This paper introduces a general class of hierarchical nonparametric prior distributions which includes new hierarchical mixture priors such as the hierarchical Gnedin measures, and other well-known prior distributions such as the hierarchical Pitman-Yor and the hierarchical normalized random measures. The random probability measures are constructed by a hierarchy of generalized species sampling processes with possibly non-diffuse base measures. The proposed framework provides a probabilistic foundation for hierarchical random measures, and allows for studying their properties under the alternative assumptions of diffuse, atomic and mixed base measure. We show that hierarchical species sampling models have a Chinese Restaurants Franchise representation and can be used as prior distributions to undertake Bayesian nonparametric inference. We provide a general sampling method for posterior approximation which easily accounts for non-diffuse base measures such as spike-and-slab.

This paper studies the forecasting ability of cryptocurrency time series. This study is about the four most capitalised cryptocurrencies: Bitcoin, Ethereum, Litecoin and Ripple. Different Bayesian models are compared, including models with constant and time-varying volatility, such as stochastic volatility and GARCH. Moreover, some cryptopredictors are included in the analysis, such as S&P 500 and Nikkei 225. In this paper, the results show that stochastic volatility is significantly outperforming the benchmark of VAR in both point and density forecasting. Using a different type of distribution, for the errors of the stochastic volatility, the student-t distribution is shown to outperform the standard normal approach.

Summary: Several studies on heritability in twins aim at understanding the different contribution of environmental and genetic factors to specific traits. Considering the national merit twin study, our purpose is to analyse correctly the influence of socio-economic status on the relationship between twins’ cognitive abilities. Our methodology is based on conditional copulas, which enable us to model the effect of a covariate driving the strength of dependence between the main variables. We propose a flexible Bayesian non-parametric approach for the estimation of conditional copulas, which can model any conditional copula density. Our methodology extends the work of Wu, Wang and Walker in 2015 by introducing dependence from a covariate in an infinite mixture model. Our results suggest that environmental factors are more influential in families with lower socio-economic position.