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We consider spatially homogeneous marked point patterns in an unboundedly expanding convex sampling window. Our main objective is to identify the distribution of the typical mark by constructing an asymptotic \chi^2-goodness-of-fit test.…
The beta normal distribution is a generalization of both the normal distribution and the normal order statistics. Some of its mathematical properties and a few applications have been studied in the literature. We provide a better foundation…
The beta distribution is a basic distribution serving several purposes. It is used to model data, and also, as a more flexible version of the uniform distribution, it serves as a prior distribution for a binomial probability. The bivariate…
The gamma difference distribution is defined as the difference of two gamma distributions, with in general different shape and rate parameters. Starting with knowledge of the corresponding characteristic function, a second order linear…
We establish in-expectation and tail bounds on the generalization error of representation learning type algorithms. The bounds are in terms of the relative entropy between the distribution of the representations extracted from the training…
Human feedback is increasingly used across diverse applications like training AI models, developing recommender systems, and measuring public opinion -- with granular feedback often being preferred over binary feedback for its greater…
Bounded time series consisting of rates or proportions are often encountered in applications. This manuscript proposes a practical approach to analyze bounded time series, through a beta regression model. The method allows the direct…
Gradient Boosting (GB) is a popular methodology used to solve prediction problems by minimizing a differentiable loss function, $L$. GB performs very well on tabular machine learning (ML) problems; however, as a pure ML solver it lacks the…
A considerable number of systems have recently been reported in which Brownian yet non-Gaussian dynamics was observed. These are processes characterised by a linear growth in time of the mean squared displacement, yet the probability…
The computation of two Bayesian predictive distributions which are discrete mixtures of incomplete beta functions is considered. The number of iterations can easily become large for these distributions and thus, the accuracy of the result…
The recently introduced second order total generalised variation functional $\mathrm{TGV}_{\beta,\alpha}^{2}$ has been a successful regulariser for image processing purposes. Its definition involves two positive parameters $\alpha$ and…
We introduce a general class of continuous univariate distributions with positive support obtained by transforming the class of two-piece distributions. We show that this class of distributions is very flexible, easy to implement, and…
We consider the problem of linear fitting of noisy data in the case of broad (say $\alpha$-stable) distributions of random impacts ("noise"), which can lack even the first moment. This situation, common in statistical physics of small…
Ordinal regression with a high-dimensional covariate space has many important application areas including gene expression studies. The lack of an intrinsic numeric value associated with ordinal responses, however, makes methods based on…
Emotion annotation is inherently subjective and cognitively demanding, producing signals that reflect diverse perceptions across annotators rather than a single ground truth. In continuous affect prediction, this variability is typically…
Modeling human preferences is crucial for aligning foundation models with human values. Traditional reward modeling methods, such as the Bradley-Terry (BT) reward model, fall short in expressiveness, particularly in addressing intransitive…
We study the distribution of residence time or equivalently that of ``mean magnetization" for a family of Gaussian Markov processes indexed by a positive parameter $\alpha$. The persistence exponent for these processes is simply given by…
Bayesian optimization is an effective methodology for the global optimization of functions with expensive evaluations. It relies on querying a distribution over functions defined by a relatively cheap surrogate model. An accurate model for…
Correlated proportions appear in many real-world applications and present a unique challenge in terms of finding an appropriate probabilistic model due to their constrained nature. The bivariate beta is a natural extension of the well-known…
Feedback alignment and related weight-transport-free algorithms are often proposed as biologically plausible alternatives to backpropagation, yet they are typically formulated in discrete phases with implicitly synchronized forward and…