Marginally Constrained Nonparametric Bayesian Inference through Gaussian Processes

Nonparametric Bayesian models are used routinely as flexible and powerful models of complex data. Many times, a statistician may have additional informative beliefs about data distribution of interest, e.g., its mean or subset components, that is not part of, or even compatible with, the nonparametric prior. An important challenge is then to incorporate this partial prior belief into nonparametric Bayesian models. In this paper, we are motivated by settings where practitioners have additional distributional information about a subset of the coordinates of the observations being modeled. Our approach links this problem to that of conditional density modeling. Our main idea is a novel constrained Bayesian model, based on a perturbation of a parametric distribution with a transformed Gaussian process prior on the perturbation function. We also develop a corresponding posterior sampling method based on data augmentation. We illustrate the efficacy of our proposed constrained nonparametric Bayesian model in a variety of real-world scenarios including modeling environmental and earthquake data

A Hierarchical Bayesian Approach to Neutron Spectrum Unfolding with Organic Scintillators

We propose a hierarchical Bayesian model and state-of-art Monte Carlo sampling method to solve the unfolding problem, i.e., to estimate the spectrum of an unknown neutron source from the data detected by an organic scintillator. Inferring neutron spectra is important for several applications, including nonproliferation and nuclear security, as it allows the discrimination of fission sources in special nuclear material (SNM) from other types of neutron sources based on the differences of the emitted neutron spectra. Organic scintillators interact with neutrons mostly via elastic scattering on hydrogen nuclei and therefore partially retain neutron energy information. Consequently, the neutron spectrum can be derived through deconvolution of the measured light output spectrum and the response functions of the scintillator to monoenergetic neutrons. The proposed approach is compared to three existing methods using simulated data to enable controlled benchmarks. We consider three sets of detector responses. One set corresponds to a 2.5 MeV monoenergetic neutron source and two sets are associated with (energy-wise) continuous neutron sources ($^{252}$Cf and $^{241}$AmBe). Our results show that the proposed method has similar or better unfolding performance compared to other iterative or Tikhonov regularization-based approaches in terms of accuracy and robustness against limited detection events, while requiring less user supervision. The proposed method also provides a posteriori confidence measures, which offers additional information regarding the uncertainty of the measurements and the extracted information.Comment: 10 page

Bayesian inference for indirectly observed stochastic processes, applications to epidemic modelling

Stochastic processes are mathematical objects that offer a probabilistic representation of how some quantities evolve in time. In this thesis we focus on estimating the trajectory and parameters of dynamical systems in cases where only indirect observations of the driving stochastic process are available. We have first explored means to use weekly recorded numbers of cases of Influenza to capture how the frequency and nature of contacts made with infected individuals evolved in time. The latter was modelled with diffusions and can be used to quantify the impact of varying drivers of epidemics as holidays, climate, or prevention interventions. Following this idea, we have estimated how the frequency of condom use has evolved during the intervention of the Gates Foundation against HIV in India. In this setting, the available estimates of the proportion of individuals infected with HIV were not only indirect but also very scarce observations, leading to specific difficulties. At last, we developed a methodology for fractional Brownian motions (fBM), here a fractional stochastic volatility model, indirectly observed through market prices. The intractability of the likelihood function, requiring augmentation of the parameter space with the diffusion path, is ubiquitous in this thesis. We aimed for inference methods robust to refinements in time discretisations, made necessary to enforce accuracy of Euler schemes. The particle Marginal Metropolis Hastings (PMMH) algorithm exhibits this mesh free property. We propose the use of fast approximate filters as a pre-exploration tool to estimate the shape of the target density, for a quicker and more robust adaptation phase of the asymptotically exact algorithm. The fBM problem could not be treated with the PMMH, which required an alternative methodology based on reparameterisation and advanced Hamiltonian Monte Carlo techniques on the diffusion pathspace, that would also be applicable in the Markovian setting

From habitat to management: a simulation framework for improving statistical methods in fisheries science

224 p.Monte Carlo simulation consists in computer experiments that involve creating data by pseudo-random sampling and has shown to be a powerful tool for studying the performance of statistical methods. In this thesis Monte Carlo simulation was used to improve statistical methodology related to three different fields of fisheries science: 1) Species distribution models (SDM) field, where focusing on regression-based models, we proposed using shape-constrained generalised additive models (SC-GAMs) to build SDMs in agreement with the ecological niche theory imposing concavity constraints in the linear predictor scale and testing their performance trough Monte Carlos simulation, 2) stock assessment models field, where uncertainty estimation methods for statistical catch-at-age models with non-parametric effects on fishing mortality were compared through simulation in addition to the comparison of two available stock assessment models to an ad-hoc Bayesian approach, and 3) management advice field, where a full-feedback management strategy evaluation (MSE) is developed for the sardine in the Bay of Biscay, incorporating the official Stoch Synthesis assessment model within the Monte Carlo simulation, and introducing gradually different sources of uncertainty such as process, parameter and observation error in order to study their effect in management advice. Monte Carlo simulation was an adequate tool to accomplish the objectives of this thesis that definitely could not have been achieved using only available real data or analytical solutions

From habitat to management: a simulation framework for improving statistical methods in fisheries science

Monte Carlo simulation consists of computer experiments that involve creating data by pseudo-random sampling and has shown to be a powerful tool for studying the performance of statistical methods. In this thesis Monte Carlo simulation was used to improve statistical methodology related to three different fields of fisheries science: 1) Species distribution models (SDM) field, where focusing on regression-based models, we proposed using shape-constrained generalised additive models (SC-GAMs) to build SDMs in agreement with the ecological niche theory imposing concavity constraints in the linear predictor scale and testing their performance trough Monte Carlo simulation, 2) stock assessment models field, where uncertainty estimation methods for statistical catch-at-age models with non-parametric effects on fishing mortality were compared through simulation in addition to the comparison of two available stock assessment models to an ad-hoc Bayesian approach, and 3) management advice field, where a full-feedback management strategy evaluation (MSE) was developed for the sardine in the Bay of Biscay, incorporating the official Stoch Synthesis assessment model within the Monte Carlo simulation, and introducing gradually different sources of uncertainty such as process, parameter and observation error in order to study their effect in management advice. Monte Carlo simulation was an adequate tool to accomplish the objectives of this thesis that definitely could not have been achieved using only available real data or analytical solutions

Differential geometric MCMC methods and applications

This thesis presents novel Markov chain Monte Carlo methodology that exploits the natural representation of a statistical model as a Riemannian manifold. The methods developed provide generalisations of the Metropolis-adjusted Langevin algorithm and the Hybrid Monte Carlo algorithm for Bayesian statistical inference, and resolve many shortcomings of existing Monte Carlo algorithms when sampling from target densities that may be high dimensional and exhibit strong correlation structure. The performance of these Riemannian manifold Markov chain Monte Carlo algorithms is rigorously assessed by performing Bayesian inference on logistic regression models, log-Gaussian Cox point process models, stochastic volatility models, and both parameter and model level inference of dynamical systems described by nonlinear differential equations

Bayesian approaches for modeling protein biophysics

textProteins are the fundamental unit of computation and signal processing in biological systems. A quantitative understanding of protein biophysics is of paramount importance, since even slight malfunction of proteins can lead to diverse and severe disease states. However, developing accurate and useful mechanistic models of protein function can be strikingly elusive. I demonstrate that the adoption of Bayesian statistical methods can greatly aid in modeling protein systems. I first discuss the pitfall of parameter non-identifiability and how a Bayesian approach to modeling can yield reliable and meaningful models of molecular systems. I then delve into a particular case of non-identifiability within the context of an emerging experimental technique called single molecule photobleaching. I show that the interpretation of this data is non-trivial and provide a rigorous inference model for the analysis of this pervasive experimental tool. Finally, I introduce the use of nonparametric Bayesian inference for the analysis of single molecule time series. These methods aim to circumvent problems of model selection and parameter identifiability and are demonstrated with diverse applications in single molecule biophysics. The adoption of sophisticated inference methods will lead to a more detailed understanding of biophysical systems.Neuroscienc