# Bayesian Parameter Estimations for Grey System Models in Online Traffic Speed Predictions

arXiv: https://arxiv.org/abs/2108.06839 · HTML: https://mlsanity.com/paper/2108.06839/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 16 references that are in the map.
- First posted on arXiv 15 Aug 2021.

## Builds on (most cited first, 3 of 3)

- [Grey Models for Short-Term Queue Length Predictions for Adaptive Traffic Signal Control](https://mlsanity.com/paper/1912.12676/) (2019)
- [Improved Grey System Models for Predicting Traffic Parameters](https://mlsanity.com/paper/2011.09469/) (2020)
- [Gaussian Processes for Traffic Speed Prediction at Different Aggregation Levels](https://mlsanity.com/paper/2011.11866/) (2020)

## Abstract (arXiv)

This paper presents Bayesian parameter estimation for first order Grey system models' parameters (or sometimes referred to as hyperparameters). There are different forms of first-order Grey System Models. These include GM(1,1), GM(1,1| cos(ω t), GM(1,1| sin(ω t), and GM(1,1| cos(ω t), sin(ω t). The whitenization equation of these models is a first-order linear differential equation of the form [ fracdxdt + a x = f(t) ] where a is a parameter and f(t) = b in GM(1,1|) , f(t) = b1cos(ω t) + b2 in GM(1,1| cos(ω t), f(t) = b1sin(ω t)+b2 in GM(1,1| sin(ω t), f(t) = b1sin(ω t) + b2cos(ω t) + b3 in GM(1,1| cos(ω t), sin(ω t), f(t) = b x2 in Grey Verhulst model (GVM), and where b, b1, b2, and b3 are parameters. The results from Bayesian estimations are compared to the least square estimated models with fixed ω. We found that using rolling Bayesian estimations for GM parameters can allow us to estimate the parameters in all possible forms. Based on the data used for the comparison, the numerical results showed that models with Bayesian parameter estimations are up to 45% more accurate in mean squared errors.