Bayesian Model Selection for Beta Autoregressive Processes

We deal with Bayesian inference for Beta autoregressive processes. We restrict our attention to the class of conditionally linear processes. These processes are particularly suitable for forecasting purposes, but are difficult to estimate due to the constraints on the parameter space. We provide a full Bayesian approach to the estimation and include the parameter restrictions in the inference problem by a suitable specification of the prior distributions. Moreover in a Bayesian framework parameter estimation and model choice can be solved simultaneously. In particular we suggest a Markov-Chain Monte Carlo (MCMC) procedure based on a Metropolis-Hastings within Gibbs algorithm and solve the model selection problem following a reversible jump MCMC approach

Loss-based prior for tree topologies in BART models

We present a novel prior for tree topology within Bayesian Additive Regression Trees (BART) models. This approach quantifies the hypothetical loss in information and the loss due to complexity associated with choosing the wrong tree structure. The resulting prior distribution is compellingly geared toward sparsity, a critical feature considering BART models' tendency to overfit. Our method incorporates prior knowledge into the distribution via two parameters that govern the tree's depth and balance between its left and right branches. Additionally, we propose a default calibration for these parameters, offering an objective version of the prior. We demonstrate our method's efficacy on both simulated and real datasets

Survival Regression Models With Dependent Bayesian Nonparametric Priors

We present a novel Bayesian nonparametric model for regression in survival analysis. Our model builds on the classical neutral to the right model of Doksum and on the Cox proportional hazards model of Kim and Lee. The use of a vector of dependent Bayesian nonparametric priors allows us to efficiently model the hazard as a function of covariates while allowing nonproportionality. The model can be seen as having competing latent risks. We characterize the posterior of the underlying dependent vector of completely random measures and study the asymptotic behavior of the model. We show how an MCMC scheme can provide Bayesian inference for posterior means and credible intervals. The method is illustrated using simulated and real data. Supplementary materials for this article are available online

Compound random measures and their use in Bayesian non‐parametrics

A new class of dependent random measures which we call compound random measures is proposed and the use of normalized versions of these random measures as priors in Bayesian non‐parametric mixture models is considered. Their tractability allows the properties of both compound random measures and normalized compound random measures to be derived. In particular, we show how compound random measures can be constructed with gamma, σ‐stable and generalized gamma process marginals. We also derive several forms of the Laplace exponent and characterize dependence through both the Lévy copula and the correlation function. An augmented Pólya urn scheme sampler and a slice sampler are described for posterior inference when a normalized compound random measure is used as the mixing measure in a non‐parametric mixture model and a data example is discussed

Modelling and Computation Using NCoRM Mixtures for Density Regression

Normalized compound random measures are flexible nonparametric priors for related distributions. We consider building general nonparametric regression models using normalized compound random measure mixture models. Posterior inference is made using a novel pseudo-marginal Metropolis-Hastings sampler for normalized compound random measure mixture models. The algorithm makes use of a new general approach to the unbiased estimation of Laplace functionals of compound random measures (which includes completely random measures as a special case). The approach is illustrated on problems of density regression

Geochemical and micro-textural fingerprints of boiling in pyrite

The chemical composition, textures and mineral associations of pyrite provide key information that help elucidate the evolution of hydrothermal systems. However, linking the compositional and micro-textural features of pyrite with a specific physico-chemical process, e.g., boiling versus non-boiling, remains elusive and challenging. In this study we examine pyrite geochemical and micro-textural features and relate these results to pyrite-forming processes at the active Cerro Pabellón Geothermal System (CPGS) in the Altiplano of the northern Chile. We integrate electron microprobe analysis (EMPA) and laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS) data with micro-textural observations of pyrite and associated gangue minerals recovered from a ∼500 m long drill core that crosscuts the argillic, sub-propylitic and propylitic alteration zones of the CPGS. Additionally, we carried out a Principal Component Analysis (PCA) in order to inspect and understand the main data structure of the pyrite geochemical dataset. The concentrations of precious metals (Au and Ag), metalloids (As, Sb, Se, Bi and Tl), and base and heavy metals (Cu, Co, Ni and Pb) in pyrite from the CPGS are significant. Among the elements analyzed, As, Cu and Pb are the most abundant with concentrations that vary from a few parts per million (ppm) to wt% levels (up to 4.4 wt% of As, 0.5 wt% of Cu and 0.2 wt% of Pb). Based on contemporaneous gangue mineral associations and textures, the mechanisms of pyrite precipitation in the CPGS were inferred. Pyrite formed during vigorous boiling is characterized by relatively high concentrations of As, Cu, Pb, Ag and Au and lower concentrations of Co and Ni compared to pyrite formed under different conditions. These anhedral to euhedral pyrite grains display zones with a porous texture and abundant mineral micro- to nano-inclusions (mainly galena and chalcopyrite) indicating a formation by rapid crystallization. In contrast, pyrite formed under gentle boiling (more gradual cooling and less abrupt physico-chemical variations than in vigorous boiling) to non-boiling conditions is characterized by a higher concentration of Co and Ni, and relatively low concentrations of As, Cu, Pb, Ag and Au. Texturally, these pyrites form aggregates of euhedral and pristine pyrite crystals with scarce pores and mineral inclusions suggesting formation under steadier physico-chemical conditions. Our results show that pyrite can not only record the chemical evolution of hydrothermal fluids, but can also provide critical information related to physico-chemical process such as boiling and phase separation. Since boiling of aqueous fluids is a common phenomenon occurring in a variety of pyrite-forming environments, e.g., active continental and seafloor hydrothermal systems, and porphyry Cu-epithermal Au-Ag deposits, pyrite compositional and textural features are a valuable complement for discriminating and tracking boiling events in modern and fossil hydrothermal systems

Application of LANDSAT data and digital image processing

There are no author-identified significant results in this report

Interacting Multiple Try Algorithms with Different Proposal Distributions

We propose a new class of interacting Markov chain Monte Carlo (MCMC) algorithms designed for increasing the efficiency of a modified multiple-try Metropolis (MTM) algorithm. The extension with respect to the existing MCMC literature is twofold. The sampler proposed extends the basic MTM algorithm by allowing different proposal distributions in the multiple-try generation step. We exploit the structure of the MTM algorithm with different proposal distributions to naturally introduce an interacting MTM mechanism (IMTM) that expands the class of population Monte Carlo methods. We show the validity of the algorithm and discuss the choice of the selection weights and of the different proposals. We provide numerical studies which show that the new algorithm can perform better than the basic MTM algorithm and that the interaction mechanism allows the IMTM to efficiently explore the state space