Table 1 Summary of the model names, general formulation, section number, and equation number.

From: A review of geospatial exposure models and approaches for health data integration

Model

General Formulation

Section Number

Formula Number

Proximity

Y(p) = Xi(p)

4.1

(4.1.1)

Land Use Regression

Y(p) = X(p)β + ε

4.2

(4.2.1)

Geographically Weighted Regression

Y(p) = X(p)β(p) + ε

4.3

(4.3.1)

Geostatical Models

Y(p) = GP(μ(p), Σθ(p, p*))

4.4

(4.4.1)

Machine Learning

Y(p) = f(X(p))

4.5

(4.5.1)

Ensemble Model

\({{\bf{Y}}}(p)={\sum }_{m = 1}^{M}{w}_{m}{f}_{m}(X(p)){\sum }^{M}{w}_{m}=1\)

4.5.2

(4.5.3)

Boosting

Ym(p) = Ym−1(p) + νym(p)

4.5.2

(4.5.4)

Mechanistic

\(Y(p):= \frac{\partial {C}_{i}}{\partial t}=-{{\boldsymbol{\nabla }}}\cdot \left({{\bf{v}}}{C}_{i}\right)+{{\boldsymbol{\nabla }}}\cdot \left(D{{\boldsymbol{\nabla }}}{C}_{i}\right)+\mathop{\sum }_{j = 1}^{n}{r}_{i,j}+{G}_{i}\)

4.6

(4.6.1)

  1. Details of each model are provided in the given section number. Note that the statistical models result in random variables represented by bold letters. Machine learning models can produce deterministic or random variables, so the latter is represented here.