There has been growing interest on forecasting mortality. In this article, we propose a novel dynamic Bayesian approach for modeling and forecasting the age-at-death distribution, focusing on a three-components mixture of a Dirac mass, a Gaussian distribution and a Skew-Normal distribution. According to the specified model, the age-at-death distribution is characterized via seven parameters corresponding to the main aspects of infant, adult and old-age mortality. The proposed approach focuses on coherent modeling of multiple countries, and following a Bayesian approach to inference we allow to borrow information across populations and to shrink parameters towards a common mean level, implicitly penalizing diverging scenarios. Dynamic modeling across years is induced trough an hierarchical dynamic prior distribution that allows to characterize the temporal evolution of each mortality component and to forecast the age-at-death distribution. Empirical results on multiple countries indicate that the proposed approach outperforms popular methods for forecasting mortality, providing interpretable insights on the evolution of mortality.
Because of its mathematical tractability, the Gaussian mixture model holds a special place in the literature for clustering and classification. For all its benefits, however, the Gaussian mixture model poses problems when the data is skewed or contains outliers. Because of this, methods have been developed over the years for handling skewed data, and fall into two general categories. The first is to consider a mixture of more flexible skewed distributions, and the second is based on incorporating a transformation to near normality. Although these methods have been compared in their respective …
This paper presents a novel approach for modeling mortality rates above age 70 by proposing a mixture-based model. This model is compared to four other widely used models: the Beard, Gompertz, Makeham, and Perks models. Our model can capture the complex behavior of mortality rates at all ages, providing a more accurate representation of the data. To evaluate the performance of our model, we applied it to two countries with different data quality: Japan and Brazil. Our results show that the proposed model outperforms the other models in both countries, particularly in Japan where it obtained an…
In recent years, data have become increasingly higher dimensional and, therefore, an increased need has arisen for dimension reduction techniques for clustering. Although such techniques are firmly established in the literature for multivariate data, there is a relative paucity in the area of matrix variate, or three-way, data. Furthermore, the few methods that are available all assume matrix variate normality, which is not always sensible if cluster skewness or excess kurtosis is present. Mixtures of bilinear factor analyzers using skewed matrix variate distributions are proposed. In all, fou…
Non-Gaussian mixture models are gaining increasing attention for mixture model-based clustering particularly when dealing with data that exhibit features such as skewness and heavy tails. Here, such a mixture distribution is presented, based on the multivariate normal inverse Gaussian (MNIG) distribution. For parameter estimation of the mixture, a Bayesian approach via Gibbs sampler is used; for this, a novel approach to simulate univariate generalized inverse Gaussian random variables and matrix generalized inverse Gaussian random matrices is provided. The proposed algorithm will be applied t…
Mixtures of multivariate normal inverse Gaussian (MNIG) distributions can be used to cluster data that exhibit features such as skewness and heavy tails. However, for cluster analysis, using a traditional finite mixture model framework, either the number of components needs to be known $a$-$priori$ or needs to be estimated $a$-$posteriori$ using some model selection criterion after deriving results for a range of possible number of components. However, different model selection criteria can sometimes result in different number of components yielding uncertainty. Here, an infinite mixture model…
Most Item Response Theory (IRT) models for dichotomous responses are based on probit or logit link functions which assume a symmetric relationship between the probability of a correct response and the latent traits of individuals submitted to a test. This assumption restricts the use of those models to the case in which all items have a symmetric behaviour. On the other hand, asymmetric models proposed in the literature impose that all the items in a test have an asymmetric behaviour. This assumption is inappropriate for great part of the tests which are, in general, composed by both symmetric…
Cluster-weighted models (CWMs) extend finite mixtures of regressions (FMRs) in order to allow the distribution of covariates to contribute to the clustering process. In a matrix-variate framework, the matrix-variate normal CWM has been recently introduced. However, problems may be encountered when data exhibit skewness or other deviations from normality in the responses, covariates or both. Thus, we introduce a family of 24 matrix-variate CWMs which are obtained by allowing both the responses and covariates to be modelled by using one of four existing skewed matrix-variate distributions or the…
Tracking and estimating Daily Fine Particulate Matter (PM2.5) is very important as it has been shown that PM2.5 is directly related to mortality related to lungs, cardiovascular system, and stroke. That is, high values of PM2.5 constitute a public health problem in the US, and it is important that we precisely estimate PM2.5 to aid in public policy decisions. Thus, we propose a Bayesian hierarchical model for high-dimensional "multi-type" responses. By "multi-type" responses we mean a collection of correlated responses that have different distributional assumptions (e.g., continuous skewed obs…
Allocating patients to treatment arms during a trial based on the observed responses accumulated prior to the decision point, and sequential adaptation of this allocation,, could minimize the expected number of failures or maximize total benefit to patients. In this study, we developed a Bayesian response adaptive randomization (RAR) design targeting the endpoint of organ support-free days (OSFD) for patients admitted to the intensive care units (ICU). The OSFD is a mixture of mortality and morbidity assessed by the number of days of free of organ support within a predetermined time-window pos…
For a portfolio of life insurance policies observed for a stated period of time, e.g., one year, mortality is typically a rare event. When we examine the outcome of dying or not from such portfolios, we have an imbalanced binary response. The popular logistic and probit regression models can be inappropriate for imbalanced binary response as model estimates may be biased, and if not addressed properly, it can lead to serious adverse predictions. In this paper, we propose the use of skewed link regression models (Generalized Extreme Value, Weibull, and Frechet link models) as more superior mode…
Gamma shape mixtures for heavy-tailed distributions
卫生服务研究中的一个重要问题是估计超过给定阈值的医疗支出比例。通常情况下，医疗支出呈现高度偏斜的重尾分布，对于这种分布，（a）简单的变量变换不足以实现易于处理的低维参数形式，以及（b）非参数方法在估计大阈值的不确定性概率时效率不高。出于这种背景下，在本文中，我们提出了一个一般的贝叶斯方法估计的尾部概率的重尾分布，基于混合的Γ分布，其中的混合发生在形状参数。该族为重尾分布的建模提供了一种灵活而新颖的方法，它计算效率高，并且只需要为单个参数指定一个先验分布。通过模拟研究，我们比较我们的方法与常用的方法，如对数正态模型和非参数替代品。我们发现，与这些替代方案相比，混合伽马模型在估计尾部概率方面显着提高了预测性能。我们还将我们的方法应用于医疗当前受益调查（MCBS），我们估计超过吸烟归因疾病的给定住院费用的概率。我们已经在开源GSM软件包中实现了该方法，该软件包可从Comprehensive R Archive Network获得。
KTH Royal Institute of Technology（瑞典皇家理工学院）；RaySearch Laboratories（瑞镭实验室）；Silo AI（Silo AI（西洛人工智能公司））
We present a new nonparametric mixture-of-experts model for multivariate regression problems, inspired by the probabilistic k-nearest neighbors algorithm. Using a conditionally specified model, predictions for out-of-sample inputs are based on similarities to each observed data point, yielding predictive distributions represented by Gaussian mixtures. Posterior inference is performed on the parameters of the mixture components as well as the distance metric using a mean-field variational Bayes algorithm accompanied with a stochastic gradient-based optimization procedure. The proposed method is…
Mixture models are useful in a wide array of applications to identify subpopulations in noisy overlapping distributions. For example, in multiplexed immunofluorescence (mIF), cell image intensities represent expression levels and the cell populations are a noisy mixture of expressed and unexpressed cells. Among mixture models, the gamma mixture model has the strength of being flexible in fitting skewed strictly positive data that occur in many biological measurements. However, the current estimation method uses numerical optimization within the expectation maximization algorithm and is computa…
In many modern applications, there is interest in analyzing enormous data sets that cannot be easily moved across computers or loaded into memory on a single computer. In such settings, it is very common to be interested in clustering. Existing distributed clustering algorithms are mostly distance or density based without a likelihood specification, precluding the possibility of formal statistical inference. Model-based clustering allows statistical inference, yet research on distributed inference has emphasized nonparametric Bayesian mixture models over finite mixture models. To fill this gap…
Harvard University（哈佛大学）；Imperial College London（帝国理工学院）；MIT（麻省理工学院）
Sepsis is the leading cause of mortality in the ICU. It is challenging to manage because individual patients respond differently to treatment. Thus, tailoring treatment to the individual patient is essential for the best outcomes. In this paper, we take steps toward this goal by applying a mixture-of-experts framework to personalize sepsis treatment. The mixture model selectively alternates between neighbor-based (kernel) and deep reinforcement learning (DRL) experts depending on patient's current history. On a large retrospective cohort, this mixture-based approach outperforms physician, kern…
We develop a functional proportional hazards mixture cure (FPHMC) model with scalar and functional covariates measured at the baseline. The mixture cure model, useful in studying populations with a cure fraction of a particular event of interest is extended to functional data. We employ the EM algorithm and develop a semiparametric penalized spline-based approach to estimate the dynamic functional coefficients of the incidence and the latency part. The proposed method is computationally efficient and simultaneously incorporates smoothness in the estimated functional coefficients via roughness …
The distribution of single Stop Signal Reaction Times (SSRT) in the stop signal task (SST) as a measurement of the latency of the unobservable stopping process has been modeled with a nonparametric method by Hans Colonius (1990) and with a Bayesian parametric method by Eric-Jan Wagenmakers and colleagues (2012). These methods assume equal impact of the preceding trial type (go/stop) in the SST trials on the SSRT distributional estimation without addressing the case of the violated assumption. This study presents the required model by considering two-state mixture model for the SSRT distributio…
Addressing complex structures of measurement error arising in the exposure assessment in occupational epidemiology using a Bayesian hierarchical approach
Bayesian Profile Regression using Variational Inference to Identify Clusters of Multiple Long-Term Conditions Conditioning on Mortality in Population-Scale Data
Health Data Research UK, Swansea University Medical School, Swansea University（英国健康数据研究中心，斯旺西大学医学院，斯旺西大学）；Department of Statistics, University of Warwick（华威大学统计系）；Department of Pharmacology and Therapeutics, University of Liverpool（利物浦大学药理学与治疗学系）；Division of Cancer and Genetics, Cardiff University（卡迪夫大学癌症与遗传学部）
School of Management Engineering, Ulsan National Institute of Science and Technology (UNIST)（蔚山科学技术院管理工程学院）
In clinical research, the lack of events of interest often necessitates imbalanced learning. One approach to resolve this obstacle is data integration or sharing, but due to privacy concerns neither is practical. Therefore, there is an increasing demand for a platform on which an analysis can be performed in a federated environment while maintaining privacy. However, it is quite challenging to develop a federated learning algorithm that can address both privacy-preserving and class imbalanced issues. In this study, we introduce a federated generative model learning platform for generating samp…
Recent studies about cryptocurrency returns show that its distribution can be highly-peaked, skewed, and heavy-tailed, with a large excess kurtosis. To accommodate all these peculiarities, we propose the asymmetric Laplace scale mixture (ALSM) family of distributions. Each member of the family is obtained by dividing the scale parameter of the conditional asymmetric Laplace (AL) distribution by a convenient mixing random variable taking values on all or part of the positive real line and whose distribution depends on a parameter vector $\boldsymbolθ$ providing greater flexibility to the result…
