Probabilistic Modelling using Prediction Intervals

Introduction

In the world of predictive modelling, businesses rely heavily on forecasts to make strategic and tactical decisions. Traditional forecasting methods often provide a single deterministic value, which may not capture the inherent uncertainty in real-world data. This is where probabilistic modelling using ensembling technique, combined with prediction intervals, comes into play. By offering a range of possible outcomes with confidence levels, this approach allows for more informed decision-making.

Understanding Probabilistic Modeling

Probabilistic models aim to generate multiple possible forecasts rather than a single deterministic value. These forecasts follow a distribution that accounts for variability and uncertainty. The key idea is to provide a range (prediction intervals) rather than a single point estimate, ensuring better risk assessment.

Generating Forecast Distributions

The process begins by creating forecast distribution for each time step, using a combination of homogenous and heterogeneous model. This model can generate between 10 to 75 forecasts per time step, depending on the complexity of the data. Instead of assuming a fixed statistical distribution (e.g., Gaussian, Poisson), the approach utilises inequalities like Chebyshev’s and Cantelli’s to define upper and lower bounds.

Key Components:

• Point Forecast (ML Forecast): A deterministic forecast generated from the model.
• Prediction Intervals: The lower and upper bounds within which the actual value is expected to fall with a certain probability.
• Percentiles (P10 to P99): Represent different confidence levels, offering a more detailed view of forecast uncertainty.

Constructing Prediction Intervals

Prediction intervals are crucial in probabilistic modelling as they define the range within which the actual value is likely to fall. The methodology used in this approach is structured as follows:

1. Determining the Upper and Lower Bounds:
   • These bounds are derived using inequalities rather than strict statistical distributions.
   • A probability threshold (e.g., 85%) is set to ensure that the actual value falls within the bounds with high confidence.
2. Segmenting the Distribution:
   • The range is divided into two parts: lower bound to P50 and P50 as well as upper bound.
   • P50 represents the deterministic forecast, ensuring alignment with probabilistic outputs.
3. Refining the Forecast:
   • The approach allows for adjusting the probability confidence level (e.g., 75%, 85%) to fine-tune the prediction intervals.
   • The model ensures that the deterministic forecast aligns closely with the P50 of the probabilistic distribution.

Practical Applications and Business Impact

1. Improved Decision-Making

Businesses can leverage probabilistic forecasts to make more informed decisions by considering multiple scenarios rather than relying on a single number. This is particularly useful in demand planning, inventory planning, and sales production planning.

2. Reducing Forecasting uncertainty

By analyzing the prediction intervals, analysts can identify trends where forecasts deviate significantly. This allows them to refine models and improve accuracy over time.

3. Scenario Planning

Probabilistic models provide an effective framework for scenario planning, allowing businesses to evaluate different risk levels and prepare for uncertainties.

4. Human Adjustments

While models provide automated predictions, human intervention remains crucial. By incorporating business insights, such as anticipated demand shifts or external market changes, forecast accuracy can be significantly improved.

Conclusion

Probabilistic modelling with prediction intervals is transforming forecasting by offering a more flexible and accurate approach. By moving away from rigid deterministic models and embracing uncertainty, businesses can enhance their decision-making capabilities. As models continue to evolve, integrating business insights and refining prediction intervals will be key to achieving optimal forecast accuracy.