EXPLORIS
Montserrat
Volcano Observatory
Aspinall and Associates
Risk Management Solutions
1
2
3
4
5
An Evidence Science approach to
volcano hazard forecasting
Thea Hincks
1
, Willy Aspinall
1,2
, Gordon Woo
3
, Gillian Norton
4,5
Evidence science
Evidence

based medicine is the conscientious, explicit and judicious
use of current best evidence in making decisions
… the integration of individual expertise with the best available external
evidence from systematic research
After Sackett et al., 1996
Evidence Based Medicine
Need to model uncertainty and make
forecasts using
•
Expert judgment & knowledge of
physical system
•
Observational evidence
= highly complex system
Bayesian networks
Bayesian belief networks (BBNs)
Causal probabilistic network
Directed acyclic graph
Set of variables
X
i
discrete or continuous
Set of directed links
Variables can represent
hidden
or
observable
states of a system
Very useful in volcanology

our observations on internal
dynamics of the volcano are
indirect
Expert systems
NASA data analysis
MSOffice assistant…
Bayesian
Network
applications
Speech recognition
Molecular Biology
and Bioinformatics
Medical diagnosis
& decision making
VOLCANIC
HAZARD
FORECASTING
Building a Bayesian network
Sensor model:
Prior and transition models
Probability of observation
P(YX)
Probability of initial state P(X
0
)
Transition between states P(X
1
X
0
)
Bayes theorem
Filtering

estimate current state X
t
Prediction

future states X
t+n
Forward pass :
Smoothing

past unobserved states
Backward pass :
Network structure
•
Judgment, physical models, observations
factors we believe lead to instability
•
Structure learning algorithms
purely data driven model
difficult to model unobserved nodes
problem is NP

hard
algorithms slow to compute
(~ few days for 6 x ternary node graph)
BN for dome collapse on Montserrat
rainfall on
dome
dome collapse
magma flux
ground
deformation
stability
of edifice
degassing
pressure
Factors that might lead to dome collapse:
BN for dome collapse on Montserrat
rainfall on
dome
dome collapse
magma flux
ground
deformation
degassing
stability
of edifice
Can’t measure
state directly
hidden variables
pressure
BN for dome collapse on Montserrat
magma flux
deformation
SO
2
flux
observed rainfall
UEA & MVO rain gauges
degassing
stability
pressure
GPS, EDM and tilt
Seismicity: VT
earthquakes
Long period
earthquakes
Hybrid
Rockfall
LP Rockfall
BN for dome collapse on Montserrat
use sensor models for
our observations:
Data
Testing with daily data from July 95

August 04
•
S0
2
flux
•
Ground deformation (4 GPS lines)
4 nodes
•
Seismic activity (event triggered count & magnitude
data) VT, Hybrid, LP, LPRF, RF
5 nodes
•
Rainfall
•
Collapse activity
Time dependence
Structure: how are processes coupled?
What is the order of the process ?
Dynamic system

history is important
•
Variables tied over several time slices
Time series analysis of monitoring data
Autocorrelation & partial autocorrelation functions, differenced data
Approximate order for time dependent processes
Autocorrelations
Computed
autocorrelation
function and and
partial
autocorrelation
function for data
and first
differenced data
check structure
is sensible and
estimate order of
time dependence
Dynamic Bayesian Network
Rainfall

1 day autocorrelation
Hidden Markov model O(1)
Dynamic Bayesian Network
Pressure
Dynamic Bayesian Network
Magma flux
Dynamic Bayesian Network
Gas flux
Dynamic Bayesian Network
Ground deformation
Dynamic Bayesian Network
Structural integrity or stability
of the dome is dependant on
•
previous state
•
prior rock fall activity
•
prior collapse activity
(also affects pressurization)
Dynamic Bayesian Network
Current model
Where monitoring time series suggest higher order processes …
Current model
Prior distribution
•
Expert judgment
Sensor model
Transition model
•
Expert judgment to set initial
distributions
•
Parameter learning algorithms
on monitoring data
P(X
0
), P(Y
0
)
for all states X
observations Y
P(Y
t
X
t
)
P(X
t+1
X
t
)
Results so far
Parameter learning
using ~9 years of data
transition and sensor models
1.
static BN
2.
two

slice dynamic model
3.
three

slice dynamic model
Can estimate probability of collapse given new observations
Smoothing
to estimate hidden state probabilities and distributions for
missing values of observed nodes
Results so far
Structure learning
on a small (5 node) model

observed nodes only
…work still in progress!
Results so far
•
High ground deformation
•
Consistent, moderate hybrid activity
•
No SO
2
observations
Results so far
Further work…
•
Model observations with continuous nodes
•
More monitoring data

extend network
•
Look at full seismic record (not just event triggered
data)
•
Run structure learning algorithm on larger network
•
Investigate second order uncertainties
(model
uncertainty)
and scoring rules to see how well
different models perform
•
User interface for real time updating of network at
MVO
real time forecasting
probability of collapse
•
Longer range forecasting?
Conclusions
All models are wrong
(to some degree…)
but some models are better than others
EVIDENCE SCIENCE
and
BAYESIAN NETWORKS
Robust, defensible procedure for combining
observations, physical models and expert judgment
Risk informed decision making
•
Can incorporate new observations/phenomena as they occur
•
Strictly proper scoring rules

unbiased assessment of
performance & model uncertainty
References
Druzdzel
, M and
van der Gaag
, L.,
2000
.
Building Probabilistic Networks:
Where do the numbers come from?
IEEE Transactions on Knowledge
and Data Engineering 12(4):481:486
Jensen
, F.,
1996
.
An Introduction to Bayesian Networks
. UCL Press.
Matthews
, A.J.and
Barclay
J.,
2004
A thermodynamical model for rainfall

triggered volcanic dome collapse
. GRL 31(5)
Murphy
, K.,
2002
Dynamic Bayesian Networks: Representation, Inference
and Learning
. PhD Thesis, UC Berkeley. www.ai.mit.edu
openPNL
(Intel)
http://sourceforge.net/projects/openpnl
open source C++ library for probabilistic networks/directed graphs
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