Statistics and Computing最新文献

We present a novel frailty model for modeling clustered survival data. In particular, we consider the Birnbaum–Saunders (BS) distribution for the frailty terms with a new directly parameterized on the variance of the frailty distribution. This allows, among other things, compare the estimated frailty terms among traditional models, such as the gamma frailty model. Some mathematical properties of the new model are studied including the conditional distribution of frailties among the survivors, the frailty of individuals dying at time t, and the Kendall’s (tau ) measure. Furthermore, an explicit form to the derivatives of the Laplace transform for the BS distribution using the di Bruno’s formula is found. Parametric, non-parametric and semiparametric versions of the BS frailty model are studied. We use a simple Expectation-Maximization (EM) algorithm to estimate the model parameters and evaluate its performance under different censoring proportion by a Monte Carlo simulation study. We also show that the BS frailty model is competitive over the gamma and weighted Lindley frailty models under misspecification. We illustrate our methodology by using a real data sets.

The Adaptive Ridge Algorithm is an iterative algorithm designed for variable selection. It is also known under the denomination of Iteratively Reweighted Least-Squares Algorithm in the communities of Compressed Sensing and Sparse Signals Recovery. Besides, it can also be interpreted as an optimization algorithm dedicated to the minimization of possibly nonconvex (ell ^q) penalized energies (with (0<q<2)). In the literature, this algorithm can be derived using various mathematical approaches, namely Half Quadratic Minimization, Majorization-Minimization, Alternating Minimization or Local Approximations. In this work, we will show how the Adaptive Ridge Algorithm can be simply derived and analyzed from a single equation, corresponding to a variational reformulation of the (ell ^q) penalty. We will describe in detail how the Adaptive Ridge Algorithm can be numerically implemented and we will perform a thorough experimental study of its parameters. We will also show how the variational formulation of the (ell ^q) penalty combined with modern duality principles can be used to design an interesting variant of the Adaptive Ridge Algorithm dedicated to the minimization of quadratic functions over (nonconvex) (ell ^q) balls.

Cure rate models have been thoroughly investigated across various domains, encompassing medicine, reliability, and finance. The merging of machine learning (ML) with cure models is emerging as a promising strategy to improve predictive accuracy and gain profound insights into the underlying mechanisms influencing the probability of cure. The current body of literature has explored the benefits of incorporating a single ML algorithm with cure models. However, there is a notable absence of a comprehensive study that compares the performances of various ML algorithms in this context. This paper seeks to address and bridge this gap. Specifically, we focus on the well-known mixture cure model and examine the incorporation of five distinct ML algorithms: extreme gradient boosting, neural networks, support vector machines, random forests, and decision trees. To bolster the robustness of our comparison, we also include cure models with logistic and spline-based regression. For parameter estimation, we formulate an expectation maximization algorithm. A comprehensive simulation study is conducted across diverse scenarios to compare various models based on the accuracy and precision of estimates for different quantities of interest, along with the predictive accuracy of cure. The results derived from both the simulation study, as well as the analysis of real cutaneous melanoma data, indicate that the incorporation of ML models into cure model provides a beneficial contribution to the ongoing endeavors aimed at improving the accuracy of cure rate estimation.

This work is concerned with the use of Gaussian surrogate models for Bayesian inverse problems associated with linear partial differential equations. A particular focus is on the regime where only a small amount of training data is available. In this regime the type of Gaussian prior used is of critical importance with respect to how well the surrogate model will perform in terms of Bayesian inversion. We extend the framework of Raissi et. al. (2017) to construct PDE-informed Gaussian priors that we then use to construct different approximate posteriors. A number of different numerical experiments illustrate the superiority of the PDE-informed Gaussian priors over more traditional priors.

The widespread use of maximum Jeffreys’-prior penalized likelihood in binomial-response generalized linear models, and in logistic regression, in particular, are supported by the results of Kosmidis and Firth (Biometrika 108:71–82, 2021. https://doi.org/10.1093/biomet/asaa052), who show that the resulting estimates are always finite-valued, even in cases where the maximum likelihood estimates are not, which is a practical issue regardless of the size of the data set. In logistic regression, the implied adjusted score equations are formally bias-reducing in asymptotic frameworks with a fixed number of parameters and appear to deliver a substantial reduction in the persistent bias of the maximum likelihood estimator in high-dimensional settings where the number of parameters grows asymptotically as a proportion of the number of observations. In this work, we develop and present two new variants of iteratively reweighted least squares for estimating generalized linear models with adjusted score equations for mean bias reduction and maximization of the likelihood penalized by a positive power of the Jeffreys-prior penalty, which eliminate the requirement of storing O(n) quantities in memory, and can operate with data sets that exceed computer memory or even hard drive capacity. We achieve that through incremental QR decompositions, which enable IWLS iterations to have access only to data chunks of predetermined size. Both procedures can also be readily adapted to fit generalized linear models when distinct parts of the data is stored across different sites and, due to privacy concerns, cannot be fully transferred across sites. We assess the procedures through a real-data application with millions of observations.

We develop a comprehensive methodological workflow for Bayesian modelling of high-dimensional spatial extremes that lets us describe both weakening extremal dependence at increasing levels and changes in the type of extremal dependence class as a function of the distance between locations. This is achieved with a latent Gaussian version of the spatial conditional extremes model that allows for computationally efficient inference with R-INLA. Inference is made more robust using a post hoc adjustment method that accounts for possible model misspecification. This added robustness makes it possible to extract more information from the available data during inference using a composite likelihood. The developed methodology is applied to the modelling of extreme hourly precipitation from high-resolution radar data in Norway. Inference is performed quickly, and the resulting model fit successfully captures the main trends in the extremal dependence structure of the data. The post hoc adjustment is found to further improve model performance.

Model-based unsupervised learning, as any learning task, stalls as soon as missing data occurs. This is even more true when the missing data are informative, or said missing not at random (MNAR). In this paper, we propose model-based clustering algorithms designed to handle very general types of missing data, including MNAR data. To do so, we introduce a mixture model for different types of data (continuous, count, categorical and mixed) to jointly model the data distribution and the MNAR mechanism, remaining vigilant to the relative degrees of freedom of each. Several MNAR models are discussed, for which the cause of the missingness can depend on both the values of the missing variable themselves and on the class membership. However, we focus on a specific MNAR model, called MNARz, for which the missingness only depends on the class membership. We first underline its ease of estimation, by showing that the statistical inference can be carried out on the data matrix concatenated with the missing mask considering finally a standard MAR mechanism. Consequently, we propose to perform clustering using the Expectation Maximization algorithm, specially developed for this simplified reinterpretation. Finally, we assess the numerical performances of the proposed methods on synthetic data and on the real medical registry TraumaBase as well.

In this paper, we provide a unified approach to simulate diffusion bridges. The proposed method covers a wide range of processes including univariate and multivariate diffusions, and the diffusions can be either time-homogeneous or time-inhomogeneous. We provide a theoretical framework for the proposed method. In particular, using the parametrix representations we show that the approximated probability transition density function converges to that of the true diffusion, which in turn implies the convergence of the approximation. Unlike most of the methods proposed in the literature, our approach does not involve acceptance-rejection mechanics. That is, it is acceptance-rejection free. Extensive numerical examples are provided for illustration and demonstrate the accuracy of the proposed method.