| Term | Mean | 2.5% | 97.5% |
|---|---|---|---|
| (Intercept) | 31.490 | 4.140 | 56.460 |
| elev | 0.053 | 0.017 | 0.093 |
| ndvi | -21.280 | -46.220 | 4.650 |
| dist_major | 0.000 | -0.002 | 0.002 |
| dist_secondary | -0.005 | -0.011 | 0.000 |
| dist_local | 0.012 | -0.043 | 0.066 |
Bayesian Geostatistical Modeling of Noise Pollution in Madrid
Alvin Bong Jia Lok
VSRP, BAYESCOMP @ CEMSE-KAUST
https://alvinbjl.github.io/madrid-noise-geostatistics/presentation/
November 13, 2025
Introduction
Urban noise pollution affects public health and quality of life.
In 2011, an estimated one million healthy life years were lost from traffic-related noise in the western Europe alone (Organization et al. 2011).
Project objective
Understand the spatial patterns of noise exposure in Madrid.
Identify high and low-noise areas.
This supports future policy on urban noise management.
Data: Stations & EDA
- 31 Noise stations in Madrid, mostly near central roads
- Target data: Annual average of year 2024
- EDA reveal higher noise in city center
Covariates
Covariates & Prediction points
Methods
Bayesian Geostatistical Model
Let \(Y_i\) be the noise observed at locations \(i \in \{1, \dotsc, n\}\). The model we use to predict noise level at unsampled locations is as follow:
Model
\[ Y_i \mid \mu_i \sim \mathcal{N}(\mu_i,\sigma^2), \]
\[ \mu_i = \beta_0 + \sum_{k=1}^{5} \beta_k X_{ik} + S(\mathbf{x_i}) \]
Methods
Bayesian Geostatistical Model
Model
\[ Y_i \mid \mu_i \sim \mathcal{N}(\mu_i,\sigma^2), \]
\[ \mu_i = \beta_0 + \sum_{k=1}^{5} \beta_k X_{ik} + S(\mathbf{x_i}) \]
- \(\beta_0\) is the intercept,
- \(\beta_1\), \(\beta_2\), \(\beta_3\), \(\beta_4\) and \(\beta_5\) are regression coefficients for the covariates
- \(S()\) is a spatial random effect that is modeled as a zero-mean Gaussian process with Matérn covariance function. SPDE mesh constructed using
inla.nonconvex.hull()
Methods
Estimation
Model fitting performed using INLA (Rue, Martino, and Chopin 2009).
Model Performance
Assessed by Root Mean Square Error \[\text{RMSE} = \sqrt{\frac{1}{n} \sum_{i=1}^{n} \left( y_i - \hat{y}_i \right)^2 }\]
Exceedence Probability
Highlight regions with noise levels exceeding 62 dB and below 56 dB. Reason for threshold: average of WHO guidline (leisure 70dB & road noise \(\approx\) 56 dB) (Organization et al. 2018; Seto and Huang 2023; Brink et al. 2018)]
Results
Model
- Elevation: ➕ Likely because Madrid’s urban core is on higher terrain.
- Distance to secondary roads: ➖ noise decreases further from roads.
- RMSE: 3.18 dB (“moderate” performance)
Prediction
Exceedence Probability
- Central districts exhibit highest noise intensity
- Quiet zones are rare, mostly northwest vegetated regions
Conclusion
- Negative relationship between noise and distance from secondary roads
- Positive relationship with elevation
- Central cities exhibit highest noise intensity
- Quiet zones are rare
Limitations
- Noise stations biased toward roads & urban centers → quieter areas underrepresented
- Dynamic factors missing: traffic volume, land use, building morphology
- Matérn spatial effect assumes isotropy → same distance ≠ same noise in different contexts
References
Brink, Mark, Beat Schäffer, Reto Pieren, and Jean Marc Wunderli. 2018. “Conversion Between Noise Exposure Indicators Leq24h, LDay, LEvening, LNight, Ldn and Lden: Principles and Practical Guidance.” International Journal of Hygiene and Environmental Health 221 (1): 54–63.
Organization, World Health et al. 2011. “Burden of Disease from Environmental Noise: Quantification of Healthy Life Years Lost in Europe.” In Burden of Disease from Environmental Noise: Quantification of Healthy Life Years Lost in Europe.
——— et al. 2018. “Environmental Noise Guidelines for the European Region: Executive Summary.” In Environmental Noise Guidelines for the European Region: Executive Summary.
Rue, Håvard, Sara Martino, and Nicolas Chopin. 2009. “Approximate Bayesian Inference for Latent Gaussian Models by Using Integrated Nested Laplace Approximations.” Journal of the Royal Statistical Society Series B: Statistical Methodology 71 (2): 319–92.
Seto, Edmund, and Ching-Hsuan Huang. 2023. “Conversions Between Noise Exposure Metrics 24-Hour Leq, Ldn, and Lden: The Impact of Diurnal Local Bus Traffic Patterns on Population Annoyance in the United States.” medRxiv.
