Stable distribution is one of the attractive models that well describes fat-tail behaviors and scaling phenomena in various scientific fields. The approach based upon the method of moments yields a simple procedure for estimating stable law parameters with the requirement of using momental points for the characteristic function, but the selection of points is only poorly explained and has not been elaborated. We propose a new characteristic function-based approach by introducing a technique of selecting plausible points, which could bring the method of moments available for practical use. Our method outperforms other state-of-art methods that exhibit a closed-form expression of all four parameters of stable laws. Finally, the applicability of the method is illustrated by using several data of financial assets. Numerical results reveal that our approach is advantageous when modeling empirical data with stable distributions.
Network models are applied across many domains where data can be represented as a network. Two prominent paradigms for modeling networks are statistical models (probabilistic models for the observed network) and mechanistic models (models for network growth and/or evolution). Mechanistic models are better suited for incorporating domain knowledge, to study effects of interventions (such as changes to specific mechanisms) and to forward simulate, but they typically have intractable likelihoods. As such, and in a stark contrast to statistical models, there is a relative dearth of research on mod…
Cox proportional hazards model is one of the most popular models in biomedical data analysis. There have been continuing efforts to improve the flexibility of such models for complex signal detection, for example, via additive functions. Nevertheless, the task to extend Cox additive models to accommodate high-dimensional data is nontrivial. When estimating additive functions, commonly used group sparse regularization may introduce excess smoothing shrinkage on additive functions, damaging predictive performance. Moreover, an "all-in-all-out" approach makes functional selection challenging to a…
Prior work has shown that combining bootstrap imputation with tree-based machine learning variable selection methods can provide good performances achievable on fully observed data when covariate and outcome data are missing at random (MAR). This approach however is computationally expensive, especially on large-scale datasets. We propose an inference-based method, called RR-BART, which leverages the likelihood-based Bayesian machine learning technique, Bayesian additive regression trees, and uses Rubin's rule to combine the estimates and variances of the variable importance measures on multip…
The regularization approach for variable selection was well developed for a completely observed data set in the past two decades. In the presence of missing values, this approach needs to be tailored to different missing data mechanisms. In this paper, we focus on a flexible and generally applicable missing data mechanism, which contains both ignorable and nonignorable missing data mechanism assumptions. We show how the regularization approach for variable selection can be adapted to the situation under this missing data mechanism. The computational and theoretical properties for variable sele…
A mixture of joint generalized hyperbolic distributions (MJGHD) is introduced for asymmetric clustering for high-dimensional data. The MJGHD approach takes into account the cluster-specific subspace, thereby limiting the number of parameters to estimate while also facilitating visualization of results. Identifiability is discussed, and a multi-cycle ECM algorithm is outlined for parameter estimation. The MJGHD approach is illustrated on two real data sets, where the Bayesian information criterion is used for model selection.
PliableBVS: A flexible Bayesian variable selection method for modeling interactions with mandatory modifying variables
University of Oslo（奥斯陆大学）；Oslo University Hospital Rikshospitalet（奥斯陆大学医院里克斯霍斯皮塔勒分院）；Institute of Clinical Medicine, Faculty of Medicine, University of Oslo（奥斯陆大学医学院临床医学科）
Network models are applied in numerous domains where data can be represented as a system of interactions among pairs of actors. While both statistical and mechanistic network models are increasingly capable of capturing various dependencies amongst these actors, these dependencies imply the lack of independence. This poses statistical challenges for analyzing such data, especially when there is only a single observed network, and often leads to intractable likelihoods regardless of the modeling paradigm, which limit the application of existing statistical methods for networks. We explore a sub…
University of Oslo（奥斯陆大学）；Norwegian Computing Center（挪威计算中心）；Medical University of Vienna（维也纳医科大学）
Regression models are used in a wide range of applications providing a powerful scientific tool for researchers from different fields. Linear, or simple parametric, models are often not sufficient to describe complex relationships between input variables and a response. Such relationships can be better described through flexible approaches such as neural networks, but this results in less interpretable models and potential overfitting. Alternatively, specific parametric nonlinear functions can be used, but the specification of such functions is in general complicated. In this paper, we introdu…
Clinical research often focuses on complex traits in which many variables play a role in mechanisms driving, or curing, diseases. Clinical prediction is hard when data is high-dimensional, but additional information, like domain knowledge and previously published studies, may be helpful to improve predictions. Such complementary data, or co-data, provide information on the covariates, such as genomic location or p-values from external studies. Our method enables exploiting multiple and various co-data sources to improve predictions. We use discrete or continuous co-data to define possibly over…
