7,154 research outputs found
Dynamic degree-corrected blockmodels for social networks: A nonparametric approach
A nonparametric approach to the modelling of social networks using degree-corrected stochastic blockmodels is proposed. The model for static network consists of a stochastic blockmodel using a probit regression formulation, and popularity parameters are incorporated to account for degree heterogeneity. We specify a Dirichlet process prior to detect community structure as well as to induce clustering in the popularity parameters. This approach is flexible yet parsimonious as it allows the appropriate number of communities and popularity clusters to be determined automatically by the data. We further discuss and implement extensions of the static model to dynamic networks. In a Bayesian framework, we perform posterior inference through MCMC algorithms. The models are illustrated using several real-world benchmark social networks
Is infinity that far? A Bayesian nonparametric perspective of finite mixture models
Mixture models are one of the most widely used statistical tools when dealing with data from heterogeneous populations. Following a Bayesian nonparametric perspective, we introduce a new class of priors: the Normalized Independent Point Process. We investigate the probabilistic properties of this new class and present many special cases. In particular, we provide an explicit formula for the distribution of the implied partition, as well as the posterior characterization of the new process in terms of the superposition of two discrete measures. We also provide consistency results. Moreover, we design both a marginal and a conditional algorithm for finite mixture models with a random number of components. These schemes are based on an auxiliary variable MCMC, which allows handling the otherwise intractable posterior distribution and overcomes the challenges associated with the Reversible Jump algorithm. We illustrate the performance and the potential of our model in a simulation study and on real data applications
Bayesian splines versus fractional polynomials in network meta-analysis
BACKGROUND: Network meta-analysis (NMA) provides a powerful tool for the simultaneous evaluation of multiple treatments by combining evidence from different studies, allowing for direct and indirect comparisons between treatments. In recent years, NMA is becoming increasingly popular in the medical literature and underlying statistical methodologies are evolving both in the frequentist and Bayesian framework. Traditional NMA models are often based on the comparison of two treatment arms per study. These individual studies may measure outcomes at multiple time points that are not necessarily homogeneous across studies. METHODS: In this article we present a Bayesian model based on B-splines for the simultaneous analysis of outcomes across time points, that allows for indirect comparison of treatments across different longitudinal studies. RESULTS: We illustrate the proposed approach in simulations as well as on real data examples available in the literature and compare it with a model based on P-splines and one based on fractional polynomials, showing that our approach is flexible and overcomes the limitations of the latter. CONCLUSIONS: The proposed approach is computationally efficient and able to accommodate a large class of temporal treatment effect patterns, allowing for direct and indirect comparisons of widely varying shapes of longitudinal profiles
Integrating dynamic mixed-effect modelling and penalized regression to explore genetic association with pharmacokinetics
In a previous work, we have shown that penalized regression approaches can allow many genetic variants to be incorporated into sophisticated pharmacokinetic (PK) models in a way that is both computationally and statistically efficient. The phenotypes were the individual model parameter estimates, obtained a posteriori of the model fit and known to be sensitive to the study design
Bayesian estimation of the number of protonation sites for urinary metabolites from NMR spectroscopic data
INTRODUCTION: To aid the development of better algorithms for 11 H NMR data analysis, such as alignment or peak-fitting, it is important to characterise and model chemical shift changes caused by variation in pH. The number of protonation sites, a key parameter in the theoretical relationship between pH and chemical shift, is traditionally estimated from the molecular structure, which is often unknown in untargeted metabolomics applications.
OBJECTIVE: We aim to use observed NMR chemical shift titration data to estimate the number of protonation sites for a range of urinary metabolites.
METHODS: A pool of urine from healthy subjects was titrated in the range pH 2–12, standard 11 H NMR spectra were acquired and positions of 51 peaks (corresponding to 32 identified metabolites) were recorded. A theoretical model of chemical shift was fit to the data using a Bayesian statistical framework, using model selection procedures in a Markov Chain Monte Carlo algorithm to estimate the number of protonation sites for each molecule.
RESULTS: The estimated number of protonation sites was found to be correct for 41 out of 51 peaks. In some cases, the number of sites was incorrectly estimated, due to very close pKa values or a limited amount of data in the required pH range.
CONCLUSIONS: Given appropriate data, it is possible to estimate the number of protonation sites for many metabolites typically observed in 11 H NMR metabolomics without knowledge of the molecular structure. This approach may be a valuable resource for the development of future automated metabolite alignment, annotation and peak fitting algorithms
On the Possibility of Measuring the Gravitomagnetic Clock Effect in an Earth Space-Based Experiment
In this paper the effect of the post-Newtonian gravitomagnetic force on the
mean longitudes of a pair of counter-rotating Earth artificial satellites
following almost identical circular equatorial orbits is investigated. The
possibility of measuring it is examined. The observable is the difference of
the times required to in passing from 0 to 2 for both senses of
motion. Such gravitomagnetic time shift, which is independent of the orbital
parameters of the satellites, amounts to 5 s for Earth; it is
cumulative and should be measured after a sufficiently high number of
revolutions. The major limiting factors are the unavoidable imperfect
cancellation of the Keplerian periods, which yields a constraint of 10
cm in knowing the difference between the semimajor axes of the satellites,
and the difference of the inclinations of the orbital planes which, for
, should be less than . A pair of spacecrafts
endowed with a sophisticated intersatellite tracking apparatus and drag-free
control down to 10 cm s Hz level might allow to meet
the stringent requirements posed by such a mission.Comment: LaTex2e, 22 pages, no tables, 1 figure, 38 references. Final version
accepted for publication in Classical and Quantum Gravit
Bayesian Autoregressive Frailty Models for Inference in Recurrent Events
We propose autoregressive Bayesian semi-parametric models for gap times between recurrent events. The aim is two-fold: inference on the effect of possibly time-varying covariates on the gap times and clustering of individuals based on the time trajectory of the recurrent event. Time-dependency between gap times is taken into account through the specification of an autoregressive component for the frailty parameters influencing the response at different times. The order of the autoregression may be assumed unknown and is an object of inference. We consider two alternative approaches to perform model selection under this scenario. Covariates may be easily included in the regression framework and censoring and missing data are easily accounted for. As the proposed methodologies lie within the class of Dirichlet process mixtures, posterior inference can be performed through efficient MCMC algorithms. We illustrate the approach through simulations and medical applications involving recurrent hospitalizations of cancer patients and successive urinary tract infections
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