Bayesian Inference for partially observed SDEs Driven by Fractional Brownian Motion

We consider continuous-time diffusion models driven by fractional Brownian motion. Observations are assumed to possess a non-trivial likelihood given the latent path. Due to the non-Markovianity and high-dimensionality of the latent paths, estimating posterior expectations is a computationally challenging undertaking. We present a reparameterization framework based on the Davies and Harte method for sampling stationary Gaussian processes and use this framework to construct a Markov chain Monte Carlo algorithm that allows computationally efficient Bayesian inference. The Markov chain Monte Carlo algorithm is based on a version of hybrid Monte Carlo that delivers increased efficiency when applied on the high-dimensional latent variables arising in this context. We specify the methodology on a stochastic volatility model allowing for memory in the volatility increments through a fractional specification. The methodology is illustrated on simulated data and on the S&P500/VIX time series and is shown to be effective. Contrary to a long range dependence attribute of such models often assumed in the literature, with Hurst parameter larger than 1/2, the posterior distribution favours values smaller than 1/2, pointing towards medium range dependence

Likelihood-based inference for correlated diffusions

We address the problem of likelihood based inference for correlated diffusion processes using Markov chain Monte Carlo (MCMC) techniques. Such a task presents two interesting problems. First, the construction of the MCMC scheme should ensure that the correlation coefficients are updated subject to the positive definite constraints of the diffusion matrix. Second, a diffusion may only be observed at a finite set of points and the marginal likelihood for the parameters based on these observations is generally not available. We overcome the first issue by using the Cholesky factorisation on the diffusion matrix. To deal with the likelihood unavailability, we generalise the data augmentation framework of Roberts and Stramer (2001 Biometrika 88(3):603-621) to d-dimensional correlated diffusions including multivariate stochastic volatility models. Our methodology is illustrated through simulation based experiments and with daily EUR /USD, GBP/USD rates together with their implied volatilities

Generalised Bayesian Structural Equation Modelling

We propose a generalised framework for Bayesian Structural Equation Modelling (SEM) that can be applied to a variety of data types. The introduced framework focuses on the approximate zero approach, according to which parameters that would before set to zero (e.g. factor loadings) are now formulated to be approximate zero. It extends previously suggested models by \citeA{MA12} and can handle continuous, binary, and ordinal data. Moreover, we propose a novel model assessment paradigm aiming to address shortcomings of posterior predictive $p-$values, which provide the default metric of fit for Bayesian SEM. The introduced model assessment procedure monitors the out-of-sample predictive performance of the fitted model, and together with a list of guidelines we provide, one can investigate whether the hypothesised model is supported by the data. We incorporate scoring rules and cross-validation to supplement existing model assessment metrics for Bayesian SEM. We study the performance of the proposed methodology via simulations. The model for continuous and binary data is fitted to data on the `Big-5' personality scale and the Fagerstrom test for nicotine dependence respectively

Inference for stochastic volatility model using time change transformations

We address the problem of parameter estimation for diffusion driven stochastic volatility models through Markov chain Monte Carlo (MCMC). To avoid degeneracy issues we introduce an innovative reparametrisation defined through transformations that operate on the time scale of the diffusion. A novel MCMC scheme which overcomes the inherent difficulties of time change transformations is also presented. The algorithm is fast to implement and applies to models with stochastic volatility. The methodology is tested through simulation based experiments and illustrated on data consisting of US treasury bill rates.Imputation, Markov chain Monte Carlo, Stochastic volatility

Likelihood-based inference for correlated diffusions

We address the problem of likelihood based inference for correlated diffusion processes using Markov chain Monte Carlo (MCMC) techniques. Such a task presents two interesting problems. First, the construction of the MCMC scheme should ensure that the correlation coefficients are updated subject to the positive definite constraints of the diffusion matrix. Second, a diffusion may only be observed at a finite set of points and the marginal likelihood for the parameters based on these observations is generally not available. We overcome the first issue by using the Cholesky factorisation on the diffusion matrix. To deal with the likelihood unavailability, we generalise the data augmentation framework of Roberts and Stramer (2001 Biometrika 88(3):603-621) to d-dimensional correlated diffusions including multivariate stochastic volatility models. Our methodology is illustrated through simulation based experiments and with daily EUR /USD, GBP/USD rates together with their implied volatilities.Markov chain Monte Carlo, Multivariate stochastic volatility, Multivariate CIR model, Cholesky Factorisation

Role of intestinal microbiome in the pathogenesis of age-related macular degeneration

Background: The microbiome is strongly linked to many extra-intestinal disorders. Gut commensal microbiota, in particular, plays an active role in human immune and intestinal homeostasis. Complex interactions of the microbiota with host genetics and other underlying factors lead to intestinal dysbiosis, which is thought to be linked to ocular inflammatory diseases. Thus, the aim of this review is to analyze the role of intestinal microbiome in age-related macular degeneration (AMD). Methods: A thorough literature search was performed using PubMed/MEDLINE, limited to English language publications, from January 2004 to March 2020. An additional search was made employing Google Scholar to complete the collected data as per the above-mentioned time-line and language limitations. The main keywords used included age-related macular degeneration, microbiome, dysbiosis, autoimmunity, gut microbiota, epigenetics, immune-mediated inflammatory diseases, and gut-retina axis. Results: Recent studies have proposed the role of intestinal microbiota in the pathogenesis of AMD. Changes in the microbiome have been shown to trigger several ocular inflammatory processes. There is increasing evidence demonstrating that intestinal microbial imbalance may play an important role in the pathogenesis of AMD. Conclusions: This review summarizes how alterations in the intestinal microbiota can be associated with the pathogenesis of AMD and how new therapeutic modalities can be designed to target this microbiome to limit the severe nature of this disease. Future advances in microbiome research may unveil a new era in understanding and managing AMD

A modeling framework for the analysis of the SARS-CoV2 transmission dynamics

Despite the progress in medical data collection the actual burden of SARS-CoV-2 remains unknown due to under-ascertainment of cases. This was apparent in the acute phase of the pandemic and the use of reported deaths has been pointed out as a more reliable source of information, likely less prone to under-reporting. Since daily deaths occur from past infections weighted by their probability of death, one may infer the total number of infections accounting for their age distribution, using the data on reported deaths. We adopt this framework and assume that the dynamics generating the total number of infections can be described by a continuous time transmission model expressed through a system of nonlinear ordinary differential equations where the transmission rate is modeled as a diffusion process allowing to reveal both the effect of control strategies and the changes in individuals behavior. We develop this flexible Bayesian tool in Stan and study 3 pairs of European countries, estimating the time-varying reproduction number (Rt) as well as the true cumulative number of infected individuals. As we estimate the true number of infections we offer a more accurate estimate of Rt. We also provide an estimate of the daily reporting ratio and discuss the effects of changes in mobility and testing on the inferred quantities

Inference for stochastic volatility models using time change transformations

We address the problem of parameter estimation for diffusion driven stochastic volatility models through Markov chain Monte Carlo (MCMC). To avoid degeneracy issues we introduce an innovative reparametrisation defined through transformations that operate on the time scale of the diffusion. A novel MCMC scheme which overcomes the inherent difficulties of time change transformations is also presented. The algorithm is fast to implement and applies to models with stochastic volatility. The methodology is tested through simulation based experiments and illustrated on data consisting of US treasury bill rates

The Effect of Cone-Beam Computed Tomography (CBCT) Evaluation on Treatment Planning after Endodontic Instrument Fracture

Intracanal instrument fracture is a procedural iatrogenic event during endodontic treatment that may affect treatment planning and eventually treatment outcome. Cone Beam Computed Tomography (CBCT) has offered several advantages, especially in endodontic cases in which information from conventional periapical radiograph may not be adequate to allow a precise treatment planning decision and a subsequent appropriate management of the cases. The present study was firstly conducted to assess the effect of CBCT evaluation on the decision-making process after instrument fracture; secondly, to introduce a new clinical approach in cases with fractured instruments located in the mesial roots of mandibular and maxillary molars. The study design was observational. The sample comprised all cases of mandibular and maxillary molars where an instrument fracture had occurred in the mesial roots. Two qualified (National and Kapodistrian University of Athens, Greece) and experienced (more than fifteen years of daily practicing) endodontists evaluated all the cases. The initial treatment plan made by evaluating periapical radiographs of each case was compared to the final plan set after CBCT evaluation. A marginal homogeneity test for paired data was conducted to test the concordance of treatment planning with periapical radiographs versus CBCT. Multivariable logistic regression was structured to identify predictors of modification in treatment planning following CBCT assessment, and to record estimators for decision to remove, bypass or retain the fragment. The level of statistical significance was pre-specified at p < 0.05. Of a total 52 cases evaluated, change in treatment planning with conventional periapical radiograph as a reference, following evaluation of CBCT, was observed in more than half of the teeth. The difference was statistically significant (p < 0.001). Apical location of the fragment was more likely to induce a perceived change in treatment planning after CBCT evaluation (p < 0.01). Canal merging induced 95% lower odds (p = 0.01) for taking a decision to remove or bypass, revealing that retaining the fragment was by far a more likely decision. A significant impact of CBCT preoperative evaluation on treatment planning for the management of such cases was demonstrated. Apical location of the fragment and canal merging seem to influence the decision-making process. Keywords: cone-beam computed tomography; decision making; instrument fracture; treatment plannin