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We study nonparametric Bayesian models for reversible multidimensional diffusions with periodic drift. For continuous observation paths, reversibility is exploited to prove a general posterior contraction rate theorem the drift gradient vector field under approximation-theoretic conditions on induced prior invariant measure. The applied Gaussian priors and p-exponential priors, which are shown converge truth at optimal over Sobolev smoothness classes in any dimension.

We consider the statistical inverse problem of recovering an unknown function $f$ from a linear measurement corrupted by additive Gaussian white noise. employ nonparametric Bayesian approach with standard priors, for which posterior-based reconstruction corresponds to Tikhonov regularizer $\bar f$ reproducing kernel Hilbert space norm penalty. prove semiparametric Bernstein--von Mises theorem large collection functionals $f$, implying that posterior estimation and uncertainty quantification...

We rigorously prove that deep Gaussian process priors can outperform if the target function has a compositional structure. To this end, we study information-theoretic lower bounds for posterior contraction rates regression in continuous model. show true is generalized additive function, then based on any mean-zero only recover truth at rate strictly slower than minimax by factor polynomially suboptimal sample size $n$.

We consider the problem of making nonparametric inference in multi-dimensional diffusion models from low-frequency data. Statistical analysis this setting is notoriously challenging due to intractability likelihood and its gradient, computational methods have thus far largely resorted expensive simulation-based techniques. In article, we propose a new approach which motivated by PDE theory built around characterisation transition densities as solutions associated heat (Fokker-Planck)...

We congratulate the authors for their methodological and theoretical contribution to statistical literature on networks.A natural extension of proposed PAPER model is included, with K communities growing simultaneously where new nodes are either assigned an existing community or elected as a root.The employed assignment rule Pólya-urn type, which leads logarithmic growth number (Korwar Hollander, 1972) known coincide predictive scheme exchangeable sequences associated Dirichlet process.The...

We consider the statistical linear inverse problem of making inference on an unknown source function in elliptic partial differential equation from noisy observations its solution. employ nonparametric Bayesian procedures based Gaussian priors, leading to convenient conjugate formulae for posterior inference. review recent results providing theoretical guarantees quality resulting posterior-based estimation and uncertainty quantification, we discuss application theory important classes...

In this article, we investigate the problem of estimating a spatially inhomogeneous function and its derivatives in white noise model using Besov-Laplace priors. We show that smoothness-matching priors attains minimax optimal posterior contraction rates, strong Sobolev metrics, over Besov spaces $B^\beta_{11}$, $\beta > d/2$, closing gap existing literature. Our rates also imply distributions arising from with matching regularity enjoy desirable plug-in property for derivative estimation,...

Besov priors are nonparametric that can model spatially inhomogeneous functions. They routinely used in inverse problems and imaging, where they exhibit attractive sparsity-promoting edge-preserving features. A recent line of work has initiated the study their asymptotic frequentist convergence properties. In present paper, we consider theoretical recovery performance posterior distributions associated to Besov-Laplace density estimation model, under assumption observations generated by a...

We consider the statistical inverse problem of recovering an unknown function $f$ from a linear measurement corrupted by additive Gaussian white noise. employ nonparametric Bayesian approach with standard priors, for which posterior-based reconstruction corresponds to Tikhonov regulariser $\bar f$ reproducing kernel Hilbert space norm penalty. prove semiparametric Bernstein-von Mises theorem large collection functionals $f$, implying that posterior estimation and uncertainty quantification...

We study nonparametric Bayesian models for reversible multi-dimensional diffusions with periodic drift. For continuous observation paths, reversibility is exploited to prove a general posterior contraction rate theorem the drift gradient vector field under approximation-theoretic conditions on induced prior invariant measure. The applied Gaussian priors and $p$-exponential priors, which are shown converge truth at minimax optimal over Sobolev smoothness classes in any dimension.

Besov priors are nonparametric that can model spatially inhomogeneous functions. They routinely used in inverse problems and imaging, where they exhibit attractive sparsity-promoting edge-preserving features. A recent line of work has initiated the study their asymptotic frequentist convergence properties. In present paper, we consider theoretical recovery performance posterior distributions associated to Besov-Laplace density estimation model, under assumption observations generated by a...

Parameter identification problems in partial differential equations (PDEs) consist determining one or more unknown functional parameters a PDE. Here, the Bayesian nonparametric approach to such is considered. Focusing on representative example of inferring diffusivity function an elliptic PDE from noisy observations solution, performance procedures based Gaussian process priors investigated. Recent asymptotic theoretical guarantees establishing posterior consistency and convergence rates are...

This work studies nonparametric Bayesian estimation of the intensity function an inhomogeneous Poisson point process in important case where depends on covariates, based observation a single realisation pattern over large area. It is shown how presence covariates allows to borrow information from far away locations window, enabling consistent inference growing domain asymptotics. In particular, optimal posterior contraction rates under both global and point-wise loss functions are derived....

For $\mathcal{O}$ a bounded domain in $\mathbb{R}^d$ and given smooth function $g:\mathcal{O}\to\mathbb{R}$, we consider the statistical nonlinear inverse problem of recovering conductivity $f&gt;0$ divergence form equation $$ \nabla\cdot(f\nabla u)=g\ \textrm{on}\ \mathcal{O}, \quad u=0\ \partial\mathcal{O}, from $N$ discrete noisy point evaluations solution $u=u_f$ on $\mathcal O$. We study performance Bayesian nonparametric procedures based flexible class Gaussian (or hierarchical...

We introduce a continuous-time Markov chain describing dynamic allelic partitions which extends the branching process construction of Pitman sampling formula in ( 2006) and classical birth-and-death with immigration studied Karlin McGregor (1967), turn related to celebrated Ewens formula.A biological basis for scheme is provided terms population individuals grouped into families, that evolves according sequence births, deaths immigrations.We investigate asymptotic behaviour show that, as...

Introduzione. L'Organizzazione Mondiale della Sanit&amp;agrave; (OMS) definisce la Comorbilit&amp;agrave; o Doppia Diagnosi come coesistenza nel medesimo individuo di un disturbo dovuto al consumo sostanze psicoattive ed altro psichiatrico (OMS, 1995). Per quanto piuttosto criticata tale definizione consente individuare una popolazione pazienti le cui caratteristiche psicopatologiche appaiono peculiari e molto spesso difficile non univoca interpretazione diagnostica; da tali...