Matteo Ruggiero

Constraining the Schwarzschild–de Sitter solution in models of modified gravity

The Schwarzschild-de Sitter (SdS) solution exists in the large majority of modified gravity theories, as expected, and in particular the effective cosmological constant is determined by the specific parameters of the given theory. We explore the possibility to use future extended radio-tracking data from the currently ongoing New Horizons mission in the outskirts peripheries of the Solar System, at about 40 au, in order to constrain this effective cosmological constant, and thus to impose constrain on each scenarios parameters. We investigate some of the recently most studied modified gravities, namely

Wright-Fisher construction of the two-parameter Poisson-Dirichlet diffusion

f(R)

Alpha-diversity processes and normalized inverse-Gaussian diffusions.

and

Optimal filtering and the dual process

f(T)

Bayesian nonparametric forecasting of monotonic functional time series

theories, dRGT massive gravity, and Hov{r}ava-Lifshitz gravity, and we show that New Horizons mission may bring an improvement of one-two orders of magnitude with respect to the present bounds from planetary orbital dynamics.

Conjugacy properties of time-evolving Dirichlet and gamma random measures

The two-parameter Poisson–Dirichlet diffusion, introduced in 2009 by Petrov, extends the infinitely-many-neutral-alleles diffusion model, related to Kingman’s one-parameter Poisson–Dirichlet distribution and to certain Fleming–Viot processes. The additional parameter has been shown to regulate the clustering structure of the population, but is yet to be fully understood in the way it governs the reproductive process. Here we shed some light on these dynamics by formulating a K-allele Wright–Fisher model for a population of size N, involving a uniform mutation pattern and a specific state-dependent migration mechanism. Suitably scaled, this process converges in distribution to a K-dimensional diffusion process as N → ∞. Moreover, the descending order statistics of the K-dimensional diffusion converge in distribution to the two-parameter Poisson–Dirichlet diffusion as K → ∞. The choice of the migration mechanism depends on a delicate balance between reinforcement and redistributive effects. The proof of convergence to the infinite-dimensional diffusion is nontrivial because the generators do not converge on a core. Our strategy for overcoming this complication is to prove a priori that in the limit there is no “loss of mass”, i.e., that, for each limit point of the sequence of finite-dimensional diffusions (after a reordering of components by size), allele frequencies sum to one.

Clustering dynamics in a class of normalised generalised gamma dependent priors

The infinitely-many-neutral-alleles model has recently been extended nto a class of diffusion processes associated with Gibbs partitions nof two-parameter Poisson-Dirichlet type. This paper introduces na family of infinite-dimensional diffusions associated with a ndifferent subclass of Gibbs partitions, induced by normalized inverse- nGaussian random probability measures. Such diffusions describe the nevolution of the frequencies of infinitely-many types together with nthe dynamics of the time-varying mutation rate, which is driven by nan alpha-diversity diffusion. Constructed as a dynamic version, relative nto this framework, of the corresponding notion for Gibbs partitions, nthe latter is explicitly derived from an underlying population model nand shown to coincide, in a special case, with the diffusion approximation nof a critical Galton-Watson branching process. The class of ninfinite-dimensional processes is characterized in terms of its infinitesimal ngenerator on an appropriate domain, and shown to be the limit nin distribution of a certain sequence of Feller diffusions with finitelymany ntypes. Moreover, a discrete representation is provided by means nof appropriately transformed Moran-type particle processes, where nthe particles are samples from a normalized inverse-Gaussian random nprobability measure. The relationship between the limit diffusion and nthe two-parameter model is also discussed.

Geometric Stick-Breaking Processes for Continuous-Time Nonparametric Modeling

We link optimal filtering for hidden Markov models to the notion of duality for Markov processes. We show that when the signal is dual to a process that has two components, one deterministic and one a pure death process, and with respect to functions that define changes of measure conjugate to the emission density, the filtering distributions evolve in the family of finite mixtures of such measures and the filter can be computed at a cost that is polynomial in the number of observations. Special cases of our framework include the Kalman filter, and computable filters for the Cox-Ingersoll-Ross process and the one-dimensional Wright-Fisher process, which have been investigated before. The dual we obtain for the Cox-Ingersoll-Ross process appears to be new in the literature.

Bayesian Nonparametric Construction of the Fleming-Viot Process with Fertility Selection

We propose a Bayesian nonparametric approach to modelling and predicting a class of functional time series with application to energy markets, based on fully observed, noise-free functional data. Traders in such contexts conceive profitable strategies if they can anticipate the impact of their bidding actions on the aggregate demand and supply curves, which in turn need to be predicted reliably. Here we propose a simple Bayesian nonparametric method for predicting such curves, which take the form of monotonic bounded step functions. We borrow ideas from population genetics by defining a class of interacting particle systems to model the functional trajectory, and develop an implementation strategy which uses ideas from Markov chain Monte Carlo and approximate Bayesian computation techniques and allows to circumvent the intractability of the likelihood. Our approach shows great adaptation to the degree of smoothness of the curves and the volatility of the functional series, proves to be robust to an increase of the forecast horizon and yields an uncertainty quantification for the functional forecasts. We illustrate the model and discuss its performance with simulated datasets and on real data relative to the Italian natural gas market.

COUNTABLE REPRESENTATION FOR INFINITE DIMENSIONAL DIFFUSIONS DERIVED FROM THE TWO-PARAMETER POISSON-DIRICHLET PROCESS

We extend classic characterisations of posterior distributions under Dirichlet process and gamma random measures priors to a dynamic framework. We consider the problem of learning, from indirect observations, two families of time-dependent processes of interest in Bayesian nonparametrics: the first is a dependent Dirichlet process driven by a Fleming–Viot model, and the data are random samples from the process state at discrete times; the second is a collection of dependent gamma random measures driven by a Dawson–Watanabe model, and the data are collected according to a Poisson point process with intensity given by the process state at discrete times. Both driving processes are diffusions taking values in the space of discrete measures whose support varies with time, and are stationary and reversible with respect to Dirichlet and gamma priors respectively. A common methodology is developed to obtain in closed form the time-marginal posteriors given past and present data. These are shown to belong to classes of finite mixtures of Dirichlet processes and gamma random measures for the two models respectively, yielding conjugacy of these classes to the type of data we consider. We provide explicit results on the parameters of the mixture components and on the mixing weights, which are time-varying and drive the mixtures towards the respective priors in absence of further data. Explicit algorithms are provided to recursively compute the parameters of the mixtures. Our results are based on the projective properties of the signals and on certain duality properties of their projections.