Combining Statistical Forecasts and Expert Scenarios Under ImpreciseWeights: A Probability-Box Approach to Long-Term Natural Gas Demand

Long-term energy forecasting in a dynamically changing environment requires combining information contained in historical data with expert knowledge about structural, technological and policy changes. However, expert scenarios often disagree, and their relative credibility is difficult to assess. We propose a framework for combining a statistical forecast with expert scenarios while explicitly retaining uncertainty about both scenario outcomes and their relative importance. We examine this problem using gas demand in Poland up to 2040. A statistical forecast based on historical data provides a transparent reference, while expert scenarios developed by three organizations represent alternative structural developments that may not be captured by historical extrapolation alone. Uncertainty around the statistical forecast is represented by a probability distribution, while expert deviations from it are represented by triangular fuzzy numbers. We fix the total weight assigned to expert alternatives but leave its allocation among them unspecified. The combined result is a probability box, which gives lower and upper probability bounds. In the current case study, all expert scenarios imply higher demand than the statistical reference in 2030, while their demand levels differ strongly in 2040. In 2035, the midpoint of the combined expected-value interval remains close to the statistical reference despite disagreement among scenarios. Giving more weight to expert alternatives raises this midpoint in 2030 but lowers it in 2040. The results show that combining statistical forecasts with expert knowledge can reveal the dependence of long-term conclusions on structural assumptions and scenario credibility, particularly when historical relationships may not remain stable. The proposed framework therefore supports a transparent synthesis of statistical evidence and expert judgement without requiring a single precise weighting of alternative future scenarios.