Dealing with Label Switching in Mixture Models Under Genuine Multimodality

The fitting of finite mixture models is an ill-defined estimation problem as completely different parameterizations can induce similar mixture distributions. This leads to multiple modes in the likelihood which is a problem for frequentist maximum likelihood estimation, and complicates statistical inference of Markov chain Monte Carlo draws in Bayesian estimation. For the analysis of the posterior density of these draws a suitable separation into different modes is desirable. In addition, a unique labelling of the component specific estimates is necessary to solve the label switching problem. This paper presents and compares two approaches to achieve these goals: relabelling under multimodality and constrained clustering. The algorithmic details are discussed and their application is demonstrated on artificial and real-world data

Improving Inference of Gaussian Mixtures Using Auxiliary Variables

Expanding a lower-dimensional problem to a higher-dimensional space and then projecting back is often beneficial. This article rigorously investigates this perspective in the context of finite mixture models, namely how to improve inference for mixture models by using auxiliary variables. Despite the large literature in mixture models and several empirical examples, there is no previous work that gives general theoretical justification for including auxiliary variables in mixture models, even for special cases. We provide a theoretical basis for comparing inference for mixture multivariate models with the corresponding inference for marginal univariate mixture models. Analytical results for several special cases are established. We show that the probability of correctly allocating mixture memberships and the information number for the means of the primary outcome in a bivariate model with two Gaussian mixtures are generally larger than those in each univariate model. Simulations under a range of scenarios, including misspecified models, are conducted to examine the improvement. The method is illustrated by two real applications in ecology and causal inference

Magnetic resonance imaging-guided phase 1 trial of putaminal AADC gene therapy for Parkinson's disease.

ObjectiveTo understand the safety, putaminal coverage, and enzyme expression of adeno-associated viral vector serotype-2 encoding the complementary DNA for the enzyme, aromatic L-amino acid decarboxylase (VY-AADC01), delivered using novel intraoperative monitoring to optimize delivery.MethodsFifteen subjects (three cohorts of 5) with moderately advanced Parkinson's disease and medically refractory motor fluctuations received VY-AADC01 bilaterally coadministered with gadoteridol to the putamen using intraoperative magnetic resonance imaging (MRI) guidance to visualize the anatomic spread of the infusate and calculate coverage. Cohort 1 received 8.3 × 1011 vg/ml and ≤450 μl per putamen (total dose, ≤7.5 × 1011 vg); cohort 2 received the same concentration (8.3 × 1011 vg/ml) and ≤900 μl per putamen (total dose, ≤1.5 × 1012 vg); and cohort 3 received 2.6 × 1012 vg/ml and ≤900 μl per putamen (total dose, ≤4.7 × 1012 vg). (18)F-fluoro-L-dihydroxyphenylalanine positron emission tomography (PET) at baseline and 6 months postprocedure assessed enzyme activity; standard assessments measured clinical outcomes.ResultsMRI-guided administration of ascending VY-AADC01 doses resulted in putaminal coverage of 21% (cohort 1), 34% (cohort 2), and 42% (cohort 3). Cohorts 1, 2, and 3 showed corresponding increases in enzyme activity assessed by PET of 13%, 56%, and 79%, and reductions in antiparkinsonian medication of -15%, -33%, and -42%, respectively, at 6 months. At 12 months, there were dose-related improvements in clinical outcomes, including increases in patient-reported ON-time without troublesome dyskinesia (1.6, 3.3, and 1.5 hours, respectively) and quality of life.InterpretationNovel intraoperative monitoring of administration facilitated targeted delivery of VY-AADC01 in this phase 1 study, which was well tolerated. Increases in enzyme expression and clinical improvements were dose dependent. ClinicalTrials.gov Identifier: NCT01973543 Ann Neurol 2019;85:704-714

Glandular trichomes on the leaves of Rosmarinus officinalis: Morphology, stereology and histochemistry

Stereological and histochernical analyses of the glandular trichomes on leaves of Rosmarinus officinalis were carried out using light and fluorescence microscopy. Non-glandular and two types of glandular trichomes - peltate and capitate - are described. The stereological method was used for estimating the volume density of epidermis, mesophyll, mechanical tissue, central cylinder, intercellular spaces and volume density of different types of glandular trichomes. The results showed that the volume density of adaxial epidermis was higher than abaxial epidermis. The volume density of peltate trichomes was higher than the volume density of capitate ones. The values obtained for number of peltate and capitate trichomes showed that the capitate trichomes type I were more numerous. The histochernical tests showed positive reactions to proteins and polysaccharides for both types of trichomes, while the phenolic substances were found only in peltate trichomes

HST/ACS colour-magnitude diagrams of M31 globular clusters

With the aim of increasing the sample of M31 clusters for which a colour magnitude diagram is available, we searched the HST archive for ACS images containing objects included in the Revised Bologna Catalogue of M31 globular clusters. Sixty-three such objects were found. We used the ACS images to confirm or revise their classification and we obtained useful CMDs for 11 old globular clusters and 6 luminous young clusters. We obtained simultaneous estimates of the distance, reddening, and metallicity of old clusters by comparing their observed field-decontaminated CMDs with a grid of template clusters of the Milky Way. We estimated the age of the young clusters by fitting with theoretical isochrones. For the old clusters, we found metallicities in the range -0.4<=[Fe/H]<=-1.9, that generally agree with existing spectroscopic extimates. At least four of them display a clear blue HB, indicating ages >10 Gyr. All six candidate young clusters are found to have ages <1Gyr. With the present work the total number of M31 GCs with reliable optical CMD increases from 35 to 44 for the old clusters, and from 7 to 11 for the young ones. The old clusters show similar characteristics to those of the MW. We discuss the case of the cluster B407, with a metallicity [Fe/H] ~-0.6 and located at a large projected distance from the centre of M31 and from the galaxy major axis. Metal-rich globulars at large galactocentric distances are rare both in M31 and in the MW. B407, in addition, has a velocity in stark contrast with the rotation pattern shared by the bulk of M31 clusters of similar metallicity. This, along with other empirical evidence, supports the hypothesis that the cluster is physically associated with a substructure in the M31 halo that has been interpreted as the relic of a merging event.Comment: 19 pages, 14 figures, 6 tables. Accepted for publication on Astronomy and Astrophysic

An Adaptive Interacting Wang-Landau Algorithm for Automatic Density Exploration

While statisticians are well-accustomed to performing exploratory analysis in the modeling stage of an analysis, the notion of conducting preliminary general-purpose exploratory analysis in the Monte Carlo stage (or more generally, the model-fitting stage) of an analysis is an area which we feel deserves much further attention. Towards this aim, this paper proposes a general-purpose algorithm for automatic density exploration. The proposed exploration algorithm combines and expands upon components from various adaptive Markov chain Monte Carlo methods, with the Wang-Landau algorithm at its heart. Additionally, the algorithm is run on interacting parallel chains -- a feature which both decreases computational cost as well as stabilizes the algorithm, improving its ability to explore the density. Performance is studied in several applications. Through a Bayesian variable selection example, the authors demonstrate the convergence gains obtained with interacting chains. The ability of the algorithm's adaptive proposal to induce mode-jumping is illustrated through a trimodal density and a Bayesian mixture modeling application. Lastly, through a 2D Ising model, the authors demonstrate the ability of the algorithm to overcome the high correlations encountered in spatial models.Comment: 33 pages, 20 figures (the supplementary materials are included as appendices