A Bayesian Hierarchical Model for Combining Several Crop Yield Indications Nathan B. Cruze National Agricultural Statistics Service (NASS) United States Department of Agriculture [email protected]FCSM 2015 Washington, D.C. December 1, 2015 “... providing timely, accurate, and useful statistics in service to U.S. agriculture.” 1
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A Bayesian Hierarchical Model for CombiningSeveral Crop Yield Indications
Nathan B. Cruze
National Agricultural Statistics Service (NASS)United States Department of Agriculture
Constrained State Model–Enforce constraint by conditioning (9)on µt =
∑j wjµtj(
µt1, µt2, . . . , µt(J−1))∼ MVN(µ̄, Σ̄) (10)
µtJ = µt −1
wtJ
J−1∑j=1
wtjµtj (11)
FCSM 2015–A Bayesian Hierarchical Model for Combining Several Crop Yield Indications 8
Summary of model outputsSpeculative Region Model Constrained State Model Unconstrained State Model
Region yield and error Benchmarked state yields anderrors
Region forecast decomposition State forecast decompositionsand benchmarking adjustments
Wang et al. (2012) Adrian (2012), Nandram et al.(2014),Cruze (2015)
Kass and Steffey (1989)
State 1 State 2 · · · State J SPECOverall Forecast µ̂Tj x x · · · x xError x x · · · x x
OYS yOTm∗j − b̂Om∗ x x · · · x x
AYS yATm∗j − b̂Am∗ x x · · · x x
Covariates z′T β̂ x x · · · x x
Sept. APS yQTj x x · · · x xBenchmarking Adj. dj x x · · · x
µ̂tj ≈∑
k∈{O,A,Q,Covariates}
ck(SOURCE )k + dj (12)
ck ∝ (variance)−1k
FCSM 2015–A Bayesian Hierarchical Model for Combining Several Crop Yield Indications 9
Winter wheat speculative region
1.8%2.5%2.7%
5.1%
8.7% 35.8%
16.9%
11.4%
8.5%6.6%
25
30
35
40
45
50
−120 −110 −100 −90 −80long
lat
I 10 state region–some states geographically isolatedI Kansas has major share of harvested acres (Plotted: wj , 2012)I Four distinct types of winter wheatI Differential planting and harvest
FCSM 2015–A Bayesian Hierarchical Model for Combining Several Crop Yield Indications 10
Winter wheat speculative region–types of wheat
0
25
50
75
100
Was
hing
ton
Mon
tana
Col
orad
o
Neb
rask
a
Kan
sas
Okl
ahom
a
Texa
s
Mis
sour
i
Illin
ois
Ohi
o
State
Per
cent
.Pro
duct
ion
TypeRed HardRed SoftWhite HardWhite Soft
State Winter Wheat Production by Percent Type
25
30
35
40
45
50
−120 −110 −100 −90 −80long
lat
I States ‘specialize’
I Soft varieties associatedwith higher yield
I Washington, Missouri,Illinois, Ohio have higheryields
I Confounding with state
FCSM 2015–A Bayesian Hierarchical Model for Combining Several Crop Yield Indications 11
CO 8 15 April 21 May 21 MayIL 17 15 April 19 May 19 MayKS 20 15 April 19 May 19 MayMO 29 15 April 19 May 19 MayMT 30 15 April 19 May 24 JuneNE 31 15 April 21 May 21 MayOH 39 15 April 21 May 21 MayOK 40 15 April 17 April 17 AprilTX 48 15 April 17 April 17 AprilWA 53 15 April 22 May 22 May
FCSM 2015–A Bayesian Hierarchical Model for Combining Several Crop Yield Indications 13
Comparing ASB estimates and model outputs–2012
State 1 State 2 State 3 State 4 State 5 State 6 State 7 State 8 State 9 State 10 Region
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t
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July
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t
May
June
July
Aug
Sep
t
May
June
July
Aug
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t
May
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t
May
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July
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t
May
June
July
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t
May
June
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t
May
June
July
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July
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May
June
July
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Month
Yie
ld
Source●
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ASBModel95% CI.u95% CI.l
Year 2012 Comparisons: Published Yield and Model−based Yield Indications
FCSM 2015–A Bayesian Hierarchical Model for Combining Several Crop Yield Indications 14
Weights applied in wheat forecast decomposition
May June July August September
0.00
0.25
0.50
0.75
1.00C
O IL KS
MO
MT
NE
OH
OK TX
WA
SP
EC
CO IL KS
MO
MT
NE
OH
OK TX
WA
SP
EC
CO IL KS
MO
MT
NE
OH
OK TX
WA
SP
EC
CO IL KS
MO
MT
NE
OH
OK TX
WA
SP
EC
CO IL KS
MO
MT
NE
OH
OK TX
WA
SP
EC
Unit
Wei
ght Source
AYS Covariates OYS Sept. APS
I Early season emphasis on covariates
I Increasing emphasis on OYS in July
I Heavy emphasis on last AYS in August
I Heavy emphasis on quarterly survey in September
FCSM 2015–A Bayesian Hierarchical Model for Combining Several Crop Yield Indications 15
Extensions and conclusions
1. NASS yield models (corn, soybeans, winter wheat)capture expert assessment in manner which isreproducible and provide justifiable measures ofuncertainty.
2. This methodology is flexible enough to accommodatemany types of auxiliary data.
I Additional commodities
I Non-spec region states
I New technologies, e.g., soil moisture monitors
FCSM 2015–A Bayesian Hierarchical Model for Combining Several Crop Yield Indications 16
Select references
Adrian, D. (2012). A model-based approach to forecasting corn and soybeanyields. Fourth International Conference on Establishment Surveys.
Cruze, N. B. (2015). Integrating survey data with auxiliary sources ofinformation to estimate crop yields. In JSM Proceedings, Survey ResearchMethods Section. Alexandria, VA: American Statistical Association.
Kass, R. and Steffey, D. (1989). Approximate Bayesian inference inconditionally independent hierarchical models (parametric empirical Bayesmodels). Journal of the American Statistical Association, 84(407):717–726.
Nandram, B., Berg, E., and Barboza, W. (2014). A hierarchical Bayesianmodel for forecasting state-level corn yield. Environmental and EcologicalStatistics, 21(3):507–530.
Wang, J. C., Holan, S. H., Nandram, B., Barboza, W., Toto, C., andAnderson, E. (2012). A Bayesian approach to estimating agricultural yieldbased on multiple repeated surveys. Journal of Agricultural, Biological, andEnvironmental Statistics, 17(1):84–106.
FCSM 2015–A Bayesian Hierarchical Model for Combining Several Crop Yield Indications 17