15,063 research outputs found
Sequential Bayesian inference for implicit hidden Markov models and current limitations
Hidden Markov models can describe time series arising in various fields of
science, by treating the data as noisy measurements of an arbitrarily complex
Markov process. Sequential Monte Carlo (SMC) methods have become standard tools
to estimate the hidden Markov process given the observations and a fixed
parameter value. We review some of the recent developments allowing the
inclusion of parameter uncertainty as well as model uncertainty. The
shortcomings of the currently available methodology are emphasised from an
algorithmic complexity perspective. The statistical objects of interest for
time series analysis are illustrated on a toy "Lotka-Volterra" model used in
population ecology. Some open challenges are discussed regarding the
scalability of the reviewed methodology to longer time series,
higher-dimensional state spaces and more flexible models.Comment: Review article written for ESAIM: proceedings and surveys. 25 pages,
10 figure
Subspace Leakage Analysis and Improved DOA Estimation with Small Sample Size
Classical methods of DOA estimation such as the MUSIC algorithm are based on
estimating the signal and noise subspaces from the sample covariance matrix.
For a small number of samples, such methods are exposed to performance
breakdown, as the sample covariance matrix can largely deviate from the true
covariance matrix. In this paper, the problem of DOA estimation performance
breakdown is investigated. We consider the structure of the sample covariance
matrix and the dynamics of the root-MUSIC algorithm. The performance breakdown
in the threshold region is associated with the subspace leakage where some
portion of the true signal subspace resides in the estimated noise subspace. In
this paper, the subspace leakage is theoretically derived. We also propose a
two-step method which improves the performance by modifying the sample
covariance matrix such that the amount of the subspace leakage is reduced.
Furthermore, we introduce a phenomenon named as root-swap which occurs in the
root-MUSIC algorithm in the low sample size region and degrades the performance
of the DOA estimation. A new method is then proposed to alleviate this problem.
Numerical examples and simulation results are given for uncorrelated and
correlated sources to illustrate the improvement achieved by the proposed
methods. Moreover, the proposed algorithms are combined with the pseudo-noise
resampling method to further improve the performance.Comment: 37 pages, 10 figures, Submitted to the IEEE Transactions on Signal
Processing in July 201
The Lazy Bootstrap. A Fast Resampling Method for Evaluating Latent Class Model Fit
The latent class model is a powerful unsupervised clustering algorithm for
categorical data. Many statistics exist to test the fit of the latent class
model. However, traditional methods to evaluate those fit statistics are not
always useful. Asymptotic distributions are not always known, and empirical
reference distributions can be very time consuming to obtain. In this paper we
propose a fast resampling scheme with which any type of model fit can be
assessed. We illustrate it here on the latent class model, but the methodology
can be applied in any situation.
The principle behind the lazy bootstrap method is to specify a statistic
which captures the characteristics of the data that a model should capture
correctly. If those characteristics in the observed data and in model-generated
data are very different we can assume that the model could not have produced
the observed data. With this method we achieve the flexibility of tests from
the Bayesian framework, while only needing maximum likelihood estimates. We
provide a step-wise algorithm with which the fit of a model can be assessed
based on the characteristics we as researcher find important. In a Monte Carlo
study we show that the method has very low type I errors, for all illustrated
statistics. Power to reject a model depended largely on the type of statistic
that was used and on sample size. We applied the method to an empirical data
set on clinical subgroups with risk of Myocardial infarction and compared the
results directly to the parametric bootstrap. The results of our method were
highly similar to those obtained by the parametric bootstrap, while the
required computations differed three orders of magnitude in favour of our
method.Comment: This is an adaptation of chapter of a PhD dissertation available at
https://pure.uvt.nl/portal/files/19030880/Kollenburg_Computer_13_11_2017.pd
Multiple-dose design and bias-reducing methods for limiting dilution assays
This paper gives an overview of several (mostly recent) statistical contributions to the theory of Limiting and Serial Dilution Assays (LDA's, SDA's). A simple and useful method is presented for the setup of a design for an LDA or an SDA. This method is based on several user-supplied design parameters, consisting in the researcher's advance information and other parameters inherent to the particular problem. The commonly used Maximum Likelihood (ML) and Minimum Chi-square methods for the estimation of the unknown parameter in an LDA or an SDA are described and compared to several bias-reducing estimation methods, e.g. jackknife and bootstrap versions of the ML method. One particular jackknife version is recommended
- …