173 research outputs found
On the Bayesian analysis of species sampling mixture models for density estimation
The mixture of normals model has been extensively applied to density estimation problems.
This paper proposes an alternative parameterisation that naturally leads to new forms
of prior distribution. The parameters can be interpreted as the location, scale and smoothness
of the density. Priors on these parameters are often easier to specify. Alternatively, improper
and default choices lead to automatic Bayesian density estimation. The ideas are extended to
multivariate density estimation
On Bayesian nonparametric modelling of two correlated distributions
In this paper, we consider the problem of modelling a pair of related distributions
using Bayesian nonparametric methods. A representation of the distributions as
weighted sums of distributions is derived through normalisation. This allows us to
define several classes of nonparametric priors. The properties of these distributions
are explored and efficient Markov chain Monte Carlo methods are developed. The
methodology is illustrated on simulated data and an example concerning hospital efficiency
measurement
Adaptive MC^3 and Gibbs algorithms for Bayesian Model Averaging in Linear Regression Models
The MC (Madigan and York, 1995) and Gibbs (George and McCulloch, 1997)
samplers are the most widely implemented algorithms for Bayesian Model
Averaging (BMA) in linear regression models. These samplers draw a variable at
random in each iteration using uniform selection probabilities and then propose
to update that variable. This may be computationally inefficient if the number
of variables is large and many variables are redundant. In this work, we
introduce adaptive versions of these samplers that retain their simplicity in
implementation and reduce the selection probabilities of the many redundant
variables. The improvements in efficiency for the adaptive samplers are
illustrated in real and simulated datasets
A loss discounting framework for model averaging and selection in time series models
We introduce a Loss Discounting Framework for model and forecast combination
which generalises and combines Bayesian model synthesis and generalized Bayes
methodologies. We use a loss function to score the performance of different
models and introduce a multilevel discounting scheme which allows a flexible
specification of the dynamics of the model weights. This novel and simple model
combination approach can be easily applied to large scale model
averaging/selection, can handle unusual features such as sudden regime changes,
and can be tailored to different forecasting problems. We compare our method to
both established methodologies and state of the art methods for a number of
macroeconomic forecasting examples. We find that the proposed method offers an
attractive, computationally efficient alternative to the benchmark
methodologies and often outperforms more complex techniques
Bayesian methods of vector autoregressions with tensor decompositions
Vector autoregressions (VARs) are popular in analyzing economic time series.
However, VARs can be over-parameterized if the numbers of variables and lags
are moderately large. Tensor VAR, a recent solution to overparameterization,
treats the coefficient matrix as a third-order tensor and estimates the
corresponding tensor decomposition to achieve parsimony. In this paper, the
inference of Tensor VARs is inspired by the literature on factor models.
Firstly, we determine the rank by imposing the Multiplicative Gamma Prior to
margins, i.e. elements in the decomposition, and accelerate the computation
with an adaptive inferential scheme. Secondly, to obtain interpretable margins,
we propose an interweaving algorithm to improve the mixing of margins and
introduce a post-processing procedure to solve column permutations and
sign-switching issues. In the application of the US macroeconomic data, our
models outperform standard VARs in point and density forecasting and yield
interpretable results consistent with the US economic history
Two-sample Bayesian Nonparametric Hypothesis Testing
In this article we describe Bayesian nonparametric procedures for two-sample
hypothesis testing. Namely, given two sets of samples
\stackrel{\scriptscriptstyle{iid}}{\s
im} and \stackrel{\scriptscriptstyle{iid}}{\sim},
with unknown, we wish to
evaluate the evidence for the null hypothesis
versus the
alternative . Our
method is based upon a nonparametric P\'{o}lya tree prior centered either
subjectively or using an empirical procedure. We show that the P\'{o}lya tree
prior leads to an analytic expression for the marginal likelihood under the two
hypotheses and hence an explicit measure of the probability of the null
.Comment: Published at http://dx.doi.org/10.1214/14-BA914 in the Bayesian
Analysis (http://projecteuclid.org/euclid.ba) by the International Society of
Bayesian Analysis (http://bayesian.org/
Bayesian Models Applied to Cyber Security Anomaly Detection Problems
Cyber security is an important concern for all individuals, organisations and
governments globally. Cyber attacks have become more sophisticated, frequent
and dangerous than ever, and traditional anomaly detection methods have been
proved to be less effective when dealing with these new classes of cyber
threats. In order to address this, both classical and Bayesian models offer a
valid and innovative alternative to the traditional signature-based methods,
motivating the increasing interest in statistical research that it has been
observed in recent years. In this review we provide a description of some
typical cyber security challenges, typical types of data and statistical
methods, paying special attention to Bayesian approaches for these problems
On a Bayesian Approach to Malware Detection and Classification through -gram Profiles
Detecting and correctly classifying malicious executables has become one of
the major concerns in cyber security, especially because traditional detection
systems have become less effective with the increasing number and danger of
threats found nowadays. One way to differentiate benign from malicious
executables is to leverage on their hexadecimal representation by creating a
set of binary features that completely characterise each executable. In this
paper we present a novel supervised learning Bayesian nonparametric approach
for binary matrices, that provides an effective probabilistic approach for
malware detection. Moreover, and due to the model's flexible assumptions, we
are able to use it in a multi-class framework where the interest relies in
classifying malware into known families. Finally, a generalisation of the model
which provides a deeper understanding of the behaviour across groups for each
feature is also developed
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