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Results for “generalized Bayesian information criterion”

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At least 19 recordsLinked to original sources
PubMed2026

A flexible framework for robust and efficient Mendelian randomization with debiasing.

Mendelian randomization (MR) has been widely used to infer causal relationships between exposures and outcomes in epidemiological studies. However, classical MR assumptions can be violated when genetic variants are associated with outcomes through pathways other than the exposure, leading to uncorrelated and/or correlated pleiotropy. Additionally, measurement error arising from the inherent uncertainty in summary statistics obtained from large-scale genome-wide association studies can introduce bias into the causal effect estimate. To address these issues, we develop a debiased mixture inverse variance weighting ($\mathsf{dmIVW}$) method with three major advantages. First, it is capable of simultaneously handling various types of pleiotropy and eliminating the bias caused by uncertainty. Second, it can guard against distortion caused by invalid genetic variants while effectively harnessing their information. Third, our unified framework facilitates a fair comparison and combination of a series of submodels, encompassing several popular MR methods as special cases. Through real data applications, the effectiveness and robustness of $\mathsf{dmIVW}$ in estimating the causal effects of risk factors on common diseases are demonstrated.

Mendelian Randomization Analysis↗
PubMed1994

Designing an optimal experiment for Bayesian estimation: application to the kinetics of iodine thyroid uptake.

We consider the problem of designing an optimal experiment for Bayesian estimation of the parameters of a non-linear model. When their distribution is known, the Bayesian approach allows individual estimation from a small number of measurements; the design determines the accuracy of the estimates. We propose to optimize this design by maximizing a general criterion: the expectation of the information supplied by the experiment. This approach is applied to optimize the two sampling times for Bayesian estimation of the kinetics of radioiodine thyroid uptake from an estimated non-parametric prior distribution.

Bayes Theorem↗
PubMed1996

Optimized sampling and parameter estimation for quantification in whole body PET.

Whole-body positron emission tomography (PET) has recently emerged as an important imaging tool for cancer detection and staging. Initial applications of the technique have been primarily qualitative. One of the major reasons is the limits imposed by kinetically undersampled data over the whole body, as opposed to the standard method of continuous dynamic sampling in one body location. In this paper, a new estimation method using weighted nonlinear least squares (WNLS) for the first bed position and Bayesian regression (BR) for subsequent positions is proposed. A general criterion for designing optimal sampling schedules which maximizes the measurement information with multiple bed positions is developed. The overall approach is illustrated with the problem of estimating the metabolic rate of glucose (MRGLu) in tumors at different axial positions (image bed positions) in the body by using computer simulations and patient data. The results show that estimates of MRGLu using sparse data and the optimized Bayesian approach are comparable with those obtained by standard methods and fully sampled data. This study demonstrates the potential of the technique described for quantification where several bed positions have to be used to image all the regions of interest (ROI).

Abdominal Muscles↗
PubMed2004

Advances on BYY harmony learning: information theoretic perspective, generalized projection geometry, and independent factor autodetermination.

The nature of Bayesian Ying-Yang harmony learning is reexamined from an information theoretic perspective. Not only its ability for model selection and regularization is explained with new insights, but also discussions are made on its relations and differences from the studies of minimum description length (MDL), Bayesian approach, the bit-back based MDL, Akaike information criterion (AIC), maximum likelihood, information geometry, Helmholtz machines, and variational approximation. Moreover, a generalized projection geometry is introduced for further understanding such a new mechanism. Furthermore, new algorithms are also developed for implementing Gaussian factor analysis (FA) and non-Gaussian factor analysis (NFA) such that selecting appropriate factors is automatically made during parameter learning.

Algorithms↗
PubMed2004

Recursive penalized least squares solution for dynamical inverse problems of EEG generation.

In the dynamical inverse problem of electroencephalogram (EEG) generation where a specific dynamics for the electrical current distribution is assumed, we can impose general spatiotemporal constraints onto the solution by casting the problem into a state space representation and assuming a specific class of parametric models for the dynamics. The Akaike Bayesian Information Criterion (ABIC), which is based on the Type II likelihood, was used to estimate the parameters and evaluate the model. In addition, dynamic low-resolution brain electromagnetic tomography (LORETA), a new approach for estimating the current distribution is introduced. A recursive penalized least squares (RPLS) step forms the main element of our implementation. To obtain improved inverse solutions, dynamic LORETA exploits both spatial and temporal information, whereas LORETA uses only spatial information. A considerable improvement in performance compared to LORETA was found when dynamic LORETA was applied to simulated EEG data, and the new method was applied also to clinical EEG data.

Brain↗
PubMed2006

A comparison of the latent class structure of cannabis problems among adult men and women who have used cannabis repeatedly.

BACKGROUND: Little empirical evidence exists to determine if there are alternative classification schemes for cannabis abuse and dependence beyond the definitions provided by Diagnostic and Statistical Manual (DSM) criteria. Current evidence is not conclusive regarding gender differences for cannabis use, abuse and dependence. It is not known if symptom profiles differ by gender. METHODS: Latent class analysis (LCA) was used to assess whether cannabis abuse and dependence symptom patterns suggest a severity spectrum or distinct subtypes and to test whether symptom patterns differ by gender. Data from 3312 men and 2509 women in the National Longitudinal Alcohol Epidemiologic Survey (NLAES) who had used cannabis 12 + times life-time were included in the present analyses. The comparability of the solutions for men and women was examined through likelihood ratio chi(2) tests. RESULTS: Based on the Bayesian information criterion and interpretability, a four-class solution was selected, and the classes were labeled as 'unaffected/mild hazardous use', 'hazardous use/abuse', 'abuse/moderate dependence' and 'severe abuse/dependence'. The solutions were generally suggestive of a severity spectrum. Compared to men, women were more likely to be in the 'unaffected/mild hazardous use' class and less likely to be in the 'abuse/moderate dependence' or 'severe abuse/dependence' classes. The results were generally similar for men and women. However, men had consistently and substantially higher endorsements of hazardous use than women, women in the 'abuse/moderate dependence' class had moderately higher rates for four dependence symptoms, and women in two of the classes were more likely to endorse withdrawal. CONCLUSION: Our findings generally support the severity dimension for DSM-IV cannabis abuse and dependence symptomatology for both men and women. While our results indicate that public health messages may have generic and not gender-specific content, treatment providers should focus more effort on reducing hazardous use in men and alleviating withdrawal in women.

Adolescent↗
PubMed2006

An artificial neural network-based expert system for the appraisal of two-car crash accidents.

This paper employs artificial neural network (ANN) to develop an accident appraisal expert system. Two ANN models-- party-based and case-based-- with different hidden neurons are trained and validated by k-fold (k=3) cross validation method. A total of 537 two-car crash accidents (1074 parties involved) are randomly and equally divided into three subsets. For the comparison, a discrimination analysis (DA) model is also calibrated. The results show that the ANN model can achieve a high correctness rate of 85.72% in training and 77.91% in validation and a low Schwarz's Bayesian information criterion (SBC) of -0.82 in training and 0.13 in validation, which indicates that the ANN model is suitable for accident appraisal. Furthermore, in order to measure the importance of each explanatory variable, a general influence (GI) index is computed based on the trained weights of ANN. It is found that the most influential variable is right-of-way, followed by location and alcoholic use. This finding concurs with the prior knowledge in accident appraisal. Thus, for the fair assessment of accident liabilities the correctness of these three key variables is of critical importance to police investigation reports.

Accidents, Traffic↗
PubMed2005

Detection of intensity change points in time-resolved single-molecule measurements.

We present a method for the analysis of optical single molecule emission data that exhibit discrete intensity jumps. This new method uses a generalized likelihood ratio test that determines the location of an intensity change point based on individual photon arrival times. This test is applied recursively to an entire single molecule intensity trajectory, thus finding each change points. Expectation-maximization clustering and the Bayesian information criterion is then used for accurate determination of the true number of states accessible to the system. This procedure allows rigorous and quantitative determination of intensity change points without the artificial time resolution limitations that arise from binning and thresholding.

Journal Article↗
PubMedDate not supplied

Comparing hierarchical models for spatio-temporally misaligned data using the deviance information criterion.

Bayes and empirical Bayes methods have proven effective in smoothing crude maps of disease risk, eliminating the instability of estimates in low-population areas while maintaining overall geographic trends and patterns. Recent work extends these methods to the analysis of areal data which are spatially misaligned, that is, involving variables (typically counts or rates) which are aggregated over differing sets of regional boundaries. The addition of a temporal aspect complicates matters further, since now the misalignment can arise either within a given time point, or across time points (as when the regional boundaries themselves evolve over time). Hierarchical Bayesian methods (implemented via modern Markov chain Monte Carlo computing methods) enable the fitting of such models, but a formal comparison of their fit is hampered by their large size and often improper prior specifications. In this paper, we accomplish this comparison using the deviance information criterion (DIC), a recently proposed generalization of the Akaike information criterion (AIC) designed for complex hierarchical model settings like ours. We investigate the use of the delta method for obtaining an approximate variance estimate for DIC, in order to attach significance to apparent differences between models. We illustrate our approach using a spatially misaligned data set relating a measure of traffic density to paediatric asthma hospitalizations in San Diego County, California.

Asthma↗
PubMed2006

Adjustments for heterogeneous herd-year variances in a random regression model for genetic evaluations of Polish Black-and-White cattle.

The study investigated the existence of heterogeneous variance in first-lactation daily milk yield of Polish Black-and-White cows across herds in different years. Bayesian Information Criterion was used to show that the model with unequal residual variances for different herd-years was more plausible than the model assuming equal variances. A method of adjusting phenotypic records was developed to account for unequal variability in herd-years. Factors used for the data adjustment considered variation of general residuals and residuals for specific herd-years. The size of herd-year was also taken into account. Varied power of corrections was used to analyze the effect of adjustment on estimated breeding values. The method was applied to daily milk records of 817,165 primiparous cows. The effectiveness of the data adjustment was evaluated by the analysis of differences between each bull's breeding value and its parental index. Data correction reduced the average difference and variance of differences between breeding values and parental indices. Accounting for the size of herd-year classes in correction factors improved the efficiency of heterogeneous variance adjustment.

Analysis of Variance↗
PubMed2004

Modifying the Schwarz Bayesian information criterion to locate multiple interacting quantitative trait loci.

The problem of locating multiple interacting quantitative trait loci (QTL) can be addressed as a multiple regression problem, with marker genotypes being the regressor variables. An important and difficult part in fitting such a regression model is the estimation of the QTL number and respective interactions. Among the many model selection criteria that can be used to estimate the number of regressor variables, none are used to estimate the number of interactions. Our simulations demonstrate that epistatic terms appearing in a model without the related main effects cause the standard model selection criteria to have a strong tendency to overestimate the number of interactions, and so the QTL number. With this as our motivation we investigate the behavior of the Schwarz Bayesian information criterion (BIC) by explaining the phenomenon of the overestimation and proposing a novel modification of BIC that allows the detection of main effects and pairwise interactions in a backcross population. Results of an extensive simulation study demonstrate that our modified version of BIC performs very well in practice. Our methodology can be extended to general populations and higher-order interactions.

Bayes Theorem↗
PubMed2006

Model comparison of generalized linear mixed models.

Generalized linear mixed models (GLMMs) have been widely appreciated in biological and medical research. Maximum likelihood estimation has received a great deal of attention. Comparatively, not much has been done on model comparison or hypotheses testing. In this article, we propose a path sampling procedure to compute the observed-data log-likelihood function, so that the Bayesian information criterion (BIC) can be applied to model comparison or hypothesis testing. Advantages of the proposed path sampling procedure are discussed. Two medical data sets are analysed for providing illustrative examples of the proposed methodology.

Air Pollution↗
PubMed2003

Bayesian multimodality non-rigid image registration via conditional density estimation.

We present a Bayesian multimodality non-rigid image registration method. Since the likelihood is unknown in the general multimodality setting, we use a density estimator as a drop in replacement to the true likelihood. The prior is a standard small deformation penalty on the displacement field. Since mutual information-based methods are in widespread use for multimodality registration, we attempt to relate the Bayesian approach to mutual information-based approaches. To this end, we derive a new criterion which when satisfied, guarantees that the displacement field which minimizes the Bayesian maximum a posteriori (MAP) objective also maximizes the true mutual information (with a small deformation penalty) as the number of pixels tends to infinity. The criterion imposes an upper bound on the number of configurations of the displacement field. Finally, we compare the results of the Bayesian approach with mutual information, joint entropy and joint probability approaches on synthetic data and simulated T1 and T2 2D MR images.

Algorithms↗
PubMedDate not supplied

A general approach to mixed effects modeling of residual variances in generalized linear mixed models.

We propose a general Bayesian approach to heteroskedastic error modeling for generalized linear mixed models (GLMM) in which linked functions of conditional means and residual variances are specified as separate linear combinations of fixed and random effects. We focus on the linear mixed model (LMM) analysis of birth weight (BW) and the cumulative probit mixed model (CPMM) analysis of calving ease (CE). The deviance information criterion (DIC) was demonstrated to be useful in correctly choosing between homoskedastic and heteroskedastic error GLMM for both traits when data was generated according to a mixed model specification for both location parameters and residual variances. Heteroskedastic error LMM and CPMM were fitted, respectively, to BW and CE data on 8847 Italian Piemontese first parity dams in which residual variances were modeled as functions of fixed calf sex and random herd effects. The posterior mean residual variance for male calves was over 40% greater than that for female calves for both traits. Also, the posterior means of the standard deviation of the herd-specific variance ratios (relative to a unitary baseline) were estimated to be 0.60 +/- 0.09 for BW and 0.74 +/- 0.14 for CE. For both traits, the heteroskedastic error LMM and CPMM were chosen over their homoskedastic error counterparts based on DIC values.

Analysis of Variance↗
PubMed2006

Bayesian perspectives for epidemiological research: I. Foundations and basic methods.

One misconception (of many) about Bayesian analyses is that prior distributions introduce assumptions that are more questionable than assumptions made by frequentist methods; yet the assumptions in priors can be more reasonable than the assumptions implicit in standard frequentist models. Another misconception is that Bayesian methods are computationally difficult and require special software. But perfectly adequate Bayesian analyses can be carried out with common software for frequentist analysis. Under a wide range of priors, the accuracy of these approximations is just as good as the frequentist accuracy of the software--and more than adequate for the inaccurate observational studies found in health and social sciences. An easy way to do Bayesian analyses is via inverse-variance (information) weighted averaging of the prior with the frequentist estimate. A more general method expresses the prior distributions in the form of prior data or 'data equivalents', which are then entered in the analysis as a new data stratum. That form reveals the strength of the prior judgements being introduced and may lead to tempering of those judgements. It is argued that a criterion for scientific acceptability of a prior distribution is that it be expressible as prior data, so that the strength of prior assumptions can be gauged by how much data they represent.

Bayes Theorem↗
PubMed2005

Unified SPM-ICA for fMRI analysis.

A widely used tool for functional magnetic resonance imaging (fMRI) data analysis, statistical parametric mapping (SPM), is based on the general linear model (GLM). SPM therefore requires a priori knowledge or specific assumptions about the time courses contributing to signal changes. In contradistinction, independent component analysis (ICA) is a data-driven method based on the assumption that the causes of responses are statistically independent. Here we describe a unified method, which combines ICA, temporal ICA (tICA), and SPM for analyzing fMRI data. tICA was applied to fMRI datasets to disclose independent components, whose number was determined by the Bayesian information criterion (BIC). The resulting components were used to construct the design matrix of a GLM. Parameters were estimated and regionally-specific statistical inferences were made about activations in the usual way. The sensitivity and specificity were evaluated using Monte Carlo simulations. The receiver operating characteristic (ROC) curves indicated that the unified SPM-ICA method had a better performance. Moreover, SPM-ICA was applied to fMRI datasets from twelve normal subjects performing left and right hand movements. The areas identified corresponded to motor (premotor, sensorimotor areas and SMA) areas and were consistently task related. Part of the frontal lobe, parietal cortex, and cingulate gyrus also showed transiently task-related responses. The unified method requires less supervision than the conventional SPM and enables classical inference about the expression of independent components. Our results also suggest that the method has a higher sensitivity than SPM analyses.

Adult↗
PubMed1997

Treatment-patient interactions for diagnostics of cross-over trials.

In cross-over trials, various types of responses may be recorded, not all of which can be appropriately modelled by a Normal distribution. Widening the class of models to the generalized linear model family has a number of advantages. An important one is that certain interactions, especially that between patients and treatments, can easily be fitted for frequency and count data. These can be used as diagnostics for the fit of the model used. One handicap has been the frequentist difficulty of comparing the fit of different non-nested models in this family. This can be overcome by the use of a model selection criterion such as the Akaike or Bayesian information criterion. This approach to modelling and diagnostics for cross-over trials is applied to two studies involving small counts of anginal attacks, previously analysed in the literature using classical Normal techniques.

Clinical Trials as Topic↗
PubMed2004

Parametric spatial cure rate models for interval-censored time-to-relapse data.

Several recent papers (e.g., Chen, Ibrahim, and Sinha, 1999, Journal of the American Statistical Association 94, 909-919; Ibrahim, Chen, and Sinha, 2001a, Biometrics 57, 383-388) have described statistical methods for use with time-to-event data featuring a surviving fraction (i.e., a proportion of the population that never experiences the event). Such cure rate models and their multivariate generalizations are quite useful in studies of multiple diseases to which an individual may never succumb, or from which an individual may reasonably be expected to recover following treatment (e.g., various types of cancer). In this article we extend these models to allow for spatial correlation (estimable via zip code identifiers for the subjects) as well as interval censoring. Our approach is Bayesian, where posterior summaries are obtained via a hybrid Markov chain Monte Carlo algorithm. We compare across a broad collection of rather high-dimensional hierarchical models using the deviance information criterion, a tool recently developed for just this purpose. We apply our approach to the analysis of a smoking cessation study where the subjects reside in 53 southeastern Minnesota zip codes. In addition to the usual posterior estimates, our approach yields smoothed zip code level maps of model parameters related to the relapse rates over time and the ultimate proportion of quitters (the cure rates).

Algorithms↗