We exploit Gaussian copulas to specify a class of multivariate circular distributions and obtain parametric models for the analysis of correlated circular data. This approach provides a straightforward extension of traditional multivariate normal models to the circular setting, without imposing restrictions on the marginal data distribution nor requiring overwhelming routines for parameter estimation. The proposal is illustrated on two case studies of animal orientation and sea currents, where we propose an autoregressive model for circular time series and a geostatistical model for circular spatial series.
TSCoNet: A Two-Stage Copula CNN-LSTM for Uncertainty-Aware Spatio-Temporal Forecasting
Department of Mathematical Sciences, Ball State University（数学科学系，巴尔的摩州立大学）；Statistics Discipline, Division of Science and Mathematics, University of Minnesota-Morris（统计学学科，明尼苏达-莫里斯大学）
In this work, we show that under specific choices of the copula, the lasso, elastic net, and $g$-prior are particular cases of `copula prior,' for regularization and variable selection method. We present `lasso with Gauss copula prior' and `lasso with t-copula prior.' The simulation study and real-world data for regression, classification, and large time-series data show that the `copula prior' often outperforms the lasso and elastic net while having a comparable sparsity of representation. Also, the copula prior encourages a grouping effect. The strongly correlated predictors tend to be in or…
The current literature in probabilistic forecasting is focused on quantifying the uncertainty of each random variable individually. This leads to the failure in informing about interdependence structure of uncertainty at different locations and/or different lead times. When there is a positive or negative association between a number of random variables, the prediction regions for them should be reflected by multivariate or joint uncertainty sets. The existing literature is very primitive in the area of multivariate uncertainty sets modeling. In this paper, uncertainty regions are generated in…
Semiparametric Copula Estimation for Spatially Correlated Multivariate Mixed Outcomes: Analyzing Visual Sightings of Fin Whales from a Line Transect Survey
Tokyo University of Science（东京理科大学）；Meisei University（明海大学）；Keio University（庆应义塾大学）；Institute of Marine Research（海洋研究所）；RIKEN Center for Brain Science（理化学研究所脑科学中心）
There are many research papers yielding the financial data models, where returns are tied either to the fundamental analysis or to the individual, often irrational, behaviour of investors. In the second case the bubble followed by the crisis is possible on the market. Such bubble or crisis is reflected by the cross-correlated extreme positive or negative returns of many assets. Such returns are modelled by the copula with the meaningful tail dependencies. The typical model of such cross-correlation provides the t-Student copula. The author demonstrates that the mutual information tied to this …
Joint modelling of longitudinal and time-to-event data is usually described by a joint model which uses shared or correlated latent effects to capture associations between the two processes. Under this framework, the joint distribution of the two processes can be derived straightforwardly by assuming conditional independence given the random effects. Alternative approaches to induce interdependency into sub-models have also been considered in the literature and one such approach is using copulas to introduce non-linear correlation between the marginal distributions of the longitudinal and time…
Multi-type recurrent events are often encountered in medical applications when two or more different event types could repeatedly occur over an observation period. For example, patients may experience recurrences of multi-type nonmelanoma skin cancers in a clinical trial for skin cancer prevention. The aims in those applications are to characterize features of the marginal processes, evaluate covariate effects, and quantify both the within-subject recurrence dependence and the dependence among different event types. We use copula-frailty models to analyze correlated recurrent events of differe…
Testing procedures for assessing a parametric regression model with circular response and $\mathbb{R}^d$-valued covariate are proposed and analyzed in this work both for independent and for spatially correlated data. The test statistics are based on a circular distance comparing a (non-smoothed or smoothed) parametric circular estimator and a nonparametric one. Properly designed bootstrap procedures for calibrating the tests in practice are also presented. Finite sample performance of the tests in different scenarios with independent and spatially correlated samples, is analyzed by simulations…
Data with uncertain, missing, censored, and correlated values are commonplace in many research fields including astronomy. Unfortunately, such data are often treated in an ad hoc way in the astronomical literature potentially resulting in inconsistent parameter estimates. Furthermore, in a realistic setting, the variables of interest or their errors may have non-normal distributions which complicates the modeling. I present a novel approach to compute the likelihood function for such data sets. This approach employs Gaussian copulas to decouple the correlation structure of variables and their …
