Discrete random probability measures and the exchangeable partitions they induce are key tools for addressing a variety of estimation prediction problems in Bayesian inference. Here we focus on family Gibbs–type priors, recent elegant generalization Dirichlet Pitman–Yor process priors. These share properties that appealing both from theoretical an applied point view: (i) admit intuitive predictive characterization justifying their use terms precise assumption learning mechanism; (ii) stand...

We study the distribution of unobserved states two measure-valued diffusions Fleming–Viot and Dawson–Watanabe type, conditional on observations from underlying populations collected at past, present future times. If seen as nonparametric hidden Markov models, this amounts to finding smoothing distributions these processes, which we show can be explicitly described in recursive form finite mixtures laws Dirichlet gamma random measures respectively. characterize time-dependent weights...

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

We introduce a new class of nonparametric prior distributions on the space continuously varying densities, induced by Dirichlet process mixtures which diffuse in time. These select time-indexed random functions without jumps, whose sections are continuous or discrete depending choice kernel. The construction exploits widely used stick-breaking representation and induces time dependence replacing components with one-dimensional Wright-Fisher diffusions. features combine appealing properties...

We propose a Bayesian nonparametric approach to modelling and predicting class of functional time series with application energy markets, based on fully observed, noise-free data. Traders in such contexts conceive profitable strategies if they can anticipate the impact their bidding actions aggregate demand supply curves, which turn need be predicted reliably. Here we simple method for take form monotonic bounded step functions. borrow ideas from population genetics by defining interacting...

Fleming–Viot diffusions are widely used stochastic models for population dynamics that extend the celebrated Wright–Fisher diffusions. They describe temporal evolution of relative frequencies allelic types in an ideally infinite panmictic population, whose individuals undergo random genetic drift and at birth can mutate to a new type drawn from possibly potential pool, independently their parent. Recently, Bayesian nonparametric inference has been considered this model when finite sample is...

This paper provides a countable representation for class of infinite-dimensional diffusions which extends the infinitely-many-neutral-alleles model and is related to two-parameter Poisson-Dirichlet process. By means Gibbs sampling procedures, we define reversible Moran-type population The associated process ranked relative frequencies types shown converge in distribution family diffusions, stationary ergodic with respect distribution. construction interpretation limiting terms individual dynamics.

We consider predictive inference using a class of temporally dependent Dirichlet processes driven by Fleming–Viot diffusions, which have natural bearing in Bayesian nonparametrics and lend the resulting family random probability measures to analytical posterior analysis. Formulating implied statistical model as hidden Markov model, we fully describe distribution induced these Fleming–Viot-driven processes, for sequence observations collected at certain time given another set draws several...

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 distribution and certain Fleming–Viot processes. additional parameter has been shown regulate clustering structure of population, but is yet be fully understood way it governs reproductive process. Here, we shed some light on these dynamics formulating a $K$-allele Wright–Fisher model for population size $N$, involving...

The infinitely-many-neutral-alleles model has recently been extended to a class of diffusion processes associated with Gibbs partitions two-parameter Poisson-Dirichlet type. This paper introduces family infinite-dimensional diffusions different subclass partitions, induced by normalized inverse-Gaussian random probability measures. Such describe the evolution frequencies infinitely-many types together dynamics time-varying mutation rate, which is driven an alpha-diversity diffusion....

Exact inference for hidden Markov models requires the evaluation of all distributions interest – filtering, prediction, smoothing and likelihood with a finite computational effort. This article provides sufficient conditions exact class on general state spaces given set discretely collected indirect observations linked non linearly to signal, practical algorithms inference. The we obtain are concerned existence certain type dual process, which is an auxiliary process embedded in time...

Motivated by the problem of forecasting demand and offer curves, we introduce a class nonparametric dynamic models with locally-autoregressive behaviour, provide full inferential strategy for time series piecewise-constant non-decreasing functions over arbitrary horizons. The model is induced non Markovian system interacting particles whose evolution governed resampling step drift mechanism. former based on global interaction accounts volatility functional series, while latter determined...

We define and investigate a new class of measure-valued Markov chains by resorting to ideas formulated in Bayesian nonparametrics related the Dirichlet process Gibbs sampler. Dependent random probability measures this are shown be stationary ergodic with respect law converge distribution neutral diffusion model.

The recently introduced two-parameter infinitely-many-neutral-alleles model extends the celebrated one-parameter version (which is related to Kingman's distribution) diffusive Poisson-Dirichlet frequencies. In this paper we investigate dynamics driving species heterogeneity underlying model. First show that a suitable normalization of number driven by critical continuous-state branching process with immigration. Secondly, provide finite-dimensional construction model, obtained means sequence...

We extend classic characterisations of posterior distributions under Dirichlet process and gamma random measures priors to a dynamic framework. consider the problem learning, from indirect observations, two families time-dependent processes interest in Bayesian nonparametrics: first is dependent driven by Fleming–Viot model, data are samples state at discrete times; second collection Dawson–Watanabe collected according Poisson point with intensity given times. Both driving diffusions taking...

We propose a flexible stochastic framework for modeling the market share dynamics over time in multiple markets setting, where firms interact within and between markets. Firms undergo idiosyncratic shocks, which contract their shares, compete to consolidate position by acquiring new ones both they operate The model parameters can meaningfully account phenomena such as barriers entry exit, fixed sunk costs, costs of expanding sectors with different technologies competitive advantage among...

Background: The prevalence of refractive errors has sharply risen over recent decades. Despite the established role genetics in onset and progression such conditions, environment was also shown to play a pivotal role. Indeed, COVID-19 pandemic majorly impacted people’s lifestyles healthy habits, especially among youth, which might have led significant increase this trend. Therefore, aim study investigate actual large cohort pediatric patients. Methods: A 496 participants screened through...