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$^3$ (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 $\mathbf{y}^{\scriptscriptstyle(1)}\;$\stackrel{\scriptscriptstyle{iid}}{\s im}$\;F^{\scriptscriptstyle(1)}$ and $\mathbf{y}^{\scriptscriptstyle(2 )}\;$\stackrel{\scriptscriptstyle{iid}}{\sim}$\;F^{\scriptscriptstyle( 2)}$, with $F^{\scriptscriptstyle(1)},F^{\scriptscriptstyle(2)}$ unknown, we wish to evaluate the evidence for the null hypothesis $H_0:F^{\scriptscriptstyle(1)}\equiv F^{\scriptscriptstyle(2)}$ versus the alternative $H_1:F^{\scriptscriptstyle(1)}\neq F^{\scriptscriptstyle(2)}$. 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 $\mathrm{Pr}(H_0|\{\mathbf {y}^{\scriptscriptstyle(1)},\mathbf{y}^{\scriptscriptstyle(2)}\}\mathbf{)}$.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 nn-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