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.

Learning from labeled and unlabeled data

Abstract: Due to the considerable time and expense required in labeling data, a challenge is to propose learning algorithms that can learn from a small amount of labeled data and a much larger amount of unlabeled data. In this paper, we propose one such algorithm which uses an evolutionary strategy to iteratively adjust the class membership of the patterns in the unlabeled sample. The iterative adjustment is done so that the class conditional distribution obtained from such a labeling allows a maximum a posteriori classification with minimum classification error on the labeled patterns. We detail the algorithm and provide results obtained by the proposed algorithm on 5 different datasets.

A multinomial Bayesian approach to the estimation of population and vocabulary size

Abstract: We approach estimation of the size of a population or a vocabulary through a Bayesian analysis of the multinomial distribution. We view the sample as being generated from such a distribution with an unknown number of cells and unknown cell probabilities, and develop a Bayesian procedure to estimate the number of cells and the coverage of the sample. The prior distribution of the number of cells is arbitrary. Given that number, the cell probabilities are assumed to follow a symmetric Dirichlet prior. A two-stage approach is developed for use when the flattening constant of the latter prior cannot be specified in advance. Our procedures are applied to samples of butterflies, insect species and alleles, to the works of Shakespeare and Joyce, and to Eldridge's sample of English words.

Maximum-likelihood versus maximum a posteriori parameter estimation of physiological system models: the c-peptide impulse response case study

Abstract: Maximum-likelihood (ML), also given its connection to least squares (LS), is widely adopted in parameter estimation of physiological system models, i.e., assigning numerical values to the unknown model parameters from the experimental data. A more sophisticated but less used approach is maximum a posteriori (MAP) estimation. Conceptually, while ML adopts a Fisherian approach, i.e., only experimental measurements are supplied to the estimator, MAP estimation is a Bayesian approach, i.e., a priori available statistical information on the unknown parameters is also exploited for their estimation. Here, after a brief review of the theory behind ML and MAP estimators, the authors compare their performance in the solution of a case study concerning the determination of the parameters of a sum of exponential model which describes the impulse response of C-peptide (CP), a key substance for reconstructing insulin secretion. The results show that MAP estimation always leads to parameter estimates with a precision (sometimes significantly) higher than that obtained through ML, at the cost of only a slightly worse fit. Thus, a 3 exponential model can be adopted to describe the CP impulse response model in place of the two exponential model usually identified in the literature by the ML/LS approach. Simulated case studies are also reported to evidence the importance of taking into account a priori information in a data poor situation, e.g., when a few or too noisy measurements are available. In conclusion, the authors' results show that, when a priori information on the unknown model parameters is available, Bayes estimation can be of relevant interest, since it can significantly improve the precision of parameter estimates with respect to Fisher estimation. This may also allow the adoption of more complex models than those determinable by a Fisherian approach.

Aircraft initial mass estimation using Bayesian inference method

Abstract: Aircraft mass is a crucial piece of information for studies on aircraft performance, trajectory prediction, and many other topics of aircraft traffic management. However, It is a common challenge for researchers, as well as air traffic control, to access this proprietary information. Previously, several studies have proposed methods to estimate aircraft weight based on specific parts of the flight. Due to inaccurate input data or biased assumptions, this often leads to less confident or inaccurate estimations. In this paper, combined with a fuel-flow model, different aircraft initial masses are computed independently using the total energy model and reference model at first. It then adopts a Bayesian approach that uses a prior probability of aircraft mass based on empirical knowledge and computed aircraft initial masses to produce the maximum a posteriori estimation. Variation in results caused by dependent factors such as prior, thrust and wind are also studied. The method is validated using 50 test flights of a Cessna Citation II aircraft, for which measurements of the true mass were available. The validation results show a mean absolute error of 4.3% of the actual aircraft mass.

Estimation of the scale parameter of the Rayleigh distribution under general progressive censoring

Abstract: Based on a general progressively type II censored sample, the maximum likelihood estimator (MLE), Bayes estimator under squared error loss and credible intervals for the scale parameter and the reliability function of the Rayleigh distribution are derived. Also, the Bayes predictive estimator and highest posterior density (HPD) prediction interval for future observation are considered. Comparisons among estimators are investigated through Monte Carlo simulations. An illustrative example with real data concerning 23 ball bearings in a life test is presented.