Search

The nonparametric view of Bayesian inference has transformed statistics and many of its applications. The canonical Dirichlet process and other more general families of nonparametric priors have served as a gateway to solve frontier uncertainty quantification problems of large, or infinite, nature. This success has been greatly due to available constructions and representations of such distributions, the two most useful constructions are the one based on normalization of homogeneous completely random measures and that based on stick-breaking processes. Hence, understanding their distributional features and how different random probability measures compare among themselves is a key ingredient for their proper application. In this paper, we analyse the discrepancy among some nonparametric priors employed in the literature. Initially, we compute the mean and variance of the random Kullback-Leibler divergence between the Dirichlet process and the geometric process. Subsequently, we extend our analysis to encompass a broader class of exchangeable stick-breaking processes, which includes the Dirichlet and geometric processes as extreme cases. Our results establish quantitative conditions where all the aforementioned priors are close in total variation distance. In such instances, adhering to Occam's razor principle advocates for the preference of the simpler process.

Since only a small number of traces generated from distributed tracing helps in troubleshooting, its storage requirement can be significantly reduced by biasing the selection towards anomalous traces. To aid in this scenario, we propose SampleHST, a novel approach to sample on-the-fly from a stream of traces in an unsupervised manner. SampleHST adjusts the storage quota of normal and anomalous traces depending on the size of its budget. Initially, it utilizes a forest of Half Space Trees (HSTs) for trace scoring. This is based on the distribution of the mass scores across the trees, which characterizes the probability of observing different traces. The mass distribution from HSTs is subsequently used to cluster the traces online leveraging a variant of the mean-shift algorithm. This trace-cluster association eventually drives the sampling decision. We have compared the performance of SampleHST with a recently suggested method using data from a cloud data center and demonstrated that SampleHST improves sampling performance up to by 9.5x., Comment: 10 pages, 5 figures

$n$-gram profiles have been successfully and widely used where long sequences of potentially differing lengths are analysed for clustering or classification. Mostly, machine learning algorithms have been used for this purpose but, despite their superb predictive performance, these methods cannot discover hidden structure or provide a full probabilistic representation of the data. That is why in this paper we centre our attention on a novel class of Bayesian generative models designed for $n$-gram profiles used as binary attributes. The flexibility of our modelling allows us to consider a straightforward approach to feature selection in this generative model. Furthermore, we derive a slice sampling algorithm for a fast inferential procedure which is applied to both synthetic and real data scenarios and shows that feature selection can improve classification accuracy.

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.