explosive remnants of war: estimating the number of anti...
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Explosive Remnants of War: Estimating the Number of Anti-PersonnelMines in Colombia Using a Bayesian Framework
Haley Castele, Krystine HoangDepartment of Mathematics & Statistics, Loyola University Chicago, Chicago, IL, USA
Motivation
I Landmines are weapons of war that are placed below the earth and detonate whenput under a certain amount of pressure.
I Anti-personnel landmines can remain dormant for years until a person or animalcrosses its path.
I Landmines have been placed across Colombia throughout the Colombian Conflict,with reports of detonation in 32 of 33 states.
I Goal: Estimate the number of anti-personnel landmines in Colombia and estimatethe probability of landmine accidents by state using historical incidents to generatethe posterior distributions.
Data
I The UN office for the Coordination of Humanitarian Affairs (OCHA) in Colombia,which coordinates the Presidential Program for Comprehensive Action againstAnti-personnel Mines, publishes an updated report of every landmine accidenteach month.
I There have been 6,447 anti-personnel landmine accidents between January 1990and March 2016.
Figure 1: Landmine Accidents in Colombia and the Estimated Density
Covariates
I X1 = population estimate for 2010 based off the 2005 censusI X2 = number of mines the government was able to disarm and removeI X3 = number of suspected minefieldsI S = spatial random effect
Hierarchical Regression
I Non-spatial Components. Y ∼ Binomial(n, p)
. n ∼ Poisson(µ)
. µ = λ/p
I Additional Spatial Component. S ∼ N(µ2, inverse covariance matrix)
Non-spatial JAGS Model
p = 0.11
Table 1: Non-spatial JAGS Model Estimates
State Unmined Hit Tot. Found Est. of n Remaining ProportionAmazonas 1 1 2 285.42 283.42 0.99Antioquia 2946 1555 4501 14499.85 9998.85 0.69
Arauca 1588 353 1941 2560.82 619.82 0.24Atlantico 4 1 5 611.61 606.61 0.99
Bogota DC 99 11 110 338.05 228.05 0.67Bolivar 854 330 1184 2604.48 1420.48 0.55Boyaca 169 39 208 1331.17 1123.17 0.84Caldas 155 118 273 388.90 115.90 0.30
Caqueta 2104 578 2682 2796.70 114.70 0.04Casanare 144 49 193 668.93 475.93 0.71
Cauca 1266 286 1552 3042.38 1490.38 0.49Cesar 173 65 238 306.40 68.40 0.22Choco 181 84 265 531.93 266.93 0.50
Cordoba 409 196 605 1351.27 746.27 0.55Cundinamarca 339 85 424 870.99 446.99 0.51
Guainia 3 1 4 465.73 461.73 0.99Guaviare 445 106 551 1105.00 554.00 0.50
Huila 735 154 889 2189.58 1300.58 0.59La Guajira 96 20 116 286.36 170.36 0.59Magdalena 28 14 42 1152.59 1110.59 0.96
Meta 4012 608 4620 7426.73 2806.73 0.38Narino 944 506 1450 2423.05 973.05 0.40
Norte De Santander 1128 427 1555 3192.42 1637.42 0.51Putumayo 1154 219 1373 1520.01 147.01 0.10
Quindio 38 6 44 370.80 326.80 0.88Risaralda 34 10 44 234.82 190.82 0.81Santander 346 167 513 1421.65 908.65 0.64
Sucre 106 25 131 311.00 180.00 0.58Tolima 1184 262 1446 2611.67 1165.67 0.45
Valle Del Cauca 559 135 694 867.44 173.44 0.20Vaupes 106 30 136 492.50 356.50 0.72Vichada 47 6 53 335.95 282.95 0.84
Figure 2: Trace Plot and Density Estimate of Number of Mines in Antioquia
Figure 3: Trace Plot and Density Estimate of Number of Mines in Caqueta
(1)λ = exp(4.972 − 0.0543X1 + 0.0008X2 + 0.002X3)
I There are at least ni mines in a given state i
JAGS CAR Model with Spatial Random Effect
p = 0.09
Figure 4: Trace Plot and Density Estimate of Number of Mines in Antioquia from aspatial JAGS model
Figure 5: Trace Plot and Density Estimate of Number of Mines in Caqueta from aspatial JAGS model
Figure 6: Trace Plot and Density Estimate of the Spatial Random Effect for Antioquia
(2)λ = exp(4.113 − 0.052X1 + 0.002X2 + 0.002X3 + S)
I Probability p was decreased to ensure 95% of estimate for n was above recordedtotals
I Spatial random effect, S , accounts for the number of neighbors for each state iI No convergence in S , but it lowers the estimate of n for states with low mine
numbers
Conclusions
I p is constant because an unbiased estimator for n is unreachable when p isunknown.
I States with high numbers of previously recorded mines that also have highproportions of remaining mines (i.e., n2: Antioquia) need to be the focus ofde-mining efforts.
I Decreasing de-mining efforts in states with high numbers of previously recordedmines and low proportions of remaining mines (i.e., n9: Caqueta) is suggested.
I Proportions drastically changed with inclusion of spatial random effect.. Spatial random effect CAR model did not converge; may not be a great fit for
this data or needs to be revised.
Future Considerations
I Revisit CAR model to improve fit and ensure convergence.I Examine kernel density of mines over space as another spatial random effect.I Research unbiased estimators for n with unknown p.
Acknowledgements
I Software used: (www.r-project.org)
I Maps made with: ggmap package in .I Data acquired from: Avian Compendium (NOAA)I Thanks: Allison Sussman, Mark Wimer, Brian Kinlan, and the following
organizations: