about the reliability of new products faster than would be possible if the product was left to fail in normal use. This paper presents the multiple step-stress accelerated life test using type-II censored data and assuming a cumulative exposure model. The authors propose a Bayesian inference with the lifetimes of test item under gamma distribution. The choice of the loss function is an essential part in the Bayesian estimation problems. Therefore, the Bayesian estimators for the parameters are obtained based on different loss functions and a comparison with the usual maximum likelihood (MLE) approach is carried out. Finally, an example is presented to illustrate the proposed procedure in this paper.Design/methodology/approachA Bayesian inference is performed and the parameter estimators are obtained under symmetric and asymmetric loss functions. A sensitivity analysis of these Bayes and MLE estimators are presented by Monte Carlo simulation to verify if the Bayesian analysis is performed better.FindingsThe authors demonstrated that Bayesian estimators give better results than MLE with respect to MSE and bias. The authors also consider three types of loss functions and they show that the most dominant estimator that had the smallest MSE and bias is the Bayesian under general entropy loss function followed closely by the Linex loss function. In this case, the use of a symmetric loss function as the SELF is inappropriate for the SSALT mainly with small data.Originality/valueMost of papers proposed in the literature present the estimation of SSALT through the MLE. In this paper, the authors developed a Bayesian analysis for the SSALT and discuss the procedures to obtain the Bayes estimators under symmetric and asymmetric loss functions. The choice of the loss function is an essential part in the Bayesian estimation problems.

This paper studies three discretization methods to formulate discrete analogues of the well-known continuous generalized Pareto distribution. The generalized Pareto distribution provides a wide variety of probability spaces, which support threshold exceedances, and hence, it is suitable for modeling many failure time issues. Bayesian inference is applied to estimate the discrete models with different symmetric and asymmetric loss functions. The symmetric loss function being used is the squared error loss function, while the two asymmetric loss functions are the linear exponential and general entropy loss functions. A detailed simulation analysis was performed to compare the performance of the Bayesian estimation using the proposed loss functions. In addition, the applicability of the optimal discrete generalized Pareto distribution was compared with other discrete distributions. The comparison was based on different goodness-of-fit criteria. The results of the study reveal that the discretized generalized Pareto distribution is quite an attractive alternative to other discrete competitive distributions.

Symmetric loss functions are widely used in regression algorithms to focus on estimating the means. Huber loss, a symmetric smooth loss function, has been proved that it can be optimized with high efficiency and certain robustness. However, mean estimators may be poor when the noise distribution is asymmetric (even outliers caused heavy-tailed distribution noise) and estimators beyond the means are necessary. Under the circumstances, quantile regression is a natural choice which estimates quantiles instead of means through asymmetric loss functions. In this paper, an asymmetric Huber loss function is proposed to implement different penalty for overestimation and underestimation so as to deal with more general noise. Moreover, a smooth truncated version of the proposed loss is introduced to enhance stronger robustness to outliers. Concave-convex procedure is developed in the primal space with the proof of convergence to handle the non-convexity of the involved truncated objective. Experiments are carried out on both artificial and benchmark datasets and robustness of the proposed methods are verified.

Sample size determination (SSD) is an important issue to consider when estimating any parameter. A number of researchers have studied the Bayesian SSD problem. One group considered utility (or loss) functions and cost functions in their SSD problem and the others did not. Among the former, most of the SSD problems are based on symmetric squared error (SE) loss function. On the other hand, in a situation when under estimation is more serious than overestimation or vice versa, then an asymmetric loss function should be used. In such a situation how many samples do we need to take to estimate the parameter under study? In this article, we consider sample size using the asymmetric linex loss function and a linear cost function for various distributions. We compare the sample size obtained from this asymmetric loss function with the sample size from the symmetric SE loss function. We also consider the situation where it is not worth sampling due to high sampling cost or strong prior information.

Recent theoretical and empirical work has cast doubt on the hypotheses of a linear Phillips curve and a symmetric quadratic loss function underlying traditional thinking on monetary policy. This paper analyzes the Barro-Gordon optimal monetary policy problem under alternative loss functions—including an asymmetric loss function corresponding to the “opportunistic approach” to disinflation—when the Phillips curve is convex. Numerical simulations are used to compare the implications of the alternative loss functions for equilibrium levels of inflation and unemployment. For parameter estimates relevant to the United States, the symmetric loss function dominates the asymmetric alternative.

Monetary Policy with a Convex Phillips Curve and Asymmetric Loss

Burr distribution is one of the most important types of distribution in Burr system and has gained special attention. It has an important role in various disciplines, such as reliability analysis, life testing, survival analysis, actuarial science, economics, forestry, hydrology and meteorology. Thus, the parameter estimation for Burr distribution becomes an important thing to do. The frequentist approach using the maximum likelihood method is the most commonly used way to estimate the parameters of a distribution. In this paper we considered using the Bayesian method to estimate the shape parameter k of Burr distribution using gamma prior which is a conjugate prior. The Bayes estimate for the shape parameter k is obtained under the squared-error loss function (SELF) which is one of the symmetric loss function and the precautionary loss function (PLF) which is one of the asymmetric loss function. Through a simulation study, the comparison was made on the performance of the Bayes estimate for the shape parameter k under these two loss functions with respect to the mean-squared error (MSE) and the posterior risk.

For high-voltage and extra-high-voltage consumers, the electricity cost depends not only on the power consumed but also on the contract capacity. For the same amount of power consumed, the smaller the difference between the contract capacity and the power consumed, the smaller the electricity cost. Thus, predicting the future power demand for setting the contract capacity is of great economic interest. In the literature, most works predict the future power demand based on a symmetric loss function, such as mean squared error. However, the electricity pricing structure is asymmetric to the under- and overestimation of the actual power demand. In this work, we proposed several loss functions derived from the asymmetric electricity pricing structure. We experimented with the Long Short-Term Memory neural network with these loss functions using a real dataset from a large manufacturing company in the electronics industry in Taiwan. The results show that the proposed asymmetric loss functions outperform the commonly used symmetric loss function, with a saving on the electricity cost ranging from 0.88% to 2.42%.

Seizure prediction are necessary for epileptic patients. The global spatial interactions among channels, and long-range temporal dependencies play a crucial role in seizure onset prediction. In addition, it is necessary to search for seizure prediction features in a vast space to learn new generalized feature representations. Many previous deep learning algorithms have achieved some results in automatic seizure prediction. However, most of them do not consider global spatial interactions among channels and long-range temporal dependencies together, and only learn the feature representation in the deep space. To tackle these issues, in this study, an novel bi-level programming seizure prediction model, B2-ViT Net, is proposed for learning the new generalized spatio-temporal long-range correlation features, which can characterize the global interactions among channels in spatial, and long-range dependencies in temporal required for seizure prediction. In addition, the proposed model can comprehensively learn generalized seizure prediction features in a vast space due to its strong deep and broad feature search capabilities. Sufficient experiments are conducted on two public datasets, CHB-MIT and Kaggle datasets. Compared with other existing methods, our proposed model has shown promising results in automatic seizure prediction tasks, and provides a certain degree of interpretability.

Previous studies on Sound Event Localization and Detection (SELD) have primarily focused on CNN- and Transformer-based designs. While CNNs possess local receptive fields, making it difficult to capture global dependencies over long sequences, Transformers excel at modeling long-range dependencies but have limited sensitivity to local time–frequency features. Recently, the VMamba architecture, built upon the Visual State Space (VSS) model, has shown great promise in handling long sequences, yet it remains limited in modeling local spatial details. To address this issue, we propose a novel state space model with an attention-enhanced feature fusion mechanism, termed FFMamba, which balances both local spatial modeling and long-range dependency capture. At a fine-grained level, we design two key modules: the Multi-Scale Fusion Visual State Space (MSFVSS) module and the Wavelet Transform-Enhanced Downsampling (WTED) module. Specifically, the MSFVSS module integrates a Multi-Scale Fusion (MSF) component into the VSS framework, enhancing its ability to capture both long-range temporal dependencies and detailed local spatial information. Meanwhile, the WTED module employs a dual-branch design to fuse spatial and frequency domain features, improving the richness of feature representations. Comparative experiments were conducted on the DCASE2021 Task 3 and DCASE2022 Task 3 datasets. The results demonstrate that the proposed FFMamba model outperforms recent approaches in capturing long-range temporal dependencies and effectively integrating multi-scale audio features. In addition, ablation studies confirmed the effectiveness of the MSFVSS and WTED modules.

Based on the record samples, the empirical Bayes estimators of parameter and reliability function for Compound Rayleigh distribution is investigated under the symmetric and asymmetric loss function. In this case the symmetric loss function is squared error and for the asymmetric loss functions, we consider LINEX and general Entropy loss function.

Recent theoretical and empirical work has cast doubt on the hypotheses of a linear Phillips curve and a symmetric quadratic loss function underlying traditional thinking on monetary policy. This paper studies the one-period optimal monetary policy problem under an asymmetric loss function corresponding to the "opportunistic approach" to disinflation and a convex Phillips curve. The policy-inaction range and its properties are derived analytically. Numerical simulations are then used to assess the implications of asymmetric loss for the distributional properties of the equilibrium levels of inflation and unemployment. For parameter values relevant to the U.S., it is found that the asymmetric loss function yields an average inflation rate in excess of the target, and that bias is larger than the standard symmetric loss function. For moderate policy-maker preferences, the asymmetric loss function also yields a smaller gap between average unemployment and the natural rate, and higher (lower) variance of inflation (unemployment) compared to the symmetric benchmark. Calibrating the model to match the observed average unemployment rate requires a high degree of inflation aversion and small asymmetry.