Improved methods to construct prediction intervals for network meta-analysis.

Short-term load forecasting (STLF) is of great importance for control and scheduling of electrical power systems. The uncertainty of power systems increases due to the random nature of climate and the penetration of the renewable energies such as wind and solar power. Traditional methods for generating point forecasts of load demands cannot properly handle uncertainties in datasets. To quantify these potential uncertainties associated with forecasts, this paper implements a neural network (NN)-based method for construction of prediction intervals (PIs). A newly proposed method, called lower upper bound estimation (LUBE), is applied to develop PIs using NN models. The primary multi-objective problem is firstly transformed into a constrained single-objective problem. This new problem formulation is closer to the original problem and has fewer parameters than the cost function. Particle swarm optimization (PSO) integrated with the mutation operator is used to solve the problem. Two case studies from Singapore and New South Wales (Australia) historical load datasets are used to validate the PSO-based LUBE method. Demonstrated results show that the proposed method can construct high quality PIs for load forecasting applications.

Construction of prediction intervals for carbon residual of crude oil based on deep stochastic configuration networks

The conventional approaches to constructing Prediction Intervals (PIs) always follow the principle of ‘high coverage and narrow width’. However, the deviation information has been largely neglected, making the PIs unsatisfactory. For high-risk forecasting tasks, the cost of forecast failure may be prohibitive. To address this, this work introduces a multi-objective loss function that includes Prediction Interval Accumulation Deviation (PIAD) within the Lower Upper Bound Estimation (LUBE) framework. The proposed model can achieve the goal of ‘high coverage, narrow width, and small bias’ in PIs, thus minimizing costs even in cases of prediction failure. A salient feature of the LUBE framework is its ability to discern uncertainty without explicit uncertainty labels, where the data uncertainty and model uncertainty are learned by Deep Neural Networks (DNN) and a model ensemble, respectively. The validity of the proposed method is demonstrated through its application to the prediction of carbon prices in China. Compared with conventional uncertainty quantification methods, the improved interval optimization method can achieve narrower PI widths.

I first of all wish to congratulate the author for this inspiring and interesting article. It offers a new, fresh view on how to construct prediction intervals in regression, and it also allows for many extensions beyond the framework of regression. Apart from proposing a novel and promising idea, the article is also a very rich source of references, not only on the topic of prediction intervals, but also on related topics like transformation models, bootstrap, and nonparametric regression. The paper also contains interesting side-comments and links with other areas in the literature, giving hence a very complete picture of the problem considered in the paper. In this comment I would like to discuss briefly an outlook on two possible further topics of research. The first one is on the construction of prediction intervals when endogeneity is present, and the second one is on the theoretical investigation of the proposed intervals.

An overview of this dissertation is provided in Chapter 1, where the concept of active learning is introduced and the main idea of the proposed method is explained at a high level. The defining mechanism of the method can be summarized as bias-correction for stable algorithms. Practically, we take advantage of the nice properties of the random forest algorithm to do active learning in a computationally economical way. In Chapter 2, we rigorously establish that random forests are stable under mild conditions. This result not only serves as the theoretical foundation of our method, but also provides coverage guarantees to the prediction intervals constructed from the out-of-bag error of random forests. In Chapter 3, the proposed active learning method is introduced in detail. Its performance on real datasets is illustrated and compared with other methods. In particular, we show that our bias-oriented method and an existing variance-oriented method are complementary to each other. In Chapter 4, we address the issue of constructing prediction intervals for active learning. If a validation set is available, we can modify the split conformal prediction method to achieve this goal with guarantees. Otherwise, we can still use the calibrated out-of-bag error to construct prediction intervals with a small coverage gap. We summarize the dissertation and discuss some future work in Chapter 5.

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A genetic algorithm-based method for improving quality of travel time prediction intervals

Technology evolution prediction, or technological forecasting, is critical for designers to make important decisions during product development planning such as R&D investment and outsourcing. In practice, designers want to supplement point forecast by prediction intervals to assess future uncertainty and make contingency plans. Available technology evolution data is a time series but is generally with non-uniform spacing. Existing methods associated with typical time series models assume uniformly spaced data, so these methods cannot be used to construct prediction intervals for technology evolution prediction. In this paper, we develop a generic method that use bootstrapping to generate prediction intervals for technology evolution. The method we develop can be applied to any technology evolution prediction model. We consider parameter uncertainty and data uncertainty and establish their empirical probability distributions. We determine an appropriate confidence level α to generate prediction intervals through a holdout sample analysis rather than set α = 0.05 as is typically done in the literature. We validate our method to generate the prediction intervals through a case study of central processing unit transistor count evolution. The case study shows that the prediction intervals generated by our method cover every actual data point in a holdout sample test. To apply our method in practice, we outline four steps for designers to generate prediction intervals for technology evolution prediction.

For analyses based on nonlinear models, agencies and policy makers are often interested in prediction intervals for small area means. We give statistics for small area predictions that can be used to construct prediction intervals in the same way that standard errors and degrees of freedom are used to construct prediction intervals based on the Student-t distribution. In a simulation study, the new parametric bootstrap prediction interval has good coverage properties and much better coverage than the bootstrap percentile prediction interval. The methods are applied in a study of soil erosion and water runoff conducted by the US Department of Agriculture.

In this research, we develop a new method for predicting order data. Our approach involves selecting the best-fitting distribution through different tests, estimating its parameters, and constructing prediction intervals that leverage observed and predicted data. In this method, we entered the predicted data one by one, along with the observed data. At each step, we found a suitable distribution and then estimated its parameters and applied the prediction method, such as pivotal quantity and modified least square with cumulative hazard function. We implemented the new method using the R programming language and conducted comparative analyses against several established methods across datasets, encompassing health insurance coverage, glass fiber strength, and COVID-19 recovery rates. The results demonstrated this method's superior performance, particularly in terms of Mean square error (MSE) and coefficient of variation (CV), as well as its ability to predict more data and outperform traditional methods in most scenarios. This method has the ability to obtain a large number of predicted observations to reach about 150% to 200% of the real observations, as explained through a simulation study and real data.

Wildfire prediction using zero-inflated negative binomial mixed models: Application to Spain

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Quantile regression forest (QRF) is a non-parametric method for estimating the distribution function of response by using the random forest algorithm and constructing conditional quantile prediction intervals. However, if the explanatory factors (covariates) are highly correlated, the quantile regression forest's performance will decrease, resulting in low accuracy of prediction intervals for the outcome variable. The selection of explanatory variables in quantile regression forest is investigated and addressed in this paper, using several selection scenarios that consist of the full model, forward selection, LASSO, ridge regression, and random forest to improve the accuracy of household income data prediction. This data was obtained from National Labour Force Survey in 2021. The results indicate that the random forest method outperforms other methods for explanatory selection utilizing RMSE metrics. With regard to the criteria of average coverage value just above the 95% target and statistical test results, the RF-QRF and Forward-QRF methods outperform the QRF, LASSO-QRF, and Ridge-QRF methods for constructing prediction intervals.

Prediction accuracy for reservation-based forecasting methods applied in Revenue Management

The purpose of this paper is to review both classic and modern methods for constructing prediction intervals. We focus, primarily, on model-based non-Bayesian methods for the prediction of a scalar random variable, but we also include Bayesian methods with objective prior distributions. Our review of non-Bayesian methods follows two lines: general methods based on (approximate) pivotal quantities and methods based on non-Bayesian predictive distributions. The connection between these two types of methods is described for distributions in the (log-)location-scale family. We also discuss extending the general prediction methods to data with complicated dependence structures as well as some nonparametric prediction methods (e.g., conformal prediction).