Giacomo Zanella

Giacomo Zanella
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Giacomo Zanella

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Statistics - Computation (3)
Mathematics - Probability (3)
Statistics - Applications (2)
Statistics - Methodology (2)
Statistics - Theory (1)
Mathematics - Statistics (1)
Statistics - Machine Learning (1)

Publications Authored By Giacomo Zanella

We study the convergence properties of the Gibbs Sampler in the context of posterior distributions arising from Bayesian analysis of Gaussian hierarchical models. We consider centred and non-centred parameterizations as well as their hybrids including the full family of partially non-centred parameterizations. We develop a novel methodology based on multi-grid decompositions to derive analytic expressions for the convergence rates of the algorithm for an arbitrary number of layers in the hierarchy, while previous work was typically limited to the two-level case. Read More

Most generative models for clustering implicitly assume that the number of data points in each cluster grows linearly with the total number of data points. Finite mixture models, Dirichlet process mixture models, and Pitman--Yor process mixture models make this assumption, as do all other infinitely exchangeable clustering models. However, for some applications, this assumption is inappropriate. Read More

This paper develops the use of Dirichlet forms to deliver proofs of optimal scaling results for Markov chain Monte Carlo algorithms (specifically, Metropolis-Hastings random walk samplers) under regularity conditions which are substantially weaker than those required by the original approach (based on the use of infinitesimal generators). The Dirichlet form methods have the added advantage of providing an explicit construction of the underlying infinite-dimensional context. In particular, this enables us directly to establish weak convergence to the relevant infinite-dimensional distributions. Read More

The notion of stability can be generalised to point processes by defining the scaling operation in a randomised way: scaling a configuration by $t$ corresponds to letting such a configuration evolve according to a Markov branching particle system for -$\log t$ time. We prove that these are the only stochastic operations satisfying basic associativity and distributivity properties and we thus introduce the notion of branching-stable point processes. We characterise stable distributions with respect to local branching as thinning-stable point processes with multiplicities given by the quasi-stationary (or Yaglom) distribution of the branching process under consideration. Read More

Common cluster models for multi-type point processes model the aggregation of points of the same type. In complete contrast, in the study of Anglo-Saxon settlements it is hypothesized that administrative clusters involving complementary names tend to appear. We investigate the evidence for such an hypothesis by developing a Bayesian Random Partition Model based on clusters formed by points of different types (complementary clustering). Read More