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Title: Tsunami source modelling
Description: These are some notes on automated Tsunami source modelling using sweeping window positive elastic net.
Description: These are some notes on automated Tsunami source modelling using sweeping window positive elastic net.
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Timely
Prediction of
Tsunami
Introduction
Data
Collection
Based on Automated Tsunami Source
Modelling Using the Sweeping Window
Positive Elastic Net
Precomputed
Models
Unit Source
Coefficient
Modeling
Concerns
Statistical
Theory
Daniel M
...
Percival Donald W
...
Huang Harold O
...
Spillane
Presented By Dhrubajyoti Ghosh
Lasso
Elastic Net
Two Results
BS1217
The Model
Indian Statistical Institute
Error Term
Unit Source
Coefficients
Localization
Parameters
March 11, 2015
Table of Contents
Timely
Prediction of
Tsunami
Introduction
Data
Collection
Precomputed
Models
Unit Source
Coefficient
Modeling
Concerns
Statistical
Theory
Lasso
Elastic Net
Two Results
The Model
Error Term
Unit Source
Coefficients
Localization
Parameters
1
2
3
4
5
6
Introduction
Data Collection
Precomputed Models
Unit Source Coefficient
Modeling Concerns
Statistical Theory
Lasso
Elastic Net
Two Results
7 The Model
Error Term
Unit Source Coefficients
Localization
Parameters
8 Example
9 Conclusion
Tsunami, Why should we care?
Timely
Prediction of
Tsunami
Introduction
Data
Collection
Precomputed
Models
Unit Source
Coefficient
Modeling
Concerns
Statistical
Theory
Lasso
Elastic Net
Two Results
The Model
Error Term
Unit Source
Coefficients
Localization
Parameters
Tsunamis are potentially devastating natural disasters for
coastal regions worldwide,from the point of view of both loss of
life and property damage
...
Transocean tsunami events can propagate slowly enough that it
is possible to issue timely warnings, with the potential of greatly
reducing loss of life
...
Unit Source A predesigned geographic section of the sea floor
...
As a tsunami event is evolving, SIFT computes these estimates using
numerical models drawing on several key components including :
Activities
Timely
Prediction of
Tsunami
Introduction
Data
Collection
Precomputed
Models
Unit Source
Coefficient
Modeling
Concerns
Statistical
Theory
Lasso
Elastic Net
Two Results
The Model
Error Term
Unit Source
Coefficients
Localization
Parameters
The purpose of SIFT is to assist TWC personnel in providing a timely
estimate of tsunami wave arrival times and amplitudes to potentially
affected coastal communities
...
Activities
Timely
Prediction of
Tsunami
Introduction
Data
Collection
Precomputed
Models
Unit Source
Coefficient
Modeling
Concerns
Statistical
Theory
Lasso
Elastic Net
Two Results
The Model
Error Term
Unit Source
Coefficients
Localization
Parameters
The purpose of SIFT is to assist TWC personnel in providing a timely
estimate of tsunami wave arrival times and amplitudes to potentially
affected coastal communities
...
2 a basin-wide precomputed propagation database of water
level and flow velocities based on potential seismic unit
sources
...
As a tsunami event is evolving, SIFT computes these estimates using
numerical models drawing on several key components including :
deep-ocean observation of tsunamis collected near the
source of the tsunami
...
3 an algorithm for estimation of coefficients associated with
selected seismic unit sources based on the deep-ocean
observation data
...
As a tsunami event is evolving, SIFT computes these estimates using
numerical models drawing on several key components including :
deep-ocean observation of tsunamis collected near the
source of the tsunami
...
3 an algorithm for estimation of coefficients associated with
selected seismic unit sources based on the deep-ocean
observation data
...
1
Objective Of this paper
Timely
Prediction of
Tsunami
Introduction
Data
Collection
Precomputed
Models
Unit Source
Coefficient
Modeling
Concerns
Statistical
Theory
Lasso
Elastic Net
Two Results
The Model
Error Term
Unit Source
Coefficients
Localization
Parameters
The present method of estimation and selection of unit source
coefficients is based on hand-tuned models and rough heuristics
...
Table of Contents
Timely
Prediction of
Tsunami
Introduction
Data
Collection
Precomputed
Models
Unit Source
Coefficient
Modeling
Concerns
Statistical
Theory
Lasso
Elastic Net
Two Results
The Model
Error Term
Unit Source
Coefficients
Localization
Parameters
1
2
3
4
5
6
Introduction
Data Collection
Precomputed Models
Unit Source Coefficient
Modeling Concerns
Statistical Theory
Lasso
Elastic Net
Two Results
7 The Model
Error Term
Unit Source Coefficients
Localization
Parameters
8 Example
9 Conclusion
How the Data is collected?
Timely
Prediction of
Tsunami
What is a Dart
Buoy?
Introduction
Data
Collection
Precomputed
Models
Unit Source
Coefficient
Modeling
Concerns
Dart buoy actually consists of two separate units, namely, a surface
buoy and a bottom unit with a pressure recorder
...
Precomputed Models
Timely
Prediction of
Tsunami
Introduction
Data
Collection
Precomputed
Models
Unit Source
Coefficient
Modeling
Concerns
Statistical
Theory
Lasso
Elastic Net
Two Results
The Model
Error Term
Unit Source
Coefficients
Localization
Parameters
Complementary to these Dart buoy observations is a database
of physical models that act as explanatory variables (predictors)
...
Precomputed Models
Timely
Prediction of
Tsunami
Introduction
Data
Collection
Precomputed
Models
Unit Source
Coefficient
Modeling
Concerns
Statistical
Theory
Lasso
Elastic Net
Two Results
The Model
Error Term
Unit Source
Coefficients
Localization
Parameters
Complementary to these Dart buoy observations is a database
of physical models that act as explanatory variables (predictors)
...
Each model assumes the perturbation by a fixed amount within
a single unit source, which is a predesignated 100 km by 50 km
section of the ocean near a coastline
...
This collection of models depends on both the location of the
seismic disturbance, and the location of the Dart buoy
...
There is a model in the database for every pairing of a particular
unit source with a particular buoy
...
This collection of models depends on both the location of the
seismic disturbance, and the location of the Dart buoy
...
There is a model in the database for every pairing of a particular
unit source with a particular buoy
...
5 earthquake were to
originate from that unit source
...
Buoys(Triangles)
Table of Contents
Timely
Prediction of
Tsunami
Introduction
Data
Collection
Precomputed
Models
Unit Source
Coefficient
Modeling
Concerns
Statistical
Theory
Lasso
Elastic Net
Two Results
The Model
Error Term
Unit Source
Coefficients
Localization
Parameters
1
2
3
4
5
6
Introduction
Data Collection
Precomputed Models
Unit Source Coefficient
Modeling Concerns
Statistical Theory
Lasso
Elastic Net
Two Results
7 The Model
Error Term
Unit Source Coefficients
Localization
Parameters
8 Example
9 Conclusion
Unit Source Coefficient
Timely
Prediction of
Tsunami
Introduction
Data
Collection
Precomputed
Models
Unit Source
Coefficient
Modeling
Concerns
Statistical
Theory
Lasso
Elastic Net
Two Results
The Model
Error Term
Unit Source
Coefficients
Localization
Parameters
The precomputed model g(t) for a pair of buoy and unit source
differ from the data xt of the buoy
...
We assume that an earthquake with an arbitrary magnitude can
be handled by multiplying g(t) by a parameter α
...
We assume that an earthquake with an arbitrary magnitude can
be handled by multiplying g(t) by a parameter α
...
We assume that an earthquake with an arbitrary magnitude can
be handled by multiplying g(t) by a parameter α
...
Unit Source Coefficient
Timely
Prediction of
Tsunami
Introduction
Data
Collection
Precomputed
Models
Unit Source
Coefficient
Modeling
Concerns
Statistical
Theory
Lasso
Elastic Net
Two Results
The Model
Error Term
Unit Source
Coefficients
Localization
Parameters
The precomputed model g(t) for a pair of buoy and unit source
differ from the data xt of the buoy
...
Accordingly we assume the model :
xt = αg (t) + et ,
where et is a residual term that represents any remaining
mismatch between the data and the amplitude-adjusted model
...
Table of Contents
Timely
Prediction of
Tsunami
Introduction
Data
Collection
Precomputed
Models
Unit Source
Coefficient
Modeling
Concerns
Statistical
Theory
Lasso
Elastic Net
Two Results
The Model
Error Term
Unit Source
Coefficients
Localization
Parameters
1
2
3
4
5
6
Introduction
Data Collection
Precomputed Models
Unit Source Coefficient
Modeling Concerns
Statistical Theory
Lasso
Elastic Net
Two Results
7 The Model
Error Term
Unit Source Coefficients
Localization
Parameters
8 Example
9 Conclusion
Modeling Concerns
Timely
Prediction of
Tsunami
Introduction
Data
Collection
Precomputed
Models
Unit Source
Coefficient
Modeling
Concerns
Statistical
Theory
Lasso
Elastic Net
Two Results
The Model
Error Term
Unit Source
Coefficients
Localization
Parameters
There are three main modeling concerns :
Modeling Concerns
Timely
Prediction of
Tsunami
Introduction
Data
Collection
Precomputed
Models
Unit Source
Coefficient
Modeling
Concerns
Statistical
Theory
Lasso
Elastic Net
Two Results
The Model
Error Term
Unit Source
Coefficients
Localization
Parameters
There are three main modeling concerns :
1
Estimation Of Unit Source Coefficients : This can by done
by Least square regression
...
2
Sparsity Although many unit sources can be associated with
each buoy, a sensible overall model should not use all
simultaneously
...
2
Sparsity Although many unit sources can be associated with
each buoy, a sensible overall model should not use all
simultaneously
...
e
...
Data
Collection
Precomputed
Models
Unit Source
Coefficient
Modeling
Concerns
Statistical
Theory
Lasso
Elastic Net
Two Results
The Model
Error Term
Unit Source
Coefficients
Localization
Parameters
Modeling Concerns
Timely
Prediction of
Tsunami
Introduction
There are three main modeling concerns :
1
Estimation Of Unit Source Coefficients : This can by done
by Least square regression
...
3
LocalizationThe selected ones should be co-located in a
geographically sensible pattern; i
...
it makes sense to insist that
the model selected for a tsunami source is a localized
geophysical process
...
Problems In Maximum Likelihood regression
Timely
Prediction of
Tsunami
Introduction
Data
Collection
Precomputed
Models
Unit Source
Coefficient
Modeling
Concerns
Statistical
Theory
Lasso
Elastic Net
Two Results
The Model
Error Term
Unit Source
Coefficients
Localization
Parameters
Maximum likelihood estimation has many wonderful properties, but is
often unsatisfactory in regression problems for two reasons:
Large variability: When columns of X are highly correlated, the
ˆ
variance of β is large
...
Penalized Maximum Likelihood
Timely
Prediction of
Tsunami
Introduction
A way of dealing with this problem is to introduce a penalty: instead
of maximizing l(θ|x) = log L(θ|x), we maximize the function:
Data
Collection
M(θ) = l(θ|x) − λP(θ)
Precomputed
Models
Unit Source
Coefficient
Modeling
Concerns
Statistical
Theory
Lasso
Elastic Net
Two Results
The Model
Error Term
Unit Source
Coefficients
Localization
Parameters
where :
Penalized Maximum Likelihood
Timely
Prediction of
Tsunami
Introduction
A way of dealing with this problem is to introduce a penalty: instead
of maximizing l(θ|x) = log L(θ|x), we maximize the function:
Data
Collection
M(θ) = l(θ|x) − λP(θ)
Precomputed
Models
Unit Source
Coefficient
Modeling
Concerns
Statistical
Theory
Lasso
Elastic Net
Two Results
The Model
Error Term
Unit Source
Coefficients
Localization
Parameters
where :
P is a function that penalizes what one would consider less
realistic values of the unknown parameters
Penalized Maximum Likelihood
Timely
Prediction of
Tsunami
Introduction
A way of dealing with this problem is to introduce a penalty: instead
of maximizing l(θ|x) = log L(θ|x), we maximize the function:
Data
Collection
M(θ) = l(θ|x) − λP(θ)
Precomputed
Models
Unit Source
Coefficient
where :
Modeling
Concerns
P is a function that penalizes what one would consider less
realistic values of the unknown parameters
Statistical
Theory
λ controls the trade-off between the two parts
...
Lasso
Elastic Net
Two Results
The Model
Error Term
Unit Source
Coefficients
Localization
Parameters
The function M is called the objective function
...
Penalized Maximum Likelihood
Timely
Prediction of
Tsunami
The two most common penalties are as follows :
p
βj2
Ridge : P(β) =
Introduction
j=1
Data
Collection
Precomputed
Models
p
Unit Source
Coefficient
Modeling
Concerns
Statistical
Theory
Lasso
Elastic Net
Two Results
The Model
Error Term
Unit Source
Coefficients
Localization
Parameters
|βj |
Lasso : P(β) =
j=1
We can think of the first one as the Gaussian Prior and the second
one a Laplace prior on the parameters
...
1
λ too small =⇒ overfit the data
...
λ is called the Regularization Parameter
...
Lasso!
Timely
Prediction of
Tsunami
Introduction
Advantages of Lasso
Data
Collection
Precomputed
Models
Unit Source
Coefficient
Modeling
Concerns
Statistical
Theory
Lasso
Elastic Net
Two Results
The Model
Error Term
Unit Source
Coefficients
Localization
Parameters
1
Lasso (l1 ) penalties have many statistical and computational
advantages
...
2
l1 penalties encourages sparsity and simplicity in the solution
3
l1 penalties are convex and the assumed sparsity can lead to
significant computational advantages
...
The number of
selected parameters is bounded by the number of samples
...
The number of
selected parameters is bounded by the number of samples
...
Unit Source
Coefficient
Modeling
Concerns
Statistical
Theory
Lasso
Elastic Net
Two Results
The Model
Error Term
Unit Source
Coefficients
Localization
Parameters
Elastic Net
Timely
Prediction of
Tsunami
Introduction
Data
Collection
To overcome the above discussed limitations, we introduce a new
regularization technique, named elastic net
...
Elastic Net
Timely
Prediction of
Tsunami
To overcome the above discussed limitations, we introduce a new
regularization technique, named elastic net
...
The quadratic part of the penalty :
Removes the limitation on the number of selected
variables;
2 Encourages grouping effect
...
Introduction
ˆ
β = argminβ ||y − X β||2 + λ2 ||β||2 + λ1 ||β||1
Data
Collection
Precomputed
Models
Unit Source
Coefficient
Modeling
Concerns
Statistical
Theory
Lasso
Elastic Net
Two Results
The Model
Error Term
Unit Source
Coefficients
Localization
Parameters
The l1 part of the penalty generates a sparse model
...
1
The above points are direct consequences of the following two
results
...
) is the penalty function
...
p
...
If J(
...
ˆˆ
ˆ
2
...
1
ˆ
(β
3
ˆ
ˆ
(βi + βj )
...
2
Then elastic net estimator can be written as :
L(γ, β) = L(γ, β ∗ ) = |y ∗ − X ∗ β ∗ |2 + γ|β|∗
1
1
ˆ
ˆ
ˆ
Let β ∗ = argminβ ∗ L(γ, β ∗ ) then β = √1+λ β ∗
2
Table of Contents
Timely
Prediction of
Tsunami
Introduction
Data
Collection
Precomputed
Models
Unit Source
Coefficient
Modeling
Concerns
Statistical
Theory
Lasso
Elastic Net
Two Results
The Model
Error Term
Unit Source
Coefficients
Localization
Parameters
1
2
3
4
5
6
Introduction
Data Collection
Precomputed Models
Unit Source Coefficient
Modeling Concerns
Statistical Theory
Lasso
Elastic Net
Two Results
7 The Model
Error Term
Unit Source Coefficients
Localization
Parameters
8 Example
9 Conclusion
Back To our Model
Timely
Prediction of
Tsunami
Introduction
Data
Collection
Precomputed
Models
Unit Source
Coefficient
Modeling
Concerns
Statistical
Theory
Lasso
Elastic Net
Two Results
The Model
Error Term
Unit Source
Coefficients
Localization
Parameters
We can cast the estimation of unit source coefficients in the
statistical frame work of linear regression
...
Suppose there are K unit sources for any given buoy
...
Back To our Model
Timely
Prediction of
Tsunami
Introduction
Data
Collection
Precomputed
Models
Unit Source
Coefficient
Modeling
Concerns
Statistical
Theory
We can cast the estimation of unit source coefficients in the
statistical frame work of linear regression
...
Suppose there are K unit sources for any given buoy
...
Based upon the K physical models, our model for buoy j can be
written as :
dj = Gj α + ej
Lasso
Elastic Net
Two Results
The Model
Error Term
Unit Source
Coefficients
Localization
Parameters
where Gj is an Nj × K matrix whose kth column is gj,k , and the
linear coefficients of the unit sources are denoted as α =
[α1 ,
...
Further, ej is a stochastic vector of error terms
...
, dJ ], G=[G1 ,
...
, eJ ]
To Err is Model!
Timely
Prediction of
Tsunami
Introduction
Data
Collection
Precomputed
Models
Unit Source
Coefficient
Modeling
Concerns
Statistical
Theory
Lasso
Elastic Net
Two Results
The Model
Error Term
Unit Source
Coefficients
Localization
Parameters
In this model, an appropriate assumption on this error structure
must reflect the fact that adjacent time points are typically
auto-correlated
...
Using Cholesky Decomposition, we transfer the model as:
−1
−1
−1
Σej 2 dj = Σej 2 Gj α + Σej 2 ej
which has uncorrelated and hence independent and identically
distributed error terms
...
To Err is Model!
Timely
Prediction of
Tsunami
Introduction
Data
Collection
Precomputed
Models
Unit Source
Coefficient
Modeling
Concerns
Statistical
Theory
Lasso
Elastic Net
Two Results
The Model
Error Term
Unit Source
Coefficients
Localization
Parameters
In our application, we assume that Σej is an Nj × Nj correlation
matrix whose entries are dictated by a first order zero mean
auto-regressive (AR(1)) process with a unit-lag auto-correlation
φ satisfying |φ| < 1
...
To Err is Model!
Timely
Prediction of
Tsunami
Introduction
Data
Collection
Precomputed
Models
Unit Source
Coefficient
Modeling
Concerns
Statistical
Theory
Lasso
Elastic Net
Two Results
The Model
Error Term
Unit Source
Coefficients
Localization
Parameters
In our application, we assume that Σej is an Nj × Nj correlation
matrix whose entries are dictated by a first order zero mean
auto-regressive (AR(1)) process with a unit-lag auto-correlation
φ satisfying |φ| < 1
...
−1
For this error structure we can write Σej 2 = Dj Lj , where Dj and
Lj are Nj × Nj matrices such that :
Dj = diag (1, √ 1 2 ,
...
,0
...
Get a vector of residuals r with a stacked buoy-by-buoy
structure paralleling that of d
...
Unit Source Coefficients
Timely
Prediction of
Tsunami
Introduction
Data
Collection
Precomputed
Models
Unit Source
Coefficient
Modeling
Concerns
Statistical
Theory
Lasso
Elastic Net
Two Results
The Model
Error Term
Unit Source
Coefficients
Localization
Parameters
It is unlikely that a geophysical process would involve a
simultaneous shift of an entire subduction zone
...
Hence it is unreasonable to build a model of the Tsunami source
using all the unit sources from the subduction zone in which the
earthquake happened
...
Hence it is unreasonable to build a model of the Tsunami source
using all the unit sources from the subduction zone in which the
earthquake happened
...
Present Method
Timely
Prediction of
Tsunami
Introduction
Data
Collection
Precomputed
Models
Unit Source
Coefficient
Modeling
Concerns
Statistical
Theory
Lasso
Elastic Net
Two Results
The Model
Error Term
Unit Source
Coefficients
Localization
Parameters
Obtain an initial selection of unit sources based upon the
location of earthquake (epicenter) and its magnitude
...
Then hand-adjust the selection using qualitative judgments from
a graphical assessment or fit
...
Disadvantage Of Present Method
Timely
Prediction of
Tsunami
Introduction
Data
Collection
Precomputed
Models
Unit Source
Coefficient
Modeling
Concerns
Statistical
Theory
Lasso
Elastic Net
Two Results
The Model
Error Term
Unit Source
Coefficients
Localization
Parameters
The by-hand adjustment is not based on quantitative measures
...
AIM : A sparse regression model that will automatically select unit
sources
...
hand selection of unit sources is potentially time-consuming and
error prone, which can compromise the ability of TWC
personnel to to achieve their primary goals of issuing timely
warnings to coastal communities of an impending Tsunami
...
Two other issues that we need to be concerned about are :
Collinearity and Positivity
...
||p denotes the lp norm
...
||p denotes the lp norm
...
Hence we Improvise!
Timely
Prediction of
Tsunami
Introduction
To simultaneously address the issues of sparsity, collinearity and
positivity, we employ the positive elastic net estimator for α :
Data
Collection
Precomputed
Models
Unit Source
Coefficient
Modeling
Concerns
Statistical
Theory
Lasso
Elastic Net
Two Results
The Model
Error Term
Unit Source
Coefficients
Localization
Parameters
α(λ1 , λ2 ) = argminα∈
ˆ
−1
k
+
−1
||Σe 2 d−Σe 2 G α||2 +λ1 ||α||1 +λ2 ||α||2 ; λ1 , λ2 >
2
In the above ||
...
Here :
We use the combination of l1 and l2 penalties to induce the
selection property of lasso along with the collinearity control of
ridge regression
...
But unit sources must be localized!
Timely
Prediction of
Tsunami
Introduction
Data
Collection
Precomputed
Models
Unit Source
Coefficient
Modeling
Concerns
Statistical
Theory
Lasso
Elastic Net
Two Results
The Model
Error Term
Unit Source
Coefficients
Localization
Parameters
The physical nature of typical earthquakes dictates that
tsunamis originate from a localized event within a subduction
zone
...
If we simply apply the positive elastic net, we have no guarantee
that the automatically selected set of unit sources with αk = 0
ˆ
will occur in a geographically localized region
...
If we simply apply the positive elastic net, we have no guarantee
that the automatically selected set of unit sources with αk = 0
ˆ
will occur in a geographically localized region
...
Sweeping Window
Timely
Prediction of
Tsunami
Introduction
Data
Collection
Precomputed
Models
Unit Source
Coefficient
Modeling
Concerns
Statistical
Theory
Lasso
Elastic Net
Two Results
The Model
Error Term
Unit Source
Coefficients
Localization
Parameters
Begin the sparse modeling process with a geographically local
set of unit sources, formed by taking a rectangular area of unit
sources
...
We then produce such a sparse model for all such local sets by
translating this window throughout the subduction zone
...
Let’s not forget the PARAMETERS
Timely
Prediction of
Tsunami
Introduction
Data
Collection
Precomputed
Models
Unit Source
Coefficient
Modeling
Concerns
Statistical
Theory
Lasso
Elastic Net
Two Results
The Model
Error Term
Unit Source
Coefficients
Localization
Parameters
The proposed model requires the choice of two tuning
parameters λ1 and λ2 and a local window of unit sources for our
final model
...
Introduction
Data
Collection
Precomputed
Models
Unit Source
Coefficient
Modeling
Concerns
Statistical
Theory
Lasso
Elastic Net
Two Results
The Model
Error Term
Unit Source
Coefficients
Localization
Parameters
We use the Akaike Information Criterion (AIC) to make these
decisions
...
Introduction
Data
Collection
We use the Akaike Information Criterion (AIC) to make these
decisions
...
Introduction
Data
Collection
We use the Akaike Information Criterion (AIC) to make these
decisions
...
d(α(λ1 , λ2 )) is an approximate degrees of freedom
...
Introduction
Data
Collection
We use the Akaike Information Criterion (AIC) to make these
decisions
...
d(α(λ1 , λ2 )) is an approximate degrees of freedom
...
0 magnitude earthquake
Unit Source
Coefficient
Epicenter: Off the east coast off Honshu Island
...
9m
Statistical
Theory
Lasso
Elastic Net
Two Results
The Model
Error Term
Unit Source
Coefficients
Localization
Parameters
Buoy Reading data
Timely
Prediction of
Tsunami
Introduction
Data
Collection
Precomputed
Models
Unit Source
Coefficient
Modeling
Concerns
Statistical
Theory
Lasso
Elastic Net
Two Results
The Model
Error Term
Unit Source
Coefficients
Localization
Parameters
Reading Of Dart
Buoy 21418, 21413 and 21401
...
Selection of Unit sources
Timely
Prediction of
Tsunami
Introduction
Data
Collection
Precomputed
Models
Unit Source
Coefficient
Modeling
Concerns
Statistical
Theory
Lasso
Elastic Net
Two Results
The Model
Error Term
Unit Source
Coefficients
Localization
Parameters
Inference: Hence the automatic selection picks nearly same unit
sources as handpicked models but in a time efficient manner
...
Prediction Performance on test buoys
Timely
Prediction of
Tsunami
Introduction
Data
Collection
Precomputed
Models
Unit Source
Coefficient
Modeling
Concerns
Statistical
Theory
Lasso
Elastic Net
Two Results
The Model
Error Term
Unit Source
Coefficients
Localization
Parameters
Observation: Automatic method gives out of sample prediction
virtually similar to second handpicked model
...
All the methods focus on a single stage of this process, namely,
selecting the unit sources (geographical locations) associated
with the earthquake-generated tsunami and estimating its
magnitude via the summation of its estimated coefficients
...
A new approach would be to select the window sizes based upon
the reported magnitude of the earthquake
Title: Tsunami source modelling
Description: These are some notes on automated Tsunami source modelling using sweeping window positive elastic net.
Description: These are some notes on automated Tsunami source modelling using sweeping window positive elastic net.