A new family of Markov branching trees: the alpha-gamma model

We introduce a simple tree growth process that gives rise to a new two-parameter family of discrete fragmentation trees that extends Ford's alpha model to multifurcating trees and includes the trees obtained by uniform sampling from Duquesne and Le Gall's stable continuum random tree. We call these new trees the alpha-gamma trees. In this paper, we obtain their splitting rules, dislocation measures both in ranked order and in sized-biased order, and we study their limiting behaviour.Comment: 23 pages, 1 figur

Fully Bayesian inference for α-stable distributions using a Poisson series representation

In this paper we develop an approach to Bayesian Monte Carlo inference for skewed α-stable distributions. Based on a series representation of the stable law in terms of infinite summations of random Poisson process arrival times, our framework leads to a simple representation in terms of conditionally Gaussian distributions for certain latent variables. Inference can therefore be carried out straightforwardly using techniques such as auxiliary variables versions of Markov chain Monte Carlo (MCMC) methods. The Poisson series representation (PSR) is further extended to practical application by introducing an approximation of the series residual terms based on exact moment calculations. Simulations illustrate the proposed framework applied to skewed α-stable simulated and real-world data, successfully estimating the distribution parameter values and being consistent with other (non-Bayesian) approaches. The methods are highly suitable for incorporation into hierarchical Bayesian models, and in this case the conditionally Gaussian structure of our model will lead to very efficient computations compared to other approaches.Godsill acknowledges partial funding for the work from the EPSRC BTaRoT project EP/K020153/1, and Tatjana Lemke acknowledges PhD funding from Fraunhofer ITWM, Kaiserslautern.This is the author accepted manuscript. The final version is available from Elsevier via http://dx.doi.org/10.1016/j.dsp.2015.08.01

The Effects of Departmental and Positional Power on Job Evaluation Outcomes: A Dual-Level Analysis of Power and Resource Allocation

We replicate research from two separate power and resource allocation research streams to test whether job evaluation outcomes at a university are simultaneously susceptible to effects of power held at both the group (i.e., academic department) and individual (i.e., a job\u27s hierarchical position) levels. In doing so, we illustrate limitations of the dominant rational model of research in job evaluation and, more generally, how dual levels of analysis can illuminate the relationship between power and resource allocation. We then investigate whether departmental and positional power interact in the allocation of resources at both levels. Results from six years of job evaluation data indicate that job evaluation outcomes are highly susceptible to both departmental and positional power. Moreover, our results suggest that positional power moderated the effect of departmental power on group level job evaluation successes. Drawing on our dual-level analysis, we propose a new model of power, resource allocation, and the perpetuation of power

Observing another in pain facilitates vicarious experiences and modulates somatosensory experiences

Objective: This study investigated whether individuals reporting vicarious pain in daily life (e.g., the self-reported vicarious pain group) display vicarious experiences during an experimental paradigm, and also show an improved detection of somatosensory stimuli while observing another in pain. Furthermore, this study investigated the stability of these phenomena. Finally, this study explored the putative modulating role of dispositional empathy and hypervigilance for pain. Methods: Vicarious pain responders (i.e., reporting vicarious pain in daily life; N = 16) and controls (N = 19) were selected from a large sample, and viewed videos depicting pain-related (hands being pricked) and non-pain related scenes, whilst occasionally experiencing vibrotactile stimuli themselves on the left, right or both hands. Participants reported the location at which they felt a somatosensory stimulus. We calculated the number of vicarious errors (i.e., the number of trials in which an illusionary sensation was reported while observing pain-related scenes) and detection accuracy. Thirty-three participants (94.29%) took part in the same experiment 5 months later to investigate the temporal stability of the outcomes. Results: The vicarious pain group reported more vicarious errors compared with controls and this effect proved to be stable over time. Detection was facilitated while observing pain-related scenes compared with non-pain related scenes. Observers' characteristics, i.e., dispositional empathy and hypervigilance for pain, did not modulate the effects. Conclusion: Observing pain facilitates the detection of tactile stimuli, both in vicarious pain responders and controls. Interestingly, vicarious pain responders reported more vicarious errors during the experimental paradigm compared to controls and this effect remained stable over time

Bayesian nonparametric inference for discovery probabilities: credible intervals and large sample asymptotics

Given a sample of size $n$ from a population of individuals belonging to different species with unknown proportions, a popular problem of practical interest consists in making inference on the probability $D_{n}(l)$ that the $(n+1)$-th draw coincides with a species with frequency $l$ in the sample, for any $l=0,1,\ldots,n$. This paper contributes to the methodology of Bayesian nonparametric inference for $D_{n}(l)$. Specifically, under the general framework of Gibbs-type priors we show how to derive credible intervals for a Bayesian nonparametric estimation of $D_{n}(l)$, and we investigate the large $n$ asymptotic behaviour of such an estimator. Of particular interest are special cases of our results obtained under the specification of the two parameter Poisson--Dirichlet prior and the normalized generalized Gamma prior, which are two of the most commonly used Gibbs-type priors. With respect to these two prior specifications, the proposed results are illustrated through a simulation study and a benchmark Expressed Sequence Tags dataset. To the best our knowledge, this illustration provides the first comparative study between the two parameter Poisson--Dirichlet prior and the normalized generalized Gamma prior in the context of Bayesian nonparemetric inference for $D_{n}(l)$

Pseudo-Marginal MCMC for Parameter Estimation in α-Stable Distributions

The α-stable distribution is very useful for modelling data with extreme values and skewed behaviour. The distribution is governed by two key parameters, tail thickness and skewness, in addition to scale and location. Inferring these parameters is difficult due to the lack of a closed form expression of the probability density. We develop a Bayesian method, based on the pseudo-marginal MCMC approach, that requires only unbiased estimates of the intractable likelihood. To compute these estimates we build an adaptive importance sampler for a latentvariable-representation of the α-stable density. This representation has previously been used in the literature for conditional MCMC sampling of the parameters, and we compare our method with this approach.This is the author accepted manuscript. The final version is available from Elsevier via http://dx.doi.org/10.1016/j.ifacol.2015.12.17