arXiv subjects

Flávio B. Gonçalves

Publications and source records attributed to Flávio B. Gonçalves.

14 recordsLinked to original sources

arXiv2026

Scalable Bernoulli Factory MCMC for Intractable Marginalised Posteriors

Bernoulli factory MCMC algorithms implement accept-reject Markov chains without explicit computation of acceptance probabilities, and are used to target posterior distributions associated with intractable likelihood models. Intractable likelihoods naturally arise in continuous-time models and mixture distributions, or from the marginalisation of a tractable augmented model. Bernoulli factory MCMC algorithms often mix better than alternatives that target a tractable augmented posterior. However, we show that their computational performance typically deteriorates exponentially with data size, as happens in naively implemented pseudo-marginal algorithms. To address this, we propose a simple divide-and-conquer Bernoulli factory MCMC algorithm and prove that it has polynomial complexity for factorizing models, with the exact degree depending on the existence of efficient unbiased estimators of the intractable likelihood ratio. We demonstrate the effectiveness of our approach with applications to Bayesian inference in two intractable likelihood models, and observe respective polynomial cost of degree 1.2 and 1 in the data size.

stat.CO↗

arXiv2026

A Reverse-BSDE Diffusion Sampler

Diffusion-based generative models have renewed interest in stochastic differential equation methods for sampling from complex distributions. We study a setting in which the target density is known only up to a normalizing constant and reformulate the reverse-time diffusion sampler as a forward-backward stochastic differential equation (FBSDE). This formulation replaces the separate pre-estimation of the time-dependent score with the solution of a coupled stochastic system. We prove the equivalence of these formulations and provide a decomposition of the approximation error arising from initializing the sampler with a standard Gaussian, applying Euler discretization to the dynamics, and solving the FBSDE approximately. We then evaluate the proposed algorithm on synthetic targets, including separated mixtures, anisotropic Gaussian distributions, and banana-shaped and ring-shaped distributions. The results demonstrate the promise of the method, particularly for targets with complex global structure.

stat.ML↗

arXiv2026

Nonparametric inference for nonstationary spatial point processes

Point pattern data often exhibit features such as abrupt changes, hotspots and spatially varying dependence in local intensity. Under a Poisson process framework, these correspond to discontinuities and nonstationarity in the underlying intensity function. These features are difficult to capture with standard modeling approaches. This paper proposes a spatial Cox process model in which nonstationarity is induced through a random partition of the spatial domain, with conditionally independent Gaussian process priors specified across the resulting regions. This construction allows for heterogeneous spatial behavior, including sharp transitions in intensity. A discretization-free MCMC algorithm is developed to target the infinite-dimensional posterior distribution without approximation, thus ensuring exact inference. The random partition framework via Voronoi tessellation also reduces the computational burden associated with Gaussian process models. Spatial covariates can be incorporated to account for structured variation in intensity. The proposed methodology is evaluated through synthetic examples and real-world applications, demonstrating its ability to flexibly capture complex spatial structures. The model performs competitively, outperforming stationary and nonstationary alternatives in a variety of scenarios. Recent computational methods are used, enabling scalability to large datasets while preserving exactness. The paper concludes with a discussion of potential extensions and directions for future work.

stat.ME↗

arXiv2026

A New Perspective on Reverse Diffusion for Monte Carlo Sampling

This paper introduces a novel perspective on the use of reverse diffusion processes for sampling from unnormalized densities. The central idea is to embed the target density as the marginal at the initial time of a suitably constructed diffusion process evolving over a finite horizon. In contrast to existing approaches, the proposed methodology involves neither time discretization error nor score function estimation, so that Monte Carlo variability is the only source of approximation. A key theoretical result characterizes the Radon-Nikodym derivative of the reverse diffusion transition distribution with respect to that of an Ornstein-Uhlenbeck (OU) process. This representation provides a tractable change-of-measure formulation and serves as the foundation for two distinct classes of Monte Carlo algorithms. The first class approximates the reverse transition distribution via a sequence of pseudo-marginal Metropolis-Hastings MCMC algorithms. The resulting scheme produces an approximate i.i.d. sample from the target distribution and is fully parallelizable, as trajectories can be generated independently. The second class consists of MCMC algorithms targeting the joint law of the whole diffusion path in $[0,T]$, for a suitably chosen horizon $T$. The proposed samplers combine three types of updates. One update simulates the diffusion forward in time according to an OU dynamics, conditional on its initial value. The remaining two update the backward component via Metropolis-type steps: one conditions on the terminal value at time $T$ and the other one does not. In both cases, acceptance probabilities are implemented using Barker-type Bernoulli factory constructions. The proposed methods perform well for targets with multimodality and complex dependence structures, providing a scalable and efficient alternative to the widely used random-walk Metropolis algorithm.

stat.CO↗

arXiv2026

Bridging Theory and Practice in Efficient Gaussian Process-Based Statistical Modeling for Large Datasets

Geostatistics is a branch of statistics concerned with stochastic processes over continuous domains, with Gaussian processes (GPs) providing a flexible and principled modelling framework. However, the high computational cost of simulating or computing likelihoods with GPs limits their scalability to large datasets. This paper introduces the piecewise continuous Gaussian process (PCGP), a new process that retains the rich probabilistic structure of traditional GPs while offering substantial computational efficiency. As will be shown and discussed, existing scalable approaches that define stochastic processes on continuous domains -- such as the nearest-neighbour GP (NNGP) and the radial-neighbour GP (RNGP) -- rely on conditional independence structures that effectively constrain the measurable space on which the processes are defined, which may induce undesirable probabilistic behaviour and compromise their practical applicability, particularly in complex latent GP models. The PCGP mitigates these limitations and provides a theoretically grounded and computationally efficient alternative, as demonstrated through numerical illustrations.

stat.CO↗

arXiv2026

From Shallow Bayesian Neural Networks to Gaussian Processes: General Convergence, Identifiability and Scalable Inference

In this work, we study scaling limits of shallow Bayesian neural networks (BNNs) via their connection to Gaussian processes (GPs), with an emphasis on statistical modeling, identifiability, and scalable inference. We first establish a general convergence result from BNNs to GPs by relaxing assumptions used in prior formulations, and we compare alternative parameterizations of the limiting GP model. Building on this theory, we propose a new covariance function defined as a convex mixture of components induced by four widely used activation functions, and we characterize key properties including positive definiteness and both strict and practical identifiability under different input designs. For computation, we develop a scalable maximum a posterior (MAP) training and prediction procedure using a Nyström approximation, and we show how the Nyström rank and anchor selection control the cost-accuracy trade-off. Experiments on controlled simulations and real-world tabular datasets demonstrate stable hyperparameter estimates and competitive predictive performance at realistic computational cost.

stat.ML↗

arXiv2024

Generation and analysis of synthetic data via Bayesian networks: a robust approach for uncertainty quantification via Bayesian paradigm

Safe and reliable disclosure of information from confidential data is a challenging statistical problem. A common approach considers the generation of synthetic data, to be disclosed instead of the original data. Efficient approaches ought to deal with the trade-off between reliability and confidentiality of the released data. Ultimately, the aim is to be able to reproduce as accurately as possible statistical analysis of the original data using the synthetic one. Bayesian networks is a model-based approach that can be used to parsimoniously estimate the underlying distribution of the original data and generate synthetic datasets. These ought to not only approximate the results of analyses with the original data but also robustly quantify the uncertainty involved in the approximation. This paper proposes a fully Bayesian approach to generate and analyze synthetic data based on the posterior predictive distribution of statistics of the synthetic data, allowing for efficient uncertainty quantification. The methodology makes use of probability properties of the model to devise a computationally efficient algorithm to obtain the target predictive distributions via Monte Carlo. Model parsimony is handled by proposing a general class of penalizing priors for Bayesian network models. Finally, the efficiency and applicability of the proposed methodology is empirically investigated through simulated and real examples.

stat.ME↗

arXiv2023

Exact Monte Carlo likelihood-based inference for jump-diffusion processes

Statistical inference for discretely observed jump-diffusion processes is a complex problem which motivates new methodological challenges. Thus existing approaches invariably resort to time-discretisations which inevitably lead to approximations in inference. In this paper, we give the first general collection of methodologies for exact (in this context meaning discretisation-free) likelihood-based inference for discretely observed finite activity jump-diffusions. The only sources of error involved are Monte Carlo error and convergence of EM or MCMC algorithms. We shall introduce both frequentist and Bayesian approaches, illustrating the methodology through simulated and real examples.

stat.ME↗

arXiv2022

Flexible Bayesian modelling in dichotomous item response theory using mixtures of skewed item curves

Most Item Response Theory (IRT) models for dichotomous responses are based on probit or logit link functions which assume a symmetric relationship between the probability of a correct response and the latent traits of individuals submitted to a test. This assumption restricts the use of those models to the case in which all items have a symmetric behaviour. On the other hand, asymmetric models proposed in the literature impose that all the items in a test have an asymmetric behaviour. This assumption is inappropriate for great part of the tests which are, in general, composed by both symmetric and asymmetric items. Furthermore, a straightforward extension of the existing models in the literature would require a prior selection of the items' symmetry/asymmetry status. This paper proposes a Bayesian IRT model that accounts for symmetric and asymmetric items in a flexible though parsimonious way. That is achieved by assigning a finite mixture prior to the skewness parameter, with one of the mixture components being a point-mass at zero. This allows for analyses under both model selection and model averaging approaches. Asymmetric item curves are designed through the centred skew normal distribution, which has a particularly appealing parametrisation in terms of parameter interpretation and computational efficiency. An efficient MCMC algorithm is proposed to perform Bayesian inference and its performance is investigated in some simulated examples. Finally, the proposed methodology is applied to a data set from a large scale educational exam in Brazil.

stat.ME↗

arXiv2021

On the definition of likelihood function

We discuss a general definition of likelihood function in terms of Radon-Nikodým derivatives. The definition is validated by the Likelihood Principle once we establish a result regarding the proportionality of likelihood functions under different dominating measures. This general framework is particularly useful when there exists no or more than one obvious choice for a dominating measure as in some infinite-dimensional models. We discuss the importance of considering continuous versions of densities and how these are related to the Likelihood Principle and the basic concept of likelihood. We also discuss the use of the predictive measure as a dominating measure in the Bayesian approach. Finally, some examples illustrate the general definition of likelihood function and the importance of choosing particular dominating measures in some cases.

math.ST↗

arXiv2019

Exact Bayesian inference in spatio-temporal Cox processes driven by multivariate Gaussian processes

In this paper we present a novel inference methodology to perform Bayesian inference for spatiotemporal Cox processes where the intensity function depends on a multivariate Gaussian process. Dynamic Gaussian processes are introduced to allow for evolution of the intensity function over discrete time. The novelty of the method lies on the fact that no discretisation error is involved despite the non-tractability of the likelihood function and infinite dimensionality of the problem. The method is based on a Markov chain Monte Carlo algorithm that samples from the joint posterior distribution of the parameters and latent variables of the model. The models are defined in a general and flexible way but they are amenable to direct sampling from the relevant distributions, due to careful characterisation of its components. The models also allow for the inclusion of regression covariates and/or temporal components to explain the variability of the intensity function. These components may be subject to relevant interaction with space and/or time. Real and simulated examples illustrate the methodology, followed by concluding remarks.

stat.ME↗

arXiv2017

Bayesian Item Response model: a generalised approach for the abilities' distribution using mixtures

Traditional Item Response Theory models assume the distribution of the abilities of the population in study to be Gaussian. However, this may not always be a reasonable assumption, which motivates the development of more general models. This paper presents a generalised approach for the distribution of the abilities in dichotomous 3-parameter Item Response models. A mixture of normal distributions is considered, allowing for features like skewness, multimodality and heavy tails. A solution is proposed to deal with model identifiability issues without compromising the flexibility and practical interpretation of the model. Inference is carried out under the Bayesian Paradigm through a novel MCMC algorithm. The algorithm is designed in a way to favour good mixing and convergence properties and is also suitable for inference in traditional IRT models. The efficiency and applicability of our methodology is illustrated in simulated and real examples.

stat.AP↗

arXiv2017

Bayesian linear regression models with flexible error distributions

This work introduces a novel methodology based on finite mixtures of Student-t distributions to model the errors' distribution in linear regression models. The novelty lies on a particular hierarchical structure for the mixture distribution in which the first level models the number of modes, responsible to accommodate multimodality and skewness features, and the second level models tail behavior. Moreover, the latter is specified in a way that no degrees of freedom parameters are estimated and, therefore, the known statistical difficulties when dealing with those parameters is mitigated, and yet model flexibility is not compromised. Inference is performed via Markov chain Monte Carlo and simulation studies are conducted to evaluate the performance of the proposed methodology. The analysis of two real data sets are also presented.

stat.ME↗

arXiv2017

Identifying down and up-regulated chromosome regions using RNA-Seq data

The number of studies dealing with RNA-Seq data analysis has experienced a fast increase in the past years making this type of gene expression a strong competitor to the DNA microarrays. This paper proposes a Bayesian model to detect down and up-regulated chromosome regions using RNA-Seq data. The methodology is based on a recent work developed to detect up-regulated regions in the context of microarray data. A hidden Markov model is developed by considering a mixture of Gaussian distributions with ordered means in a way that first and last mixture components are supposed to accommodate the under and overexpressed genes, respectively. The model is flexible enough to efficiently deal with the highly irregular spaced configuration of the data by assuming a hierarchical Markov dependence structure. The analysis of four cancer data sets (breast, lung, ovarian and uterus) is presented. Results indicate that the proposed model is selective in determining the regulation status, robust with respect to prior specifications and provides tools for a global or local search of under and overexpressed chromosome regions.

stat.AP↗