A hierarchical model for zero-inflated biomass data ...
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A hierarchical model for zero-inflated biomass data ...
A hierarchical model for zero-inflated biomass data, with a spatial structure. Jean-Baptiste Lecomte 1, Liliane Bel 1,. Hugues Benoıt 2, Eric Parent 1. ISEC.
A hierarchical model for zero-inflated biomass data, with a spatial structure
Jean-Baptiste Lecomte 1 , Liliane Bel 1 , Hugues Benoˆıt 2 , Eric Parent 1 ISEC 03-06 July 2012
1. UMR AgroParisTech/INRA 518 - Team MORSE - France 2. Gulf Fisheries, Moncton, New Brunswick, Fisheries and Oceans Canada
Introduction
Context & Objectives Context ◮
Stock management
◮
Fisheries impact
Objectives ◮
Prediction of the abundance
◮
Effect of global warming
◮
Effect of political fisheries management
Hierarchical modeling for zero-inflated biomass data N
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Dataset
Study area : Saint-Lawrence Gulf
Latitude
55
50
Study area
45
40 −75
−70
−65
Longitude
N
−60 modeling for −55zero-inflated biomass data Hierarchical
2 / 18
Dataset
Urchins in the south Saint-Lawrence Gulf 49
Latitude
48
47
46
45 −66
−64
−62
Longitude
N
−60
Hierarchical modeling for zero-inflated biomass data
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Dataset
Difficulties
◮
◮
High proportion of absence of the target species Hidden spatial structure High Inter-annual variations
Mean biomass
10
◮
8
6
4 1990
1995
2000
2005
Years
Hierarchical modeling for zero-inflated biomass data N
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Modeling
Chosen strategy
◮
Zero-inflated modeling
◮
Latent spatial structure
◮
Hierarchical modeling
◮
Bayesian paradigm
Hierarchical modeling for zero-inflated biomass data N
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Modeling
Model behaviour
Hierarchical modeling for zero-inflated biomass data N
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Modeling
Zero-Inflated Latent process
Ns ∼ Poisson(Ss µs)
Ms ,i ∼ Exp(ρ)
Hierarchical modeling for zero-inflated biomass data N
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Modeling
Zero-Inflated Latent process
Ns ∼ Poisson(Ss µs)
Ms ,i ∼ Exp(ρ)
Observation model N Ps Ms ,i if
Ys =
i =1 0
if
Ns > 0 Ns = 0
Hierarchical modeling for zero-inflated biomass data N
7 / 18
Modeling
Zero-Inflated Latent process
Ns ∼ Poisson(Ss µs)
Ms ,i ∼ Exp(ρ)
Observation model N Ps Ms ,i if
Ys =
i =1 0
if
Ns > 0 Ns = 0
Hierarchical modeling for zero-inflated biomass data N
8 / 18
Modeling
Geostatistic : Spatial structure Addition of a Spatial structure log(µs ) = α0 + vs
Hierarchical modeling for zero-inflated biomass data N
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Modeling
Geostatistic : Spatial structure Addition of a Spatial structure log(µs ) = α0 + vs
Covariance function
Cov (v s , vs ) = σ ′
2
h
exp(− ) Φ
h = d (s , s ′ )
Hierarchical modeling for zero-inflated biomass data N
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Modeling
Environmental covariate : Temperature
49
Latitude
48
47
46
45 −66
−64
−62
−60
Longitude
Temperature
0
5
10
15
Hierarchical modeling for zero-inflated biomass data N
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Modeling
Environmental covariate : Sediment type
49
25 26
27
Sediment type 48
1 : Pelite
◮
2 : Fine sand
◮
3 : Coarse sand
◮
4 : Gravel with occasional sand
31 33 32
43 42 40 20 21 23
6
34 35 8
9
47
44 10 46 5963 58
19
22
62
24
39 37 38 47 11 48
3
46
45
41
29
36
Latitude
◮
30 28 7
61
12
16 17 50 49 51 1
18 60 5756 55 54
2
53
15 14 5213
4 5
45 −66
−64
−62
−60
Longitude
Hierarchical modeling for zero-inflated biomass data N
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Modeling
Zero-Inflated Latent process
Ns ∼ Poisson(Ss µs)
Ms ,i ∼ Exp(ρ) log(µs ) = α0 + α1 ∗ Tp s + βSeds + vs
Observation model N Ps Ms ,i if
Ys =
i =1 0
if
Ns > 0 Ns = 0
Hierarchical modeling for zero-inflated biomass data N
