Bayesian inference for the half-normal and half-t distributions

In this article we consider approaches to Bayesian inference for the half-normal and half-t distributions. We show that a generalized version of the normal-gamma distribution is conjugate to the half-normal likelihood and give the moments of this new distribution. The bias and coverage of the Bayesian posterior mean estimator of the halfnormal location parameter are compared with those of maximum likelihood based estimators. Inference for the half-t distribution is performed using Gibbs sampling and model comparison is carried out using Bayes factors. A real data example is presented which demonstrates the fitting of the half-normal and half-t models

BAYESIAN INFERENCE FOR THE HALF-NORMAL AND HALF-T DISTRIBUTIONS

In this article we consider approaches to Bayesian inference for the half-normal and half-t distributions. We show that a generalized version of the normal-gamma distribution is conjugate to the half-normal likelihood and give the moments of this new distribution. The bias and coverage of the Bayesian posterior mean estimator of the halfnormal location parameter are compared with those of maximum likelihood based estimators. Inference for the half-t distribution is performed using Gibbs sampling and model comparison is carried out using Bayes factors. A real data example is presented which demonstrates the fitting of the half-normal and half-t models.

Drought and the interannual variability of stem growth in an aseasonal, everwet forest

Linking drought to the timing of physiological processes governing tree growth remains one limitation in forecasting climate change effects on tropical trees. Using dendrometers, we measured fine-scale growth for 96 trees of 25 species from 2013 to 2016 in an everwet forest in Puerto Rico. Rainfall over this time span varied, including an unusual, severe El Niño drought in 2015. We assessed how growing season onset, median day, conclusion, and length varied with absolute growth rate and tree size over time. Stem growth was seasonal, beginning in February, peaking in July, and ending in November. Species growth rates varied between 0 and 8 mm/year and correlated weakly with specific leaf area, leaf phosphorus, and leaf nitrogen, and to a lesser degree with wood specific gravity and plant height. Drought and tree growth were decoupled, and drought lengthened and increased variation in growing season length. During the 2015 drought, many trees terminated growth early but did not necessarily grow less. In the year following drought, trees grew more over a shorter growing season, with many smaller trees showing a post-drought increase in growth. We attribute the increased growth of smaller trees to release from light limitation as the canopy thinned because of the drought, and less inferred hydraulic stress than larger trees during drought. Soil type accounted for interannual and interspecific differences, with the finest Zarzal clays reducing tree growth. We conclude that drought affects the phenological timing of tree growth and favors the post-drought growth of smaller, sub-canopy trees in this everwet forest

Cross-correlating the \u3b3-ray Sky with Catalogs of Galaxy Clusters

We report the detection of a cross-correlation signal between {\it Fermi} Large Area Telescope diffuse gamma-ray maps and catalogs of clusters. In our analysis, we considered three different catalogs: WHL12, redMaPPer and PlanckSZ. They all show a positive correlation with different amplitudes, related to the average mass of the objects in each catalog, which also sets the catalog bias. The signal detection is confirmed by the results of a stacking analysis. The cross-correlation signal extends to rather large angular scales, around 1 degree, that correspond, at the typical redshift of the clusters in these catalogs, to a few to tens of Mpc, i.e. the typical scale-length of the large scale structures in the Universe. Most likely this signal is contributed by the cumulative emission from AGNs associated to the filamentary structures that converge toward the high peaks of the matter density field in which galaxy clusters reside. In addition, our analysis reveals the presence of a second component, more compact in size and compatible with a point-like emission from within individual clusters. At present, we cannot distinguish between the two most likely interpretations for such a signal, i.e. whether it is produced by AGNs inside clusters or if it is a diffuse gamma-ray emission from the intra-cluster medium. We argue that this latter, intriguing, hypothesis might be tested by applying this technique to a low redshift large mass cluster sample

Sine-skewed circular distributions

Circular statistics, Finite mixtures, Jones–Pewsey family, Likelihood-based inference, Modality, Trigonometric moments, 60E05, 62H11,