16,546 research outputs found
Suitable Algorithm Associated with a Parameterization for the Three-Parameter Log-Normal Distribution
Associated with a parameterization for the three-parameter lognormal distribution, an algorithm was proposed by Komori and Hirose, which can find a local maximum likelihood (ML) estimate surely if it exists. Nevertheless, by Vera and Díaz-García it was shown that performance in finding a local ML estimate deteriorated by adopting the parameterization only and using other algorithm. In the present article, it will be shown that Komori and Hirose’s algorithm should be used for the parameterization. This work will also give MATLAB codes as a useful tool for the parameter estimation of the distribution
A sequential sampling strategy for extreme event statistics in nonlinear dynamical systems
We develop a method for the evaluation of extreme event statistics associated
with nonlinear dynamical systems, using a small number of samples. From an
initial dataset of design points, we formulate a sequential strategy that
provides the 'next-best' data point (set of parameters) that when evaluated
results in improved estimates of the probability density function (pdf) for a
scalar quantity of interest. The approach utilizes Gaussian process regression
to perform Bayesian inference on the parameter-to-observation map describing
the quantity of interest. We then approximate the desired pdf along with
uncertainty bounds utilizing the posterior distribution of the inferred map.
The 'next-best' design point is sequentially determined through an optimization
procedure that selects the point in parameter space that maximally reduces
uncertainty between the estimated bounds of the pdf prediction. Since the
optimization process utilizes only information from the inferred map it has
minimal computational cost. Moreover, the special form of the metric emphasizes
the tails of the pdf. The method is practical for systems where the
dimensionality of the parameter space is of moderate size, i.e. order O(10). We
apply the method to estimate the extreme event statistics for a very
high-dimensional system with millions of degrees of freedom: an offshore
platform subjected to three-dimensional irregular waves. It is demonstrated
that the developed approach can accurately determine the extreme event
statistics using limited number of samples
Sophisticated and small versus simple and sizeable: When does it pay off to introduce drifting coefficients in Bayesian VARs?
We assess the relationship between model size and complexity in the
time-varying parameter VAR framework via thorough predictive exercises for the
Euro Area, the United Kingdom and the United States. It turns out that
sophisticated dynamics through drifting coefficients are important in small
data sets while simpler models tend to perform better in sizeable data sets. To
combine best of both worlds, novel shrinkage priors help to mitigate the curse
of dimensionality, resulting in competitive forecasts for all scenarios
considered. Furthermore, we discuss dynamic model selection to improve upon the
best performing individual model for each point in time
Inversion using a new low-dimensional representation of complex binary geological media based on a deep neural network
Efficient and high-fidelity prior sampling and inversion for complex
geological media is still a largely unsolved challenge. Here, we use a deep
neural network of the variational autoencoder type to construct a parametric
low-dimensional base model parameterization of complex binary geological media.
For inversion purposes, it has the attractive feature that random draws from an
uncorrelated standard normal distribution yield model realizations with spatial
characteristics that are in agreement with the training set. In comparison with
the most commonly used parametric representations in probabilistic inversion,
we find that our dimensionality reduction (DR) approach outperforms principle
component analysis (PCA), optimization-PCA (OPCA) and discrete cosine transform
(DCT) DR techniques for unconditional geostatistical simulation of a
channelized prior model. For the considered examples, important compression
ratios (200 - 500) are achieved. Given that the construction of our
parameterization requires a training set of several tens of thousands of prior
model realizations, our DR approach is more suited for probabilistic (or
deterministic) inversion than for unconditional (or point-conditioned)
geostatistical simulation. Probabilistic inversions of 2D steady-state and 3D
transient hydraulic tomography data are used to demonstrate the DR-based
inversion. For the 2D case study, the performance is superior compared to
current state-of-the-art multiple-point statistics inversion by sequential
geostatistical resampling (SGR). Inversion results for the 3D application are
also encouraging
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