Pierpaolo De Blasi

Are Gibbs-Type Priors the Most Natural Generalization of the Dirichlet Process?

Discrete random probability measures and the exchangeable random partitions they induce are key tools for addressing a variety of estimation and prediction problems in Bayesian inference. Here we focus on the family of Gibbs–type priors, a recent elegant generalization of the Dirichlet and the Pitman–Yor process priors. These random probability measures share properties that are appealing both from a theoretical and an applied point of view: (i) they admit an intuitive predictive characterization justifying their use in terms of a precise assumption on the learning mechanism; (ii) they stand out in terms of mathematical tractability; (iii) they include several interesting special cases besides the Dirichlet and the Pitman–Yor processes. The goal of our paper is to provide a systematic and unified treatment of Gibbs–type priors and highlight their implications for Bayesian nonparametric inference. We deal with their distributional properties, the resulting estimators, frequentist asymptotic validation and the construction of time–dependent versions. Applications, mainly concerning mixture models and species sampling, serve to convey the main ideas. The intuition inherent to this class of priors and the neat results they lead to make one wonder whether it actually represents the most natural generalization of the Dirichlet process.Discrete random probability measures and the exchangeable random partitions they induce are key tools for addressing a variety of estimation and prediction problems in Bayesian inference. Here we focus on the family of Gibbs-type priors, a recent elegant generalization of the Dirichlet and the Pitman-Yor process priors. These random probability measures share properties that are appealing both from a theoretical and an applied point of view: (i) they admit an intuitive predictive characterization justifying their use in terms of a precise assumption on the learning mechanism; (ii) they stand out in terms of mathematical tractability; (iii) they include several interesting special cases besides the Dirichlet and the Pitman-Yor processes. The goal of our paper is to provide a systematic and unified treatment of Gibbs-type priors and highlight their implications for Bayesian nonparametric inference. We deal with their distributional properties, the resulting estimators, frequentist asymptotic validation and the construction of time-dependent versions. Applications, mainly concerning mixture models and species sampling, serve to convey the main ideas. The intuition inherent to this class of priors and the neat results they lead to make one wonder whether it actually represents the most natural generalization of the Dirichlet process.

Cognitive function and cholinergic transmission in patients with subcortical vascular dementia and microbleeds: a TMS study

There has been little investigation on the association between cognitive impairment and the microbleeds (MBs) frequently seen in subcortical vascular dementia (SVaD). One possible mechanism of cognitive decline in individuals with SVaD could be disruption of cholinergic fibers by vascular lesions. Central cholinergic circuits in human brain can be tested non-invasively by means of a transcranial magnetic stimulation (TMS) protocol named short latency afferent inhibition (SAI) of motor cortex. In the present study, we used this test in SvaD patients with and without MBs. SAI was evaluated in 13 SVaD patients with MBs (MB-positive group) and the data were compared with those from a group of 15 SVaD patients without MBs (MB-negative group) and with those from 20 healthy subjects. Moreover, we studied covariation of individual SAI values with the Mini-Mental State Examination (MMSE) total score and subscores. SAI was significantly reduced in the MB-positive group when compared with the MB-negative group and the control subjects. Total MMSE score, “attention and calculation” and “orientation” subscores were significantly lower in the MB-positive group than in the MB-negative group; SAI showed a positive correlation with total MMSE score. Adjustment for age, gender, education, presence of lacunae, severe white matter hyperintensities or severe periventricular hyperintensities did not affect these findings. This study provides novel physiological evidence that MBs have an impact on central cholinergic function that is independent of the extent of associated white matter changes and ischaemic stroke. This finding shows that TMS have potential diagnostic and therapeutic implications. TMS studies may help in evaluating the causes of cognitive impairment in cerebrovascular diseases.

Asymptotics for posterior hazards

An important issue in survival analysis is the investigation and the modeling of hazard rates. Within a Bayesian nonparametric framework, a natural and popular approach is to model hazard rates as kernel mixtures with respect to a completely random measure. In this paper we provide a comprehensive analysis of the asymptotic behavior of such models. We investigate consistency of the posterior distribution and derive fixed sample size central limit theorems for both linear and quadratic functionals of the posterior hazard rate. The general results are then specialized to various specific kernels and mixing measures yielding consistency under minimal conditions and neat central limit theorems for the distribution of functionals.

Repetitive transcranial magnetic stimulation transiently reduces punding in Parkinson's disease: a preliminary study

Abstract Amongst the impulse-control disorders (ICDs) associated with dopamine-replacement therapy in patients with Parkinson’s disease (PD) is a repetitive, complex, stereotyped behaviour called punding. Disruption of the reciprocal loops between the striatum and structures in the prefrontal cortex (PFC) following dopamine depletion may predispose patients with PD to these behavioural disorders. The purpose of the present study was to assess the effects of repetitive transcranial magnetic stimulation (rTMS) over the dorsolateral PFC (DLPFC) on punding in PD. We used low-frequency (LF) rTMS in four PD patients presenting with punding. Punding was transiently reversed by LF-rTMS over the DLPFC without enhancing motor impairment. The effect was more sustained after right DLPFC rTMS. Therefore, LF-rTMS produced a transient beneficial effect in PD patients with punding, similar to that reported in PD patients with levodopa-induced dyskinesias. rTMS might have therapeutic potential for the treatment of punding and perhaps other ICDs in PD.

Cholinergic dysfunction and amnesia in patients with Wernicke–Korsakoff syndrome: a transcranial magnetic stimulation study

The specific neurochemical substrate underlying the amnesia in patients with Wernicke–Korsakoff syndrome (WKS) is still poorly defined. Memory impairment has been linked to dysfunction of neurons in the cholinergic system. A transcranial magnetic stimulation (TMS) protocol, the short latency afferent inhibition (SAI), may give direct information about the function of some cholinergic pathways in the human motor cortex. In the present study, we measured SAI in eight alcoholics with WKS and compared the data with those from a group of age-matched healthy individuals; furthermore, we correlated the individual SAI values of the WKS patients with memory and other cognitive functions. Mean SAI was significantly reduced in WKS patients when compared with the controls. SAI was increased after administration of a single dose of donezepil in a subgroup of four patients. The low score obtained in the Rey Complex Figure delayed recall test, the Digit Span subtest of the Wechsler Adult Intelligence Scale—Revised (WAIS-R) and the Corsi’s Block Span subtest of the WAIS-R documented a severe impairment in the anterograde memory and short-term memory. None of the correlations between SAI values and these neuropsychological tests reached significance. We provide physiological evidence of cholinergic involvement in WKS. However, this putative marker of central cholinergic activity did not significantly correlate with the memory deficit in our patients. These findings suggest that the cholinergic dysfunction does not account for the memory disorder and that damage to the cholinergic system is not sufficient to cause a persisting amnesic syndrome in WKS.

Theta burst stimulation of dorsolateral prefrontal cortex modulates pathological language switching: A case report

Although different lesion and neuroimaging studies had highlighted the importance of the dorsolateral prefrontal cortex (DLPFC) in language switching, the nature of this higher cortical disorder of communication and its neural correlates have not been clearly established. To further investigate the functional involvement of the DLPFC, we used transcranial magnetic stimulation (TMS) given as theta burst stimulation (TBS) in a bilingual patient showing pathologic language switching after an ischemic stroke involving the left frontal lobe. Inhibitory and excitatory TBS were applied to the left DLPFC, to the right DLPFC, or to an occipital cortical control site. A short-lasting interruption of the pathological language switching occurred after excitatory left DLPFC stimulation, while inhibitory left DLPFC TBS transiently increased the number of utterances produced in the unwanted second language. Effects were non-significant after right DLPFC and occipital TBS. Our findings suggest that left DLPFC is actively involved in language switching. TMS techniques may help in understanding the neural bases of bilingualism.

Posterior asymptotics of nonparametric location-scale mixtures for multivariate density estimation

Density estimation represents one of the most successful applications of Bayesian nonparametrics. In particular, Dirichlet process mixtures of normals are the gold standard for density estimation and their asymptotic properties have been studied extensively, especially in the univariate case. However a gap between practitioners and the current theoretical literature is present. So far, posterior asymptotic results in the multivariate case are available only for location mixtures of Gaussian kernels with independent prior on the common covariance matrix, while in practice as well as from a conceptual point of view a location-scale mixture is often preferable. In this paper we address posterior consistency for such general mixture models by adapting a convergence rate result which combines the usual low-entropy, high-mass sieve approach with a suitable summability condition. Specifically, we establish consistency for Dirichlet process mixtures of Gaussian kernels with various prior specifications on the covariance matrix. Posterior convergence rates are also discussed.

Bayesian nonparametric estimation and consistency of mixed multinomial logit choice models

This paper develops nonparametric estimation for discrete choice models based on the Mixed Multinomial Logit (MMNL) model. It has been shown that MMNL models encompass all discrete choice models derived under the assumption of random utility maximization, subject to the identification of an unknown distribution G. Noting the mixture model description of the MMNL, we employ a Bayesian nonparametric approach, using nonparametric priors on the unknown mixing distribution G, to estimate the unknown choice probabilities. Theoretical support for the use of the proposed methodology is provided by establishing strong consistency of a general nonparametric prior on G under simple sufficient conditions. Consistency is defined according to a L1-type distance on the space of choice probabilities and is achieved by extending to a regression model framework a recent approach to strong consistency based on the summability of square roots of prior probabilities. Moving to estimation, slightly different techniques for non-panel and panel data models are discussed. For practical implementation, we describe efficient and relatively easy to use blocked Gibbs sampling procedures. A simulation study is also performed to illustrate the proposed methods and the exibility they achieve with respect to parametric Gaussian MMNL models.

Wright-Fisher construction of the two-parameter Poisson-Dirichlet diffusion

The two-parameter Poisson–Dirichlet diffusion, introduced in 2009 by Petrov, extends the infinitely-many-neutral-alleles diffusion model, related to Kingman’s one-parameter Poisson–Dirichlet distribution and to certain Fleming–Viot processes. The additional parameter has been shown to regulate the clustering structure of the population, but is yet to be fully understood in the way it governs the reproductive process. Here we shed some light on these dynamics by formulating a K-allele Wright–Fisher model for a population of size N, involving a uniform mutation pattern and a specific state-dependent migration mechanism. Suitably scaled, this process converges in distribution to a K-dimensional diffusion process as N → ∞. Moreover, the descending order statistics of the K-dimensional diffusion converge in distribution to the two-parameter Poisson–Dirichlet diffusion as K → ∞. The choice of the migration mechanism depends on a delicate balance between reinforcement and redistributive effects. The proof of convergence to the infinite-dimensional diffusion is nontrivial because the generators do not converge on a core. Our strategy for overcoming this complication is to prove a priori that in the limit there is no “loss of mass”, i.e., that, for each limit point of the sequence of finite-dimensional diffusions (after a reordering of components by size), allele frequencies sum to one.

CAVEOLIN-1 expression in brain metastasis from lung cancer predicts worse outcome and radioresistance, irrespective of tumor histotype

Brain metastases develop in one-third of patients with non-small-cell lung cancer and are associated with a dismal prognosis, irrespective of surgery or chemo-radiotherapy. Pathological markers for predicting outcomes after surgical resection and radiotherapy responsiveness are still lacking. Caveolin 1 has been associated with chemo- and radioresistance in various tumors, including non-small-cell lung cancer. Here, caveolin 1 expression was assessed in a series of 69 brain metastases from non-small-cell lung cancer and matched primary tumors to determine its role in predicting survival and radiotherapy responsiveness. Only caveolin 1 expression in brain metastasis was associated with poor prognosis and an increased risk of death (log rank test, p = 0.015). Moreover, in the younger patients (median age of <54 years), caveolin 1 expression neutralized the favorable effect of young age on survival compared with the older patients. Among the radiotherapy-treated patients, an increased risk of death was detected in the group with caveolin 1-positive brain metastasis (14 out of 22 patients, HR=6.839, 95% CI 1.849 to 25.301, Wald test p = 0.004). Overall, caveolin 1 expression in brain metastasis from non-small-cell lung cancer is independently predictive of worse outcome and radioresistance and could become an additional tool for personalized therapy in the critical subset of brain-metastatic non-small-cell lung cancer patients.