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According to the well-known Heyde theorem the Gaussian distribution on the real line is characterized by the symmetry of the conditional distribution of one linear form of independent random variables given another. We study analogues of…
We study the notion of inhomogeneous Poissonian pair correlations, proving several properties that show similarities and differences to its homogeneous counterpart. In particular, we show that sequences with inhomogeneous Poissonian pair…
Bayesian networks are directed acyclic graphs representing independence relationships among a set of random variables. A random variable can be regarded as a set of exhaustive and mutually exclusive propositions. We argue that there are…
In this article, the theory of sheaves is studied from a categorical point of view. This perspective vastly generalizes the usual theory of sheaves of sets to a more abstract setting which allows us to investigate the theory of sheaves with…
We explore various Bayesian approaches to estimate partial Gaussian graphical models. Our hierarchical structures enable to deal with single-output as well as multiple-output linear regressions, in small or high dimension, enforcing either…
A new class of probability distributions closely connected to generalized hyperbolic distributions is introduced. It is more adapted to study the distributions of sums of random number of random variables. The properties of these…
We obtain a Stein characterisation of the distribution of the product of two correlated normal random variables with non-zero means, and more generally the distribution of the sum of independent copies of such random variables. Our Stein…
Considering the flexibility and applicability of Bayesian modeling, in this work we revise the main characteristics of two hierarchical models in a regression setting. We study the full probabilistic structure of the models along with the…
Hierarchical structure is ubiquitous in data across many domains. There are many hierarchical clustering methods, frequently used by domain experts, which strive to discover this structure. However, most of these methods limit discoverable…
We consider discrete nonparametric priors which induce Gibbs-type exchangeable random partitions and investigate their posterior behavior in detail. In particular, we deduce conditional distributions and the corresponding Bayesian…
Social foraging is a widespread form of animal foraging in which groups of individuals coordinate their decisions to exploit resources in the environment. Animals show a variety of social structures from egalitarian to hierarchical. In this…
Optimization is widely used in statistics, and often efficiently delivers point estimates on useful spaces involving structural constraints or combinatorial structure. To quantify uncertainty, Gibbs posterior exponentiates the negative loss…
We provide a new characterization of the Dirichlet distribution. This characterization implies that under assumptions made by several previous authors for learning belief networks, a Dirichlet prior on the parameters is inevitable.
We study the influence of the seed in random trees grown according to the uniform attachment model, also known as uniform random recursive trees. We show that different seeds lead to different distributions of limiting trees from a total…
In this article we provide a systematic experimental method for sorting animals according to socially relevant traits, without assaying them or even tagging them individually. Instead, they are repeatedly subjected to behavioural assays in…
For situations that may benefit from information sharing among datasets, e.g., population-based SHM of similar structures, the hierarchical Bayesian approach provides a useful modelling structure. Hierarchical Bayesian models learn…
It has been shown that some macroeconomic time series, especially those where outliers could be present, can be well modelled using heavy tailed distributions for the noise components. Methods for deciding when and where heavy-tailed models…
Many modern experiments, such as microarray gene expression and genome-wide association studies, present the problem of estimating a large number of parallel effects. Bayesian inference is a popular approach for analyzing such data by…
This survey reviews the existing literature on the most relevant Bayesian inference methods for univariate and multivariate GARCH models. The advantages and drawbacks of each procedure are outlined as well as the advantages of the Bayesian…
A new method is developed to represent probabilistic relations on multiple random events. Where previously knowledge bases containing probabilistic rules were used for this purpose, here a probability distribution over the relations is…