Matteo Giordano

• Doctor of Philosophy
• Assistant Professor at University of Turin

We consider the statistical inverse problem of recovering an unknown function $f$ from a linear measurement corrupted by additive Gaussian white noise. We employ a nonparametric Bayesian approach with standard Gaussian priors, for which the posterior-based reconstruction of $f$ corresponds to a Tikhonov regulariser $\bar f$ with a reproducing kerne...

For O a bounded domain in Rd and a given smooth function g:O→R, we consider the statistical nonlinear inverse problem of recovering the conductivity f > 0 in the divergence form equation ∇⋅(f∇u)=gonO,u=0on∂O, from N discrete noisy point evaluations of the solution u = uf on O. We study the statistical performance of Bayesian nonparametric procedure...

We study nonparametric Bayesian modelling of reversible multi-dimensional diffusions with periodic drift. For continuous observations paths, reversibility is exploited to prove a general posterior contraction rate theorem for the drift gradient vector field under approximation-theoretic conditions on the induced prior for the invariant measure. The...

Partial differential equations (PDEs) are primary mathematical tools to model the behaviour of complex real-world systems. PDEs generally include a collection of parameters in their formulation, which are often unknown in applications and need to be estimated from the data. In the present thesis, we investigate the theoretical performance of nonpar...

We rigorously prove that deep Gaussian process priors can outperform Gaussian process priors if the target function has a compositional structure. To this end, we study information-theoretic lower bounds for posterior contraction rates for Gaussian process regression in a continuous regression model. We show that if the true function is a generaliz...

Besov priors are nonparametric priors that model spatially inhomogeneous functions. They are routinely used in inverse problems and imaging, where they exhibit attractive sparsity-promoting and edge-preserving features. A recent line of work has initiated the study of the asymptotic frequentist convergence properties of Besov priors. In the present...

We introduce a continuous-time Markov chain describing dynamic allelic partitions which extends the branching process construction of the Pitman Sampling Formula (PSF) in Pitman (2006) and the classical birth-and-death process with immigration of Karlin and McGregor (1967), in turn related to the celebrated Ewens Sampling Formla. A biological basis...

For $\mathcal{O}$ a bounded domain in $\mathbb{R}^d$ and a given smooth function $g:\mathcal{O}\to\mathbb{R}$, we consider the statistical nonlinear inverse problem of recovering the conductivity $f>0$ in the divergence form equation $$ \nabla\cdot(f\nabla u)=g\ \textrm{on}\ \mathcal{O}, \quad u=0\ \textrm{on}\ \partial\mathcal{O}, $$ from $N$ disc...

We introduce a continuous-time Markov chain describing dynamic allelic partitions which extends the branching process construction of the Pitman sampling formula in Pitman (2006) and the birth-and-death process with immigration of Karlin and McGregor (1967), in turn related to the celebrated Ewens sampling formula. A biological basis for the scheme...

We consider the statistical inverse problem of approximating an unknown function $f$ from a linear measurement corrupted by additive Gaussian white noise. We employ a nonparametric Bayesian approach with standard Gaussian priors, for which the posterior-based reconstruction of $f$ corresponds to a Tikhonov regulariser $\bar f$ with a Cameron-Martin...