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.

On Small-Sample Estimation

Abstract: This paper discusses some of the concepts underlying small sample estimation and reexamines, in particular, the current notions on "unbiased" estimation. Alternatives to the usual unbiased property are examined with respect to invariance under simultaneous one-to-one transformation of parameter and estimate; one of these alternatives, closely related to the maximum likelihood method, seems to be new. The property of being unbiased in the likelihood sense is essentially equivalent to the statement that the estimate is a maximum likelihood estimate based on some distribution derived by integration from the original sampling distribution, by virtue of a "hereditary" property of maximum likelihood estimation. An exposition of maximum likelihood estimation is given in terms of optimum pairwise selection with equal weights, providing a type of rationale for small sample estimation by maximum likelihood.

Three-dimensional super-resolution structured illumination microscopy with maximum a posteriori probability image estimation

Abstract: We introduce and demonstrate a new high performance image reconstruction method for super-resolution structured illumination microscopy based on maximum a posteriori probability estimation (MAP-SIM). Imaging performance is demonstrated on a variety of fluorescent samples of different thickness, labeling density and noise levels. The method provides good suppression of out of focus light, improves spatial resolution, and allows reconstruction of both 2D and 3D images of cells even in the case of weak signals. The method can be used to process both optical sectioning and super-resolution structured illumination microscopy data to create high quality super-resolution images.

Generalized Iterated Kalman Filter and its Performance Evaluation

Abstract: In this paper, we present a generalized iterated Kalman filter (GIKF) algorithm for state estimation of a nonlinear stochastic discrete-time system with state-dependent multiplicative observation noise. The GIKF algorithm adopts the Newton–Raphson iterative optimization steps to yield an approximate maximum a posteriori estimate of the states. The mean-square estimation error (MSE) and the Cramer–Rao lower bound (CRLB) of the state estimates are also derived. In particular, the local convergence of MSE of GIKF is rigorously established. It is also proved that the GIKF yields a smaller MSE than those of the generalized extended Kalman filter and the traditional extended Kalman filter. The performance advantages and convergence of GIKF are demonstrated using Monte Carlo simulations on a target tracking application in a range measuring sensor network.

The effects of partial observability when building fully correlated maps

Abstract: This paper presents an analysis of the fully correlated approach to the simultaneous localization and map building (SLAM) problem from a control systems theory point of view, both for linear and nonlinear vehicle models. We show how partial observability hinders full reconstructibility of the state space, making the final map estimate dependent on the initial observations. Nevertheless, marginal filter stability guarantees convergence of the state error covariance to a positive semidefinite covariance matrix. By characterizing the form of the total Fisher information, we are able to determine the unobservable state space directions. Moreover, we give a closed-form expression that links the amount of reconstruction error to the number of landmarks used. The analysis allows the formulation of measurement models that make SLAM observable.

Automatic lung lobe segmentation using particles, thin plate splines, and maximum a posteriori estimation

Abstract: We present a fully automatic lung lobe segmentation algorithm that is effective in high resolution computed tomography (CT) datasets in the presence of confounding factors such as incomplete fissures (anatomical structures indicating lobe boundaries), advanced disease states, high body mass index (BMI), and low-dose scanning protocols. In contrast to other algorithms that leverage segmentations of auxiliary structures (esp. vessels and airways), we rely only upon image features indicating fissure locations. We employ a particle system that samples the image domain and provides a set of candidate fissure locations. We follow this stage with maximum a posteriori (MAP) estimation to eliminate poor candidates and then perform a post-processing operation to remove remaining noise particles. We then fit a thin plate spline (TPS) interpolating surface to the fissure particles to form the final lung lobe segmentation. Results indicate that our algorithm performs comparably to pulmonologist-generated lung lobe segmentations on a set of challenging cases.