Posterior Probability Maps Research Articles

Probabilistic Prediction of Satellite-Derived Water Quality for a Drinking Water Reservoir

A Bayesian network-based modelling framework was proposed to predict the probability of exceeding critical thresholds for chlorophyll-a and turbidity in an Australian subtropical drinking water reservoir, based on Sentinel-2 data and prior knowledge. The model was trained with quasi-synchronous historical in situ and satellite data for 2018–2023 and achieved satisfactory accuracy (Brier score < 0.27 for all models) despite limited poor water quality events in the final dataset. The graphical output of the model (posterior probability maps of high turbidity or chlorophyll-a) provides an effective means for the user to evaluate both the prediction, and the uncertainty behind the predictions in a single map. This avoids loss of trust in the model and can trigger spatially targeted data collection in order to reduce uncertainty. Future work will focus on refining the modelling methodology and its automation, as well as including other data such as in situ high-frequency sensors.

Porthole and Stormcloud: Tools for Visualisation of Spatiotemporal M/EEG Statistics.

Electro- and magneto-encephalography are functional neuroimaging modalities characterised by their ability to quantify dynamic spatiotemporal activity within the brain. However, the visualisation techniques used to illustrate these effects are currently limited to single- or multi-channel time series plots, topographic scalp maps and orthographic cross-sections of the spatiotemporal data structure. Whilst these methods each have their own strength and weaknesses, they are only able to show a subset of the data and are suboptimal at articulating one or both of the space-time components.Here, we propose Porthole and Stormcloud, a set of data visualisation tools which can automatically generate context appropriate graphics for both print and screen with the following graphical capabilities: Animated two-dimensional scalp maps with dynamic timeline annotation and optional user interaction; Three-dimensional construction of discrete clusters within sparse spatiotemporal volumes, rendered with 'cloud-like' appearance and augmented by cross-sectional scalp maps indicating local maxima. These publicly available tools were designed specifically for visualisation of M/EEG spatiotemporal statisticalparametric maps, however, we also demonstrate alternate use cases of posterior probability maps and weight maps produced by machine learning classifiers. In principle, the methods employed here are transferrable to visualisation of any spatiotemporal image.

Coral habitat mapping: a comparison between maximum likelihood, Bayesian and Dempster–Shafer classifiers

This study deals with the mixed-pixel problem of detecting benthic habitat class membership and evaluates two soft classifiers for coral habitat mapping on Lang Tengah island (Malaysia). A comparison was made between the Bayesian and Dempster–Shafer (D–S) with a traditional maximum likelihood (ML). The heterogeneous pattern of reef environment, established by field observation, four classes of coral habitats containing various combinations of live coral, dead coral with algae, rubble coral and sand. Posterior probability and belief maps, generated by Bayesian and D–S, respectively, were evaluated by visual inspection and final coral habitat distribution maps were validated via accuracy assessment estimates. The accuracy validation tests agreed with the visual inspection of the probability, uncertainty and coral distribution maps. The Bayesian algorithm performed better, with a 34.7–68.5% improvement in accuracy compared to D–S and ML, respectively. Probability maps demonstrate the advantages of the soft classifier over the hard classifier for coral mapping.

Prospectivity Mapping for Porphyry Cu–Mo Mineralization in the Eastern Tianshan, Xinjiang, Northwestern China

In order to comprehensively utilize regional-scale geological, geochemical and geophysical datasets for future exploration of undiscovered porphyry Cu–Mo polymetallic deposits (PCMPDs) in the Chinese Eastern Tianshan orogenic belt, three data-driven mineral prospectivity mapping (MPM) methods, namely ordinary weights of evidence (WofE), fuzzy weights of evidence (FWofE) and logistic regression (LR), were employed to integrate these datasets for mapping prospectivity of undiscovered PCMPDs. Firstly, the geological setting and mineralization of PCMPDs in the Eastern Tianshan district are reviewed. Then, spatial datasets based on geological maps, stream sediment geochemical data, and Bouguer gravity and aeromagnetic data are introduced, and on the basis of the prospecting model for PCMPDs, layers of structural, lithological, geophysical and geochemical evidences are constructed using the spatial datasets by means of GIS-based techniques. Finally, these evidential layers were integrated by using the WofE, FWofE and LR methods to obtain posterior probability maps of PCMPDs and the results are critically compared. The main conclusions are that: (1) the porphyry Cu–Mo mineralization in the Eastern Tianshan was occurred in the subduction boundary of the Late Paleozoic Dananhu-Dacaotan arc system of Kanguertag-Huangshan deep fault belt. This geological inference is supported by all the data-driven MPM methods; (2) the conditional independence assumption for both WofE and FWofE can be easily violated in practical applications. This issue seems very difficult to be circumvented due to geological correlations of evidence layers; (3) the uncertainty of the LR modeling approach particularly with respect to models using multiclass response variables mainly arises from over-fitting of the (ln-transformed) linear relationship; and (4) if there is no need for estimation of the number of undiscovered PCMPDs, the prospectivity map biasedly estimated by either WofE or FWofE modeling can be recommended for targeting new exploration areas with more detailed reconnaissance of potential undiscovered PCMPDs. Otherwise, the prospectivity map unbiasedly estimated by LR modeling with binary evidence modeling approach can be priority of use.

Individuals with 22q11.2 deletion syndrome show intact prediction but reduced adaptation in responses to repeated sounds: Evidence from Bayesian mapping.

One of the most common copy number variants, the 22q11.2 microdeletion, confers an increased risk for schizophrenia. Since schizophrenia has been associated with an aberrant neural response to repeated stimuli through both reduced adaptation and prediction, we here hypothesized that this may also be the case in nonpsychotic individuals with a 22q11.2 deletion.We recorded high-density EEG from 19 individuals with 22q11.2 deletion syndrome (12–25 years), as well as 27 healthy volunteers with comparable age and sex distribution, while they listened to a sequence of sounds arranged in a roving oddball paradigm. Using posterior probability maps and dynamic causal modelling we tested three different models accounting for repetition dependent changes in cortical responses as well as in effective connectivity; namely an adaptation model, a prediction model, and a model including both adaptation and prediction.Repetition-dependent changes were parametrically modulated by a combination of adaptation and prediction and were apparent in both cortical responses and in the underlying effective connectivity. This effect was reduced in individuals with a 22q11.2 deletion and was negatively correlated with negative symptom severity. Follow-up analysis showed that the reduced effect of the combined adaptation and prediction model seen in individuals with 22q11.2 deletion was driven by reduced adaptation rather than prediction failure. Our findings suggest that adaptation is reduced in individuals with a 22q11.2 deletion, which can be interpreted in light of the framework of predictive coding as a failure to suppress prediction errors.

Bayesian Model Selection Maps for Group Studies Using M/EEG Data.

Predictive coding postulates that we make (top-down) predictions about the world and that we continuously compare incoming (bottom-up) sensory information with these predictions, in order to update our models and perception so as to better reflect reality. That is, our so-called “Bayesian brains” continuously create and update generative models of the world, inferring (hidden) causes from (sensory) consequences. Neuroimaging datasets enable the detailed investigation of such modeling and updating processes, and these datasets can themselves be analyzed with Bayesian approaches. These offer methodological advantages over classical statistics. Specifically, any number of models can be compared, the models need not be nested, and the “null model” can be accepted (rather than only failing to be rejected as in frequentist inference). This methodological paper explains how to construct posterior probability maps (PPMs) for Bayesian Model Selection (BMS) at the group level using electroencephalography (EEG) or magnetoencephalography (MEG) data. The method has only recently been used for EEG data, after originally being developed and applied in the context of functional magnetic resonance imaging (fMRI) analysis. Here, we describe how this method can be adapted for EEG using the Statistical Parametric Mapping (SPM) software package for MATLAB. The method enables the comparison of an arbitrary number of hypotheses (or explanations for observed responses), at each and every voxel in the brain (source level) and/or in the scalp-time volume (scalp level), both within participants and at the group level. The method is illustrated here using mismatch negativity (MMN) data from a group of participants performing an audio-spatial oddball attention task. All data and code are provided in keeping with the Open Science movement. In doing so, we hope to enable others in the field of M/EEG to implement our methods so as to address their own questions of interest.

Bayesian Mapping Reveals That Attention Boosts Neural Responses to Predicted and Unpredicted Stimuli.

Predictive coding posits that the human brain continually monitors the environment for regularities and detects inconsistencies. It is unclear, however, what effect attention has on expectation processes, as there have been relatively few studies and the results of these have yielded contradictory findings. Here, we employed Bayesian model comparison to adjudicate between 2 alternative computational models. The "Opposition" model states that attention boosts neural responses equally to predicted and unpredicted stimuli, whereas the "Interaction" model assumes that attentional boosting of neural signals depends on the level of predictability. We designed a novel, audiospatial attention task that orthogonally manipulated attention and prediction by playing oddball sequences in either the attended or unattended ear. We observed sensory prediction error responses, with electroencephalography, across all attentional manipulations. Crucially, posterior probability maps revealed that, overall, the Opposition model better explained scalp and source data, suggesting that attention boosts responses to predicted and unpredicted stimuli equally. Furthermore, Dynamic Causal Modeling showed that these Opposition effects were expressed in plastic changes within the mismatch negativity network. Our findings provide empirical evidence for a computational model of the opposing interplay of attention and expectation in the brain.

Medical image segmentation via atlases and fuzzy object models: Improving efficacy through optimum object search and fewer models.

Statistical object shape models (SOSMs), known as probabilistic atlases, are popular in medical image segmentation. They register an image into the atlas coordinate system, such that a desired object can be delineated from the constraints of its shape model. While this strategy facilitates segmenting objects with even weak-boundary contrast, it tends to require more models per object to cope with possible registration errors. Fuzzy object shape models (FOSMs) gain substantial speed by avoiding image registration and placing more relaxed model constraints with optimum object search. However, they tend to require stronger object boundary contrast for effective delineation. In this work, the authors show that optimum object search, the essential underpinning of FOSMs, can improve segmentation efficacy of SOSMs with fewer models per object. For the sake of efficiency, the authors use three atlases per object (SOSM-3) as baseline for segmentation based on the best match with posterior probability maps. A novel strategy for SOSM with a single atlas and optimum object search (SOSM-S) is presented. When registering an image to the atlas system, one should expect that the object's boundary falls within the uncertainty region of the model-region wherein voxels show probabilities greater than 0 and less than 1 to be in the object. Since registration may fail, SOSM-S translates the atlas locally and, at each location, delineates and scores a candidate object in the uncertainty region. Segmentation is defined by the candidate with the highest score. The presented FOSM also uses a single model per object, but model construction uses only shape translations, building a fuzzy object model with larger uncertainty region. Optimum object search requires estimation of the object's location and/or optimization algorithms to speed-up segmentation. The authors evaluate SOSM-3, SOSM-S, and FOSM on 75 CT-images of the thorax and 35 MR T1-weighted images of the brain, with nine objects of interest. The results show that SOSM-S and FOSM can segment seven out of the nine objects with higher accuracy than SOSM-3, according to the average symmetric surface distance and statistical test. SOSM-S was consistently more accurate than FOSM, FOSM being 2-3 orders of magnitude faster than SOSM-S and SOSM-3 for model construction and hundreds of times faster than them for segmentation. Although multiple models per object can usually improve segmentation efficacy, the optimum object search has shown to reduce the number of required models. The efficiency gain of FOSM over SOSM-S motivates its use for interactive applications and studies with large image data sets. FOSM and SOSM impose different degrees of shape constraints from the model, making one approach more suitable than the other, depending on contrast. This suggests the use of hybrid models that can take advantage from the strengths of fuzzy and statistical models.

The Core Neural Mechanisms underlying Depression Disorder: A Meta-analysis of fMRI Studies

Depression disorder is a mental disorder characterized by a pervasive and persistent low mood, and is accompanied by low self-esteem and by a loss of interest or pleasure in normally enjoyable activities. Biological, psychological, and social factors all play a role in inducing depression. In the last decades, the rapid growth of literatures on neuroimaging psychiatry has led to major advances in our understanding of affective disorder such as depression. However, it has also made it increasingly difficult to aggregate and synthesize neuroimaging findings to reach a conclusive agreement. We try to locate the core nerural mechanisms that are specific to depression disorder based on extant literature, by employing a newly developed automated brain-mapping framework—Neurosynth that uses text-mining, meta-analysis and machine-learning techniques to decode broad cognitive states from brain activity (i.e., reverse interference). The processing stream involves the following six steps: Activation coordinates are extracted from published neuroimaging articles using an automated parser. The full text of all articles is parsed, and each article is “tagged” with a set of terms that occur at a high frequency in that article. A list of several thousand terms that occur at high frequency in 20 or more studies are generated. For each term of interest (e.g., “depression”), the entire database of coordinates is divided into two sets: those that occur in articles containing the term and those that do not. A giant meta-analysis is performed comparing the coordinates reported for studies with and without the term of interest. In addition to producing statistical inference maps (i.e., z and p value maps), we also compute posterior probability maps, which display the likelihood of a given term being used in a study if activation is observed at a particular voxel. We repeat the series of steps for depression, anxiety as well as major depression. In sum, the meta-analysis suggests that amygdala, VMPFC and DLPFC are the core nerural mechanisms underlying depression disorder. Among them, differential anlysis indicates that the dysfunction of amygdala and VMPFC is also the key brain regions for other affective disorder such as anxiety, but the malfunction of DLPFC is most predictive and specific to depression disorder. The inability to down-regulate emotion reactions may be the key neural mechanism for this particular disorder. Thus, our study provides clues for future research on neural basis underlying depression disorder, with a special emphasis on DLPFC.

Estimating anatomical trajectories with Bayesian mixed-effects modeling

We introduce a mass-univariate framework for the analysis of whole-brain structural trajectories using longitudinal Voxel-Based Morphometry data and Bayesian inference. Our approach to developmental and aging longitudinal studies characterizes heterogeneous structural growth/decline between and within groups. In particular, we propose a probabilistic generative model that parameterizes individual and ensemble average changes in brain structure using linear mixed-effects models of age and subject-specific covariates. Model inversion uses Expectation Maximization (EM), while voxelwise (empirical) priors on the size of individual differences are estimated from the data. Bayesian inference on individual and group trajectories is realized using Posterior Probability Maps (PPM). In addition to parameter inference, the framework affords comparisons of models with varying combinations of model order for fixed and random effects using model evidence. We validate the model in simulations and real MRI data from the Alzheimer's Disease Neuroimaging Initiative (ADNI) project. We further demonstrate how subject specific characteristics contribute to individual differences in longitudinal volume changes in healthy subjects, Mild Cognitive Impairment (MCI), and Alzheimer's Disease (AD).

SU‐E‐J‐241: Wavelet‐Based Temporal Feature Extraction From DCE‐MRI to Identify Sub‐Volumes of Low Blood Volume in Head‐And‐Neck Cancer

Purpose:A previous study showed that large sub‐volumes of tumor with low blood volume (BV) (poorly perfused) in head‐and‐neck (HN) cancers are significantly associated with local‐regional failure (LRF) after chemoradiation therapy, and could be targeted with intensified radiation doses. This study aimed to develop an automated and scalable model to extract voxel‐wise contrast‐enhanced temporal features of dynamic contrastenhanced (DCE) MRI in HN cancers for predicting LRF.Methods:Our model development consists of training and testing stages. The training stage includes preprocessing of individual‐voxel DCE curves from tumors for intensity normalization and temporal alignment, temporal feature extraction from the curves, feature selection, and training classifiers. For feature extraction, multiresolution Haar discrete wavelet transformation is applied to each DCE curve to capture temporal contrast‐enhanced features. The wavelet coefficients as feature vectors are selected. Support vector machine classifiers are trained to classify tumor voxels having either low or high BV, for which a BV threshold of 7.6% is previously established and used as ground truth. The model is tested by a new dataset. The voxel‐wise DCE curves for training and testing were from 14 and 8 patients, respectively. A posterior probability map of the low BV class was created to examine the tumor sub‐volume classification. Voxel‐wise classification accuracy was computed to evaluate performance of the model.Results:Average classification accuracies were 87.2% for training (10‐fold crossvalidation) and 82.5% for testing. The lowest and highest accuracies (patient‐wise) were 68.7% and 96.4%, respectively. Posterior probability maps of the low BV class showed the sub‐volumes extracted by our model similar to ones defined by the BV maps with most misclassifications occurred near the sub‐volume boundaries.Conclusion:This model could be valuable to support adaptive clinical trials with further validation. The framework could be extendable and scalable to extract temporal contrastenhanced features of DCE‐MRI in other tumors.We would like to acknowledge NIH for funding support: UO1 CA183848

Análisis espacial de la mortalidad por enfermedades cardiovasculares en la ciudad de Madrid, España

Cardiovascular disease is the leading cause of death worldwide, but its spatial distribution is not homogeneous. The objective of this study is to analyze the spatial pattern of mortality from these diseases for men and women, in the populated urban area (AUP) of the municipality of Madrid, and to identify spatial aggregations. An ecological study was carried out by census tract, for men and women in 2010. Standardized Mortality Ratio (SMR), Relative Risk Smoothing (RRS) and Posterior Probability (PP) were calculated to consider the spatial pattern of the disease. To identify spatial clusters the Moran index (Moran I) and the Local Index of Spatial Autocorrelation (LISA) were used. The results were mapped. SMR higher than 1.1 was observed mainly in central areas among men and in peripheral areas among women. The PP that RRS was higher than 1 surpassed 0.8 in the center and in the periphery, in both men and women. Moran's I was 0.04 for men and 0.03 for women (p <0.05 in both cases). Sex differences were observed in the spatial distribution of mortality cases. RME RRS and PP maps showed a heterogeneous pattern in men, whereas in women a clearer pattern was detected, with a relatively higher risk in peripheral areas of the AUP. The LISA method showed similar patterns to those previously observed.

An exploratory spatial analysis of geographical inequalities of birth intervals among young women in the Democratic Republic of Congo (DRC): a cross-sectional study.

BackgroundThe length of time between two successive live births (birth interval), is associated with child survival in the developing world. Short birth intervals (<24 months) contribute to infant and child mortality risks. Contraceptive use contributes to a reduction in short birth intervals, but evidence is lacking in the DRC. We aimed to investigate the proportion of short birth intervals at the provincial level among young women in the DRC.MethodsData from the Demographic and Health Survey undertaken in the DRC in 2007 were analyzed. Logistic regression and Bayesian geo-additive models were used to explain provincial inequalities in short birth intervals among women of reproductive age and young women. Posterior odds ratio (OR) and 95% credible region (CR) were estimated via Markov chain Monte Carlo (MCMC) techniques. Posterior spatial effects and the associated posterior probability maps were produced at the provincial-level to highlight provinces with a significant higher risk of short birth interval.ResultsThe overall proportion of short birth intervals among all women of reproductive age (15–49 years) and young women (15–24 years) were 30.2% and 38.7% respectively. In multivariate Bayesian geo-additive regression analyses, among the whole sample of women, living in rural areas [OR = 1.07, 95% CR: (0.97, 1.17)], exclusive breastfeeding [1.08 (1.00, 1.17)] and women with primary education [1.06 (1.00, 1.16)], were consistently associated with a higher risk of short birth intervals. For the young women, none of the factors considered were associated with the risk of short birth interval except a marginal effect from the lack of education. There was a spatial variation in the proportion of women reporting short birth intervals and among all women of reproductive age across provinces, with Nord-Kivu [1.12 (1.02, 1.24)], Sud Kivu [1.17 (1.05, 1.29)] and Kasai Occidental [1.18 (1.06, 1.32)] reporting a higher risk of short birth intervals. For young women, the higher risk provinces were Nord-Kivu [1.22 (1.00, 1.54)] and Sud Kivu [1.34 (1.14, 1.63)].ConclusionsThis study suggests distinct geographic patterns in the proportion of short birth intervals among Congolese women, as well as the potential role of demographic and geographic location factors driving the ongoing higher youth fertility, higher childhood and maternal mortality in the DRC.

A Wavelet‐Based Bayesian Approach to Regression Models with Long Memory Errors and Its Application to fMRI Data

This article considers linear regression models with long memory errors. These models have been proven useful for application in many areas, such as medical imaging, signal processing, and econometrics. Wavelets, being self-similar, have a strong connection to long memory data. Here we employ discrete wavelet transforms as whitening filters to simplify the dense variance-covariance matrix of the data. We then adopt a Bayesian approach for the estimation of the model parameters. Our inferential procedure uses exact wavelet coefficients variances and leads to accurate estimates of the model parameters. We explore performances on simulated data and present an application to an fMRI data set. In the application we produce posterior probability maps (PPMs) that aid interpretation by identifying voxels that are likely activated with a given confidence.

MEG for the masses: Approaches to group statistics in source space

Event Abstract Back to Event MEG for the masses: Approaches to group statistics in source space Jason R. Taylor1* and Richard Henson1 1 Cognition and Brain Sciences Unit, Medical Research Council (MRC), United Kingdom Techniques developed for fMRI analysis may be applied to distributed inverse solutions to enable group-level analysis and population inference about neural generators of MEG signals. The mass-univariate approach (statistical parametric mapping; SPM) suffers from a multiple comparison problem (MCP): Due to the large number of tests, some results are likely false positives. Random field theory, often used to correct for MCP in fMRI analyses, may be overly conservative with MEG source images because of non-monotonic smoothness kernels (long-range correlations) engendered by the inverse operator. Nonparametric analysis (SnPM) is robust to this smoothness problem but does not provide estimates of effect size and technically does not generalise to the population. Bayesian posterior probability maps (PPMs) do not require smoothness assumptions, suffer no MCP, and do provide an effect size; however, PPMs assume a Gaussian distribution over voxels. Data from a visual lexical decision experiment (240 English words, W; 240 pseudowords, PW) with 18 adult subjects, 306-sensor MEG (102 locations with one magnetometer and two planar gradiometers) were analysed. External noise was removed and head motion corrected with signal space separation (Neuromag); eye-blink artefacts were removed with independent components analysis (EEGLAB). Inverse solutions were obtained (minimum-norm and multiple sparse priors (MSP) schemes; in SPM5) for each condition. Inverse results were averaged in time-windows (170-600ms), smoothed along the cortical sheet (2D), written to image volumes, and smoothed in 3D. Group (2nd-level) analyses were conducted to compare W and PW sources using SPMs, SnPMs (both p<.05 FWE-corrected), and PPMs (P>.95 of effect>0). Results were generally consistent across methods and channel types (perisylvian PW>W sources; occipital and temporal polar W>PW sources). PPMs were the most sensitive; however, voxel distributions deviated from Gaussian, especially in the MSP scheme. Conference: Biomag 2010 - 17th International Conference on Biomagnetism , Dubrovnik, Croatia, 28 Mar - 1 Apr, 2010. Presentation Type: Poster Presentation Topic: Language Citation: Taylor JR and Henson R (2010). MEG for the masses: Approaches to group statistics in source space. Front. Neurosci. Conference Abstract: Biomag 2010 - 17th International Conference on Biomagnetism . doi: 10.3389/conf.fnins.2010.06.00262 Copyright: The abstracts in this collection have not been subject to any Frontiers peer review or checks, and are not endorsed by Frontiers. They are made available through the Frontiers publishing platform as a service to conference organizers and presenters. The copyright in the individual abstracts is owned by the author of each abstract or his/her employer unless otherwise stated. Each abstract, as well as the collection of abstracts, are published under a Creative Commons CC-BY 4.0 (attribution) licence (https://creativecommons.org/licenses/by/4.0/) and may thus be reproduced, translated, adapted and be the subject of derivative works provided the authors and Frontiers are attributed. For Frontiers’ terms and conditions please see https://www.frontiersin.org/legal/terms-and-conditions. Received: 01 Apr 2010; Published Online: 01 Apr 2010. * Correspondence: Jason R Taylor, Cognition and Brain Sciences Unit, Medical Research Council (MRC), Cambridge, United Kingdom, jason.taylor@manchester.ac.uk Login Required This action requires you to be registered with Frontiers and logged in. To register or login click here. Abstract Info Abstract The Authors in Frontiers Jason R Taylor Richard Henson Google Jason R Taylor Richard Henson Google Scholar Jason R Taylor Richard Henson PubMed Jason R Taylor Richard Henson Related Article in Frontiers Google Scholar PubMed Abstract Close Back to top Javascript is disabled. Please enable Javascript in your browser settings in order to see all the content on this page.

Bayesian model selection maps for group studies

This technical note describes the construction of posterior probability maps (PPMs) for Bayesian model selection (BMS) at the group level. This technique allows neuroimagers to make inferences about regionally specific effects using imaging data from a group of subjects. These effects are characterised using Bayesian model comparisons that are analogous to the F-tests used in statistical parametric mapping, with the advantage that the models to be compared do not need to be nested. Additionally, an arbitrary number of models can be compared together. This note describes the integration of the Bayesian mapping approach with a random effects analysis model for BMS using group data. We illustrate the method using fMRI data from a group of subjects performing a target detection task.

Conjunction analysis and propositional logic in fMRI data analysis using Bayesian statistics

To evaluate logical expressions over different effects in data analyses using the general linear model (GLM) and to evaluate logical expressions over different posterior probability maps (PPMs). In functional magnetic resonance imaging (fMRI) data analysis, the GLM was applied to estimate unknown regression parameters. Based on the GLM, Bayesian statistics can be used to determine the probability of conjunction, disjunction, implication, or any other arbitrary logical expression over different effects or contrast. For second-level inferences, PPMs from individual sessions or subjects are utilized. These PPMs can be combined to a logical expression and its probability can be computed. The methods proposed in this article are applied to data from a STROOP experiment and the methods are compared to conjunction analysis approaches for test-statistics. The combination of Bayesian statistics with propositional logic provides a new approach for data analyses in fMRI. Two different methods are introduced for propositional logic: the first for analyses using the GLM and the second for common inferences about different probability maps. The methods introduced extend the idea of conjunction analysis to a full propositional logic and adapt it from test-statistics to Bayesian statistics. The new approaches allow inferences that are not possible with known standard methods in fMRI.

Mineral Resource Prediction and Assessment of Copper Multi-mineral Deposit Based on GIS Technology in the North of Sanjiang Region, China

On the basis of the multi-information on geology, geophysics, geochemistry, and remote sensing, mineral resource prediction and assessment is one of the keystones and popular topics in quantificational geosciences both in China and abroad, for it can not only be used to extract metallogenetic information and delineate metallogenetic targets, but provide important data for the quantitative assessment of mineral resources. This article takes the northern part of Sanjiang region in the south of Qinghai Province, China, as a case study area. On the basis of the conventional mineralized factors of mineral resource prediction and assessment, combined with the research on post-ore change and preservation, a new insight into mineral resource prediction and assessment, in terms of regional mineralization, change, and preservation factors, is built on account of the features of deposits at high altitudes, big slopes, emergence in surface, and denudation in the study area. According to the 24 copper complex deposits and geological settings in the study area, 29 variations, including mineralized factors, change factors, and preservation factors have been extracted by Geographic Information System (GIS) technology. To show the effect of the new insight, two mineral resource prediction models have been built with the 29 variations and 20 mineralized variations, respectively. Weight-of-evidence modeling is applied to map copper complex potential areas in this study area. The posterior probability maps of copper complex deposits delineated by weights of evidence method are made by contrasting mineralized factors with mineralization, and also changed factors with preservation factors. The results of the latter is better than that of the former: on one hand, the latter eliminates the nonmineralized area that is produced by glacier, water, or wind denudation; on the other hand, it can delineate mineral prospects that have concealed mineralized stratum or magma.

Bayesian M/EEG source reconstruction with spatio-temporal priors

This article proposes a Bayesian spatio-temporal model for source reconstruction of M/EEG data. The usual two-level probabilistic model implicit in most distributed source solutions is extended by adding a third level which describes the temporal evolution of neuronal current sources using time-domain General Linear Models (GLMs). These comprise a set of temporal basis functions which are used to describe event-related M/EEG responses. This places M/EEG analysis in a statistical framework that is very similar to that used for PET and fMRI. The experimental design can be coded in a design matrix, effects of interest characterized using contrasts and inferences made using posterior probability maps. Importantly, as is the case for single-subject fMRI analysis, trials are treated as fixed effects and the approach takes into account between-trial variance, allowing valid inferences to be made on single-subject data. The proposed probabilistic model is efficiently inverted by using the Variational Bayes framework under a convenient mean-field approximation (VB-GLM). The new method is tested with biophysically realistic simulated data and the results are compared to those obtained with traditional spatial approaches like the popular Low Resolution Electromagnetic TomogrAphy (LORETA) and minimum variance Beamformer. Finally, the VB-GLM approach is used to analyze an EEG data set from a face processing experiment.

Implications for the Constrained MSSM from a new prediction forb→sγ

We re-examine the properties of the Constrained MSSM in light of updated constraints, paying particular attention to the impact of the recent substantial shift in the Standard Model prediction for → Xsγ. With the help of a Markov Chain Monte Carlo scanning technique, we vary all relevant parameters simultaneously and derive Bayesian posterior probability maps. We find that the case of μ > 0 remains favored, and that for μ < 0 it is considerably more difficult to find a good global fit to current constraints. In both cases we find a strong preference for a focus point region. This leads to improved prospects for detecting neutralino dark matter in direct searches, while superpartner searches at the LHC become more problematic, especially when μ < 0. In contrast, prospects for exploring the whole mass range of the lightest Higgs boson at the Tevatron and the LHC remain very good, which should, along with dark matter searches, allow one to gain access to the otherwise experimentally challenging focus point region. An alternative measure of the mean quality-of-fit which we also employ implies that present data are not yet constraining enough to draw more definite conclusions. We also comment on the dependence of our results on the choice of priors and on some other assumptions.