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Finite mixture models are a useful statistical model class for clustering and density approximation. In the Bayesian framework finite mixture models require the specification of suitable priors in addition to the data model. These priors…
Evaluation of clinical prediction models across multiple clusters, whether centers or datasets, is becoming increasingly common. A comprehensive evaluation includes an assessment of the agreement between the estimated risks and the observed…
We investigate the kinetics of constant-kernel aggregation which is augmented by either: (a) evaporation of monomers from finite-mass clusters, or (b) continuous cluster growth -- \ie, condensation. The rate equations for these two…
Finite mixture models are flexible methods that are commonly used for model-based clustering. A recent focus in the model-based clustering literature is to highlight the difference between the number of components in a mixture model and the…
We study a mean-field model for a clustering process that may be described informally as follows. At each step a random integer $k$ is chosen with probability $p_k$, and the smallest cluster merges with $k$ randomly chosen clusters. We…
The majority of model-based clustering techniques is based on multivariate Normal models and their variants. In this paper copulas are used for the construction of flexible families of models for clustering applications. The use of copulas…
Pamminger and Fruwirth-Schnatter (2010) considered a Bayesian approach to model-based clustering of categorical time series assuming a fixed number of clusters. But the popular methods for selecting the number of clusters, for example, the…
We consider a discrete latent variable model for two-way data arrays, which allows one to simultaneously produce clusters along one of the data dimensions (e.g. exchangeable observational units or features) and contiguous groups, or…
This paper deals with nonparametric estimation of conditional den-sities in mixture models in the case when additional covariates are available. The proposed approach consists of performing a prelim-inary clustering algorithm on the…
Clustered data is ubiquitous in a variety of scientific fields. In this paper, we propose a flexible and interpretable modeling approach, called grouped heterogenous mixture modeling, for clustered data, which models cluster-wise…
This article describes a model and an exact solution method for facility location problems with decision-dependent uncertainties. The model allows characterizing the probability distribution of the random elements as a function of the…
Cumulants and moments are closely related to the basic mathematics of continuous and discrete selection (respectively). These relationships generalize Fisher's fundamental theorem of natural selection and also make clear some of its…
We examine the classic problem of homogeneous nucleation and growth by deriving and analyzing a fully discrete stochastic master equation. Upon comparison with results obtained from the corresponding mean-field Becker-D\"{o}ring equations…
Conformal prediction is a generic methodology for finite-sample valid distribution-free prediction. This technique has garnered a lot of attention in the literature partly because it can be applied with any machine learning algorithm that…
We report surprising steady oscillations in aggregation-fragmentation processes. Oscillating solutions are observed for the class of aggregation kernels $K_{i,j} = i^{\nu}j^{\mu} + j^{\nu}i^{\mu}$ homogeneous in masses $i$ and $j$ of…
We study the solutions of the Smoluchowski coagulation equation with a regularisation term which removes clusters from the system when their mass exceeds a specified cut-off size, M. We focus primarily on collision kernels which would…
We present a new method for the calculation of fragment size correlations in a discrete finite system in which correlations explicitly due to the finite extent of the system are suppressed. To this end, we introduce a combinatorial model,…
We introduce an extended Smoluchowski equation describing coagulation processes for which clusters of mass s grow between collisions with $ds/dt=As^\beta$. A physical example, dropwise condensation is provided, and its collision kernel K is…
We consider the approach to self-similarity (or dynamical scaling) in Smoluchowski's coagulation equations for the solvable kernels K(x,y)=2, x+y and xy. We prove the uniform convergence of densities to the self-similar solution with…
The paper introduces a novel algorithm for computing the output admissible set of linear discrete-time systems subject to input saturation. The proposed method takes advantage of the piecewise-affine dynamics to propagate the output…