Investigating relationships between response variables and covariates in areas such as environmental science, geoscience, and public health is an important endeavor. Based on a Bayesian mixture of finite mixtures model, we present a novel spatially clustered coefficients regression model for count value data. The proposed method detects the spatial homogeneity of the Poisson regression coefficients. A Markov random field constrained mixture of finite mixtures prior provides a regularized estimator of the number of clusters of regression coefficients with geographical neighborhood information. As a by-product, we also provide the theoretical properties of our proposed method when the Markov random field is exchangeable. An efficient Markov chain Monte Carlo algorithm is developed by using the multivariate log gamma distribution as a base distribution. Simulation studies are carried out to examine the empirical performance of the proposed method. Additionally, we analyze Georgia's premature death data as an illustration of the effectiveness of our approach. The supplementary materials are provided on GitHub at https://github.com/pengzhaostat/MLG_MFM.

Effectively fitting the major features of experimental transiograms (or variograms) is crucial in characterizing spatial patterns and reproducing them in geostatistical simulations. Landscape patterns usually tend to contain neighboring structures. The experimental cross-transiograms of frequent neighboring landscape categories normally demonstrate apparent peaking features at low lag distances – they first quickly increase to a peak and then gradually flatten out. The flattening process may be smooth or may be through one or more alternate attenuating troughs and peaks. While alternate peaks and troughs may be a reflection of the cyclic occurrence of landscape categories, the single peak or the first peak at low lag section should be a signal of the neighboring structure of two related categories. This is further proved by the peaking features of some idealized transiograms calculated from single-step transition probability matrices. To effectively fit the first peak, especially when it is the single one, we propose using the gamma distribution function and the commonly used variogram models to form additive composite models. Cases of fitting experimental cross-transiograms of landscape data (here soil types and land cover classes) show that the additive gamma-exponential composite model works very well and may closely fit the single-peak features. Although it has multiple parameters to set, model fitting can be performed manually by trial and error. Other two composite models may provide alternatives for fine fitting of the root section (i.e., the left side of the peak). These models may also be applicable to fitting experimental variograms with similar features. We also reintroduce the multiplicative composite hole-effect models proposed for variogram modeling by earlier researchers, and test them on experimental cross-transiograms. It is found that composite hole-effect models are not sufficiently flexible to effectively fit the peak shapes of experimental cross-transiograms of neighboring categories, unless multiple peaks and troughs appear in regular shapes and rhythms.

BACKGROUND: The discovery of biomarkers is an important step towards the development of criteria for early diagnosis of disease status. Recently electrospray ionization (ESI) and matrix assisted laser desorption (MALDI) time-of-flight (TOF) mass spectrometry have been used to identify biomarkers both in proteomics and metabonomics studies. Data sets generated from such studies are generally very large in size and thus require the use of sophisticated statistical techniques to glean useful information. Most recent attempts to process these types of data model each compound's intensity either discretely by positional (mass to charge ratio) clustering or through each compounds' own intensity distribution. Traditionally data processing steps such as noise removal, background elimination and m/z alignment, are generally carried out separately resulting in unsatisfactory propagation of signals in the final model. RESULTS: In the present study a novel semi-parametric approach has been developed to distinguish urinary metabolic profiles in a group of traumatic patients from those of a control group consisting of normal individuals. Data sets obtained from the replicates of a single subject were used to develop a functional profile through Dirichlet mixture of beta distribution. This functional profile is flexible enough to accommodate variability of the instrument and the inherent variability of each individual, thus simultaneously addressing different sources of systematic error. To address instrument variability, all data sets were analyzed in replicate, an important issue ignored by most studies in the past. Different model comparisons were performed to select the best model for each subject. The m/z values in the window of the irregular pattern are then further recommended for possible biomarker discovery. CONCLUSION: To the best of our knowledge this is the very first attempt to model the physical process behind the time-of flight mass spectrometry. Most of the state of the art techniques does not take these physical principles in consideration while modeling such data. The proposed modeling process will apply as long as the basic physical principle presented in this paper is valid. Notably we have confined our present work mostly within the modeling aspect. Nevertheless clinical validation of our recommended list of potential biomarkers will be required. Hence, we have termed our modeling approach as a "framework" for further work.

MOTIVATION: Population allele frequencies are correlated when populations have a shared history or when they exchange genes. Unfortunately, most models for allele frequency and inference about population structure ignore this correlation. Recent analytical results show that among populations, correlations can be very high, which could affect estimates of population genetic structure. In this study, we propose a mixture beta model to characterize the allele frequency distribution among populations. This formulation incorporates the correlation among populations as well as extending the model to data with different clusters of populations. RESULTS: Using simulated data, we show that in general, the mixture model provides a good approximation of the among-population allele frequency distribution and a good estimate of correlation among populations. Results from fitting the mixture model to a dataset of genotypes at 377 autosomal microsatellite loci from human populations indicate high correlation among populations, which may not be appropriate to neglect. Traditional measures of population structure tend to overestimate the amount of genetic differentiation when correlation is neglected. Inference is performed in a Bayesian framework. CONTACT: [email protected].