Motivation
Bayes
Evaluating actions
Example
Conclusions
Better ignorant than misled: Including
uncertainty in forecasts supporting management
and policy
N. Thompson Hobbs
Natural Resource Ecology Laboratory, Department of Ecosystem Science and
Sustainability, and Graduate Degree Program in Ecology,
Colorado State University
Uncertainty Analysis: A Critical Step in Ecological Synthesis
Annual Meeting of the Ecological Society of America, 8/5/2013
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Motivation
Bayes
Evaluating actions
Example
Conclusions
Honest synthesis
Management and Policy
Theory
Published
research
Process
studies
Experiments
Monitoring
Physical
laws
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Motivation
Bayes
Evaluating actions
Example
Conclusions
The problem of management:
What actions will allow us to meet
goals for the future?
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Motivation
Bayes
Evaluating actions
Example
Conclusions
Synthesis with deterministic models
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Motivation
Bayes
Evaluating actions
Example
Conclusions
Orrin H. Pilkey and Linda Pilkey-Jarvis 2007
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Motivation
Bayes
Evaluating actions
Example
Conclusions
A broadly applicable approach to ecological modeling in
support of management
[E, θprocess, θdata |data] ∝
[data|θdata , Et ] [Et |θprocess , Et−1 ] [θprocess , θdata , E0 ]
data
Et
Et
Process
✓process ✓data
Parameters
1
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Motivation
Bayes
Evaluating actions
Example
Conclusions
Posterior predictive distributions
State
of Population
State
of Ecological
System
(E or(EE’)or E')
[E 0R|data]
=
R
0 |E , θ
[E
data , θprocess ] [E , θdata , θprocess |data] dE dθdata θprocess
θ E
Time
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Motivation
Bayes
Evaluating actions
Example
Conclusions
Probability density
State
of Population
State
of Ecological
System
(E or(EE’)or E')
Posterior predictive distribution of future states, E 0
Time
Future state of system, E'
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Motivation
Bayes
Evaluating actions
Example
Conclusions
How to evaluate actions?
Objective: reduce state below a target
Probability density
Objective
Future state of system, E'
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Motivation
Bayes
Evaluating actions
Example
Conclusions
Objective: maintain state within acceptable range
Probability density
Range
Future state of system, E'
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Motivation
Bayes
Evaluating actions
Example
Conclusions
Objective: increase state above a target
Probability density
Objective
Future state of system, E'
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Motivation
Bayes
Evaluating actions
Example
Conclusions
Action: do nothing
Probability density
Objective
Future state of system, E'
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Motivation
Bayes
Evaluating actions
Example
Conclusions
Action: implement managment
Probability density
Objective
Management
Future state of system, E'
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Motivation
Bayes
Evaluating actions
Example
Conclusions
Net effect of management
Probability density
Objective
Future state of system, E'
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Motivation
Bayes
Evaluating actions
Example
Conclusions
Net effect of management
Probability density
Objective
Future state of system, E'
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Motivation
Bayes
Evaluating actions
Example
Conclusions
Example: Managing brucellosis in Yellowstone Bison
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Motivation
Bayes
Evaluating actions
Example
Conclusions
Goal: Reduce probability of infection
by half in five years.
Action: Annually vaccinate 200
sero-positive females.
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Motivation
Bayes
Evaluating actions
Example
Conclusions
Bayesian matrix model with multiple sources of data
Mark recapture
yϕ[t]
Serology
Ysero[t]
Ground
Aerial
classifications
classifications
yp.µ[t]
yratio.calf[t]
yp.σ[t]
yσ[t]
n[t]
p
A[t] n[t
Census
yn.obs[t]
yn.sd[t]
psight
asd , bsd
1]
r[t]
Removals
yr[t]
Removal
Removal
age, sex
serology
yr.age[t]
yr.sero[t]
rcomp[t]
rsero[t]
rinfect[t]
, fc , fn , fp , , s, v
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Motivation
Bayes
Evaluating actions
Example
Conclusions
0.20
0.15
0.10
0.05
Do nothing
Vaccinate
0.00
Probability of transmission
0.25
Effect of vaccination: Treat 200 sero-positive / year
0
1
2
3
4
5
Years into the future
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Motivation
Bayes
Evaluating actions
Example
Conclusions
0.30
0.20
0.10
0.00
Probability of transmission
Effect of vaccination
0
1
2
3
4
5
Years into the future
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Motivation
Bayes
Evaluating actions
Example
Conclusions
Effect of vaccination
Objective: reduce transmission probability by half
10
Five years in the future
6
4
2
0
Density
8
Do nothing
Vaccinate
0.0
0.1
0.2
0.3
Probablity of tranmission
0.4
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Motivation
Bayes
Evaluating actions
Example
Conclusions
Comparison of alternatives
Management action
Do nothing
Vaccinate 200 sero-positives
Cull 200 sero-positives
Cull 200 females
Boundary hunting
Probability of meeting goal
.05
.33
.29
.15
.03
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Motivation
Bayes
Evaluating actions
Example
Conclusions
Multiple objectives, multiple actions
Objectives
I
Reduce P(infection) by
half
Actions
I
Vaccination
I
Remove sero-positives
I
Sero prevalence < 40%
I
Remove sero-negatives
I
Population size between
3000 - 3500
I
Boundary hunting (or removal)
I
Appropriate demographic
composition
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Motivation
Bayes
Evaluating actions
Example
Conclusions
Closing
I
Value
I
I
I
Provides honest forecasts relevant to actions and goals.
Informs the conversation
Limitations
I
I
Demonic intrusions aren’t included.
Forecasting horizons are short.
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Motivation
Bayes
Evaluating actions
Example
Conclusions
Walters, C. J. 1986. Adaptive Management of
Renewable Resources. Macmillan, New York.
Develop Bayesian
model(s) of system
Update model(s)
Observe system
behavior
Forecast system
behavior under
different policy
options
Implement policy (or
better, policies)
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Motivation
Bayes
Evaluating actions
Example
Conclusions
May 21-30, 2013 Google “NREL Bayes”
Building capacity in Bayesian modeling
for practicing ecologists
A workshop for faculty and
agency researchers. $1000
stipend. See
www.nrel.colostate.edu/projects/
bayesworkshop/
Award DEB 000347455
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