Fractional Laplace motion is obtained by subordinating fractional Brownian motion to a gamma process. Used recently to model hydraulic conductivity fields in geophysics, it might also prove useful in modeling financial time series. Its one-dimensional distributions are scale mixtures of normal laws, where the stochastic variance has the generalized gamma distribution. These one-dimensional dist...

Model selection is an important activity in modern data analysis and the conventional Bayesian approach to this problem involves calculation of marginal likelihoods for different models, together with diagnostics which examine specific aspects of model fit. Calculating the marginal likelihood is a difficult computational problem. Our article proposes some extensions of the Laplace approximation...

We describe a comprehensive framework for performing Bayesian inference for Gaussian graphical models based on the G-Wishart prior with a special focus on efficiently including nondecomposable graphs in the model space. We develop a new approximation method to the normalizing constant of a G-Wishart distribution based on the Laplace approximation. We review recent developments in stochastic sea...

Quantile regression provides a convenient framework for analyzing the impact of covariates on the complete conditional distribution of a response variable instead of only the mean. While frequentist treatments of quantile regression are typically completely nonparametric, a Bayesian formulation relies on assuming the asymmetric Laplace distribution as auxiliary error distribution that yields po...

Regularization is necessary to avoid overfitting when the number of data samples is low compared to the number of parameters of the model. In this paper, we introduce a flexible L1 regularization for the multivariate von Mises distribution. We also propose a circular distance that can be used to estimate the Kullback-Leibler divergence between two circular distributions by means of sampling, an...

Here I introduce package cmvnorm, a complex generalization of the mvtnorm package. A complex generalization of the Gaussian process is suggested and numerical results presented using the package. An application in the context of approximating the Weierstrass σ-function using a complex Gaussian process is given.