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.

An accelerated convergent ordered subsets algorithm for emission tomography.

Abstract: We propose an algorithm, E-COSEM (enhanced complete-data ordered subsets expectation-maximization), for fast maximum likelihood (ML) reconstruction in emission tomography E-COSEM is founded on an incremental EM approach Unlike the familiar OSEM (ordered subsets EM) algorithm which is not convergent, we show that E-COSEM converges to the ML solution Alternatives to the OSEM include RAMLA, and for the related maximum a posteriori (MAP) problem, the BSREM and OS-SPS algorithms These are fast and convergent, but require a judicious choice of a user-specified relaxation schedule E-COSEM itself uses a sequence of iteration-dependent parameters (very roughly akin to relaxation parameters) to control a tradeoff between a greedy, fast but non-convergent update and a slower but convergent update These parameters are computed automatically at each iteration and require no user specification For the ML case, our simulations show that E-COSEM is nearly as fast as RAMLA

Simulation-based Regularized Logistic Regression

Abstract: In this paper, we develop a simulation-based framework for regu- larized logistic regression, exploiting two novel results for scale mixtures of nor- mals. By carefully choosing a hierarchical model for the likelihood by one type of mixture, and implementing regularization with another, we obtain new MCMC schemes with varying e-ciency depending on the data type (binary v. binomial, say) and the desired estimator (maximum likelihood, maximum a posteriori, poste- rior mean). Advantages of our omnibus approach include ∞exibility, computational e-ciency, applicability in p ? n settings, uncertainty estimates, variable selection, and assessing the optimal degree of regularization. We compare our methodology to modern alternatives on both synthetic and real data. An R package called reglogit is available on CRAN.

Optimal sampling strategy development methodology using maximum a posteriori Bayesian estimation.

Abstract: Maximum a posteriori Bayesian (MAPB) pharmacokinetic parameter estimation is an accurate and flexible method of estimating individual pharmacokinetic parameters using individual blood concentrations and prior information. In the past decade, many studies have developed optimal sampling strategies to estimate pharmacokinetic parameters as accurately as possible using either multiple regression analysis or MAPB estimation. This has been done for many drugs, especially immunosuppressants and anticancer agents. Methods of development for optimal sampling strategies (OSS) are diverse and heterogeneous. This review provides a comprehensive overview of OSS development methodology using MAPB pharmacokinetic parameter estimation, determines the transferability of published OSSs, and compares sampling strategies determined by MAPB estimation and multiple regression analysis. OSS development has the following components: 1) prior distributions; 2) reference value determination; 3) optimal sampling time identification; and 4) validation of the OSS. Published OSSs often lack all data necessary for the OSS to be clinically transferable. MAPB estimation is similar to multiple regression analysis in terms of predictive performance but superior in flexibility.

Fundamental limits of Bayesian inference: order parameters and phase transitions for road tracking

Abstract: There is a growing interest in formulating vision problems in terms of Bayesian inference and, in particular, the maximum a posteriori (MAP) estimator. In this paper, we consider the special case of detecting roads from aerial images and demonstrate that analysis of this ensemble enables us to determine fundamental bounds on the performance of the MAP estimate. We demonstrate that there is a phase transition at a critical value of the order parameter; below this phase transition, it is impossible to detect the road by any algorithm. We derive closely related order parameters which determine the time and memory complexity of search and the accuracy of the solution using the n* search strategy. Our approach can be applied to other vision problems, and we briefly summarize the results when the model uses the "wrong prior". We comment on how our work relates to studies of the complexity of visual search and the critical behaviour in the computational cost of solving NP-complete problems.

Back to Basics for Bayesian Model Building in Genomic Selection

Abstract: Numerous Bayesian methods of phenotype prediction and genomic breeding value estimation based on multilocus association models have been proposed. Computationally the methods have been based either on Markov chain Monte Carlo or on faster maximum a posteriori estimation. The demand for more accurate and more efficient estimation has led to the rapid emergence of workable methods, unfortunately at the expense of well-defined principles for Bayesian model building. In this article we go back to the basics and build a Bayesian multilocus association model for quantitative and binary traits with carefully defined hierarchical parameterization of Student's t and Laplace priors. In this treatment we consider alternative model structures, using indicator variables and polygenic terms. We make the most of the conjugate analysis, enabled by the hierarchical formulation of the prior densities, by deriving the fully conditional posterior densities of the parameters and using the acquired known distributions in building fast generalized expectation-maximization estimation algorithms.