Topic
Maximum a posteriori estimation
About: Maximum a posteriori estimation is a research topic. Over the lifetime, 7486 publications have been published within this topic receiving 222291 citations. The topic is also known as: Maximum a posteriori, MAP & maximum a posteriori probability.
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TL;DR: A new prior setting for high-dimensional generalized linear models is presented, which leads to a Bayesian subset regression (BSR) with the maximum a posteriori model approximately equivalent to the minimum extended Bayesian information criterion model.
Abstract: This article presents a new prior setting for high-dimensional generalized linear models, which leads to a Bayesian subset regression (BSR) with the maximum a posteriori model approximately equivalent to the minimum extended Bayesian information criterion model. The consistency of the resulting posterior is established under mild conditions. Further, a variable screening procedure is proposed based on the marginal inclusion probability, which shares the same properties of sure screening and consistency with the existing sure independence screening (SIS) and iterative sure independence screening (ISIS) procedures. However, since the proposed procedure makes use of joint information from all predictors, it generally outperforms SIS and ISIS in real applications. This article also makes extensive comparisons of BSR with the popular penalized likelihood methods, including Lasso, elastic net, SIS, and ISIS. The numerical results indicate that BSR can generally outperform the penalized likelihood methods. The m...
69 citations
TL;DR: An adaptive MAP reconstruction method based upon a U-curve that is tested on both simulated and actual data, showing the effectiveness and robustness of this method, both in its visual effects and in quantitative terms.
Abstract: Image super-resolution (SR) reconstruction has been a hot research topic in recent years. This technique allows the recovery of a high-resolution (HR) image from several low-resolution (LR) images that are noisy, blurred and down-sampled. Among the available reconstruction frameworks, the maximum a posteriori (MAP) model is widely used. In this model, the regularization parameter plays an important role. If the parameter is too small, the noise will not be effectively restrained; conversely, the reconstruction result will become blurry. Therefore, how to adaptively select the optimal regularization parameter has been widely discussed. In this paper, we propose an adaptive MAP reconstruction method based upon a U-curve. To determine the regularization parameter, a U-curve function is first constructed using the data fidelity term and prior term, and then the left maximum curvature point of the curve is regarded as the optimal parameter. The proposed algorithm is tested on both simulated and actual data. Experimental results show the effectiveness and robustness of this method, both in its visual effects and in quantitative terms.
69 citations
TL;DR: An iterative procedure for time-recursive multitarget/multisensor tracking based on use of the expectation-maximization (EM) algorithm that provides a computationally efficient means for approaching the performance offered by theoretically optimum approaches that use explicit enumeration of the joint association probabilities.
Abstract: An important problem in surveillance and reconnaissance systems is the tracking of multiple moving targets in cluttered noise environments using outputs from a number of sensors possessing wide variations in individual characteristics and accuracies. A number of approaches have been proposed for this multitarget/multisensor tracking problem ranging from reasonably simple, though ad hoc, schemes to fairly complex, but theoretically optimum, approaches. In this paper, we describe an iterative procedure for time-recursive multitarget/multisensor tracking based on use of the expectation-maximization (EM) algorithm. More specifically, we pose the multitarget/multisensor tracking problem as an incomplete data problem with the observable sensor outputs representing the incomplete data, whereas the target-associated sensor outputs constitute the complete data. Target updates at each time use an EM-based approach that calculates the maximum a posteriori (MAP) estimate of the target states, under the assumption of appropriate motion models, based on the outputs of disparate sensors. The approach uses a Markov random field (MRF) model of the associations between observations and targets and allows for estimation of joint association probabilities without explicit enumeration. The advantage of this EM-based approach is that it provides a computationally efficient means for approaching the performance offered by theoretically optimum approaches that use explicit enumeration of the joint association probabilities. We provide selected results illustrating the performance/complexity characteristics of this EM-based approach compared with competing schemes.
69 citations
07 Jul 2001
TL;DR: A shape from texture method that constructs a maximum a posteriori estimate of surface coefficients using both the deformation of individual texture elements- as in local methods- and the overall distribution of elements-as in global methods is described.
Abstract: We describe a shape from texture method that constructs a maximum a posteriori estimate of surface coefficients using both the deformation of individual texture elements-as in local methods-and the overall distribution of elements-as in global methods. The method described applies to a much larger family of textures than any previous method, local or global. We demonstrate an analogy with shape from shading, and use this to produce a numerical method. Examples of reconstructions for synthetic images of surfaces are provided, and compared with ground truth. The method is defined for orthographic views, but can be generalised to perspective views simply.
69 citations
TL;DR: The presented approach accounts for all sources of uncertainties involved in hydrologic predictions, uses a small ensemble size, and precludes the particle degeneracy and sample impoverishment, and the effectiveness, robustness, and reliability of the method is demonstrated for several river basins across the United States.
Abstract: This article presents a novel approach to couple a deterministic four-dimensional variational (4DVAR) assimilation method with the particle filter (PF) ensemble data assimilation system, to produce a robust approach for dual-state-parameter estimation. In our proposed method, the Hybrid Ensemble and Variational Data Assimilation framework for Environmental systems (HEAVEN), we characterize the model structural uncertainty in addition to model parameter and input uncertainties. The sequential PF is formulated within the 4DVAR system to design a computationally efficient feedback mechanism throughout the assimilation period. In this framework, the 4DVAR optimization produces the maximum a posteriori estimate of state variables at the beginning of the assimilation window without the need to develop the adjoint of the forecast model. The 4DVAR solution is then perturbed by a newly defined prior error covariance matrix to generate an initial condition ensemble for the PF system to provide more accurate and reliable posterior distributions within the same assimilation window. The prior error covariance matrix is updated from one cycle to another over the main assimilation period to account for model structural uncertainty resulting in an improved estimation of posterior distribution. The premise of the presented approach is that it (1) accounts for all sources of uncertainties involved in hydrologic predictions, (2) uses a small ensemble size, and (3) precludes the particle degeneracy and sample impoverishment. The proposed method is applied on a nonlinear hydrologic model and the effectiveness, robustness, and reliability of the method is demonstrated for several river basins across the United States.
69 citations