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  • 1.
    Gu, Xuan
    et al.
    Linköping University, Department of Biomedical Engineering, Division of Biomedical Engineering. Linköping University, Faculty of Science & Engineering. Linköping University, Center for Medical Image Science and Visualization (CMIV).
    Sidén, Per
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Science & Engineering.
    Wegmann, Bertil
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Science & Engineering.
    Eklund, Anders
    Linköping University, Department of Biomedical Engineering, Division of Biomedical Engineering. Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Science & Engineering. Linköping University, Center for Medical Image Science and Visualization (CMIV).
    Villani, Mattias
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Science & Engineering.
    Knutsson, Hans
    Linköping University, Department of Biomedical Engineering, Division of Biomedical Engineering. Linköping University, Faculty of Science & Engineering. Linköping University, Center for Medical Image Science and Visualization (CMIV).
    Bayesian Diffusion Tensor Estimation with Spatial Priors2017In: CAIP 2017: Computer Analysis of Images and Patterns, 2017, Vol. 10424, p. 372-383Conference paper (Refereed)
    Abstract [en]

    Spatial regularization is a technique that exploits the dependence between nearby regions to locally pool data, with the effect of reducing noise and implicitly smoothing the data. Most of the currently proposed methods are focused on minimizing a cost function, during which the regularization parameter must be tuned in order to find the optimal solution. We propose a fast Markov chain Monte Carlo (MCMC) method for diffusion tensor estimation, for both 2D and 3D priors data. The regularization parameter is jointly with the tensor using MCMC. We compare FA (fractional anisotropy) maps for various b-values using three diffusion tensor estimation methods: least-squares and MCMC with and without spatial priors. Coefficient of variation (CV) is calculated to measure the uncertainty of the FA maps calculated from the MCMC samples, and our results show that the MCMC algorithm with spatial priors provides a denoising effect and reduces the uncertainty of the MCMC samples.

  • 2.
    Wegmann, Bertil
    Linköping University, Department of Computer and Information Science, Statistics. Linköping University, Faculty of Arts and Sciences.
    Bayesian comparison of private and common values in structural second-price auctions2015In: Journal of Applied Statistics, ISSN 0266-4763, E-ISSN 1360-0532, Vol. 42, no 2, p. 380-397Article in journal (Refereed)
    Abstract [en]

    Private and common values (CVs) are the two main competing valuation models in auction theory and empirical work. In the framework of second-price auctions, we compare the empirical performance of the independent private value (IPV) model to the CV model on a number of different dimensions, both on real data from eBay coin auctions and on simulated data. Both models fit the eBay data well with a slight edge for the CV model. However, the differences between the fit of the models seem to depend to some extent on the complexity of the models. According to log predictive score the IPV model predicts auction prices slightly better in most auctions, while the more robust CV model is much better at predicting auction prices in more unusual auctions. In terms of posterior odds, the CV model is clearly more supported by the eBay data.

  • 3.
    Wegmann, Bertil
    et al.
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Science & Engineering.
    Eklund, Anders
    Linköping University, Department of Biomedical Engineering, Division of Biomedical Engineering. Linköping University, Faculty of Science & Engineering. Linköping University, Center for Medical Image Science and Visualization (CMIV).
    Villani, Mattias
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Arts and Sciences.
    Bayesian Heteroscedastic Regression for Diffusion Tensor Imaging2017In: Modeling, Analysis, and Visualization of Anisotropy / [ed] Thomas Schultz; Evren Özarslan; Ingrid Hotz, Springer Publishing Company, 2017, 1, p. 257-282Conference paper (Refereed)
    Abstract [en]

    We propose a single-diffusion tensor model with heteroscedastic noise and a Bayesian approach via a highly efficient Markov Chain Monte Carlo (MCMC) algorithm for inference. The model is very flexible since both the noise-free signal and the noise variance are functions of diffusion covariates, and the relevant covariates in the noise are automatically selected by Bayesian variable selection. We compare the estimated diffusion tensors from our model to a homoscedastic counterpart with no covariates in the noise, and to commonly used linear and nonlinear least squares methods. The estimated single-diffusion tensors within each voxel are compared with respect to fractional anisotropy (FA) and mean diffusivity (MD). Using data from the Human Connectome Project, our results show that the noise is clearly heteroscedastic, especially the posterior variance for MD is substantially underestimated by the homoscedastic model, and inferences from the homoscedastic model are on average spuriously precise. Inferences from commonly used ordinary and weighted least squares methods (OLS and WLS) show that it is not adequate to estimate the single-diffusion tensor from logarithmic measurements.

  • 4.
    Wegmann, Bertil
    et al.
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Arts and Sciences.
    Eklund, Anders
    Linköping University, Department of Biomedical Engineering, Division of Biomedical Engineering. Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Science & Engineering. Linköping University, Faculty of Arts and Sciences. Linköping University, Center for Medical Image Science and Visualization (CMIV).
    Villani, Mattias
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Arts and Sciences.
    Bayesian Rician Regression for Neuroimaging2017In: Frontiers in Neuroscience, ISSN 1662-4548, E-ISSN 1662-453X, Vol. 11, article id 586Article in journal (Refereed)
    Abstract [en]

    It is well-known that data from diffusion weighted imaging (DWI) follow the Rician distribution. The Rician distribution is also relevant for functional magnetic resonance imaging (fMRI) data obtained at high temporal or spatial resolution. We propose a general regression model for non-central chi (NC-chi) distributed data, with the heteroscedastic Rician regression model as a prominent special case. The model allows both parameters in the Rician distribution to be linked to explanatory variables, with the relevant variables chosen by Bayesian variable selection. A highly efficient Markov chain Monte Carlo (MCMC) algorithm is proposed to capture full model uncertainty by simulating from the joint posterior distribution of all model parameters and the binary variable selection indicators. Simulated regression data is used to demonstrate that the Rician model is able to detect the signal much more accurately than the traditionally used Gaussian model at low signal-to-noise ratios. Using a diffusion dataset from the Human Connectome Project, it is also shown that the commonly used approximate Gaussian noise model underestimates the mean diffusivity (MD) and the fractional anisotropy (FA) in the single-diffusion tensor model compared to the Rician model.

  • 5.
    Wänström, Linda
    et al.
    Linköping University, Department of Computer and Information Science, Statistics. Linköping University, Faculty of Arts and Sciences.
    Wegmann, Bertil
    Linköping University, Department of Computer and Information Science, Statistics. Linköping University, Faculty of Arts and Sciences.
    Effects of sibship size on intelligence, school performance and adult income: Some evidence from Swedish data2017In: Intelligence, ISSN 0160-2896, E-ISSN 1873-7935, Vol. 62Article in journal (Refereed)
    Abstract [en]

    We examine the effects of child sibship size on intelligence, school performance and adult income for a sample of Swedish school children (n = 1326). These children were measured in grade three in 1965 (age 10) and in grades six (age 13) and nine (age 16), and the women and men were later followed up in adulthood at ages 43 and 47, respectively. Using Bayesian varying-intercept modeling we account for differences between school classes in each of our three response variables: IQ-scores, school grades and adult income, and control for background variables such as gender, socioeconomic status, and maternal- and paternal age. Consistent with previous research, we find patterns of decreasing IQ scores for increasing sibship sizes, specifically for an increasing number of older siblings. No relationships between sibship size and childrens school grades are found. We find, however, patterns of decreasing adult income for an increasing number of younger siblings. In addition, considerable amounts of variations in intelligence scores as well as school grades are found between school classes. Some implications of the findings and suggestions for future research are provided. (C) 2017 Elsevier Inc. All rights reserved.

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