Academic literature on the topic 'Maximum Posterior Marginal (MPM)'

This work presents a Bayesian statistical approach to the saliency map estimation problem. More specifically, we formalize the saliency map estimation issue in the fully automatic Markovian framework. The major and original contribution of the proposed Bayesian–Markov model resides in the exploitation of a pixel pairwise modeling and a likelihood model based on a parametric mixture of two different class-conditional likelihood distributions whose parameters are adaptively and previously estimated for each image. This allows us to adapt our saliency estimation model to the specific characteristics of each image of the dataset and to provide a nearly parameter-free—hence dataset-independent—unsupervised saliency map estimation procedure. In our case, the parameters of the likelihood model are all estimated under the principles of the iterative conditional estimation framework. Once the estimation step is completed, the MPM (maximum posterior marginal) solution of the saliency map (which we show as particularly suitable for this type of estimation), is then estimated by a stochastic sampling scheme approximating the posterior distribution (whose parameters were previously estimated). This unsupervised data-driven Markovian framework overcomes the limitations of current ad hoc or supervised energy-based or Markovian models that often involve many parameters to adapt and that are finely tuned for each different benchmark database. Experimental results show that the proposed algorithm performs favorably against state-of-the-art methods and turns out to be particularly stable across a wide variety of benchmark datasets.

Practitioners have used hidden Markov models (HMMs) in different problems for about sixty years. Moreover, conditional random fields (CRFs) are an alternative to HMMs and appear in the literature as different and somewhat concurrent models. We propose two contributions: First, we show that the basic linear-chain CRFs (LC-CRFs), considered as different from HMMs, are in fact equivalent to HMMs in the sense that for each LC-CRF there exists an HMM—that we specify—whose posterior distribution is identical to the given LC-CRF. Second, we show that it is possible to reformulate the generative Bayesian classifiers maximum posterior mode (MPM) and maximum a posteriori (MAP), used in HMMs, as discriminative ones. The last point is of importance in many fields, especially in natural language processing (NLP), as it shows that in some situations dropping HMMs in favor of CRFs is not necessary.

The problem of estimating item parameters from a two-parameter normal ogive model is considered. Gibbs sampling (Gelfand & Smith, 1990) is used to simulate draws from the joint posterior distribution of the ability and item parameters. This method gives marginal posterior density estimates for any parameter of interest; these density estimates can be used to judge the accuracy of normal approximations based on maximum likelihood estimates. This simulation technique is illustrated using data from a mathematics placement exam.

<p>The pair-wise Markov chain (PMC) model serves as an extension to the hidden Markov chain (HMC) model and has been widely used in unsupervised restoration tasks associated with reconstructing the hidden data. In fact, the PMC model can treat fairly complicated situations for which application of Bayesian restoration estimators such as maximum <italic>A Posteriori</italic> (MAP), or maximal <italic>Posterior</italic> mode (MPM) remains possible. The major novelty in this work is to construct a PMC model with observational data in two dimensions, and subsequently adapt the estimation algorithms, as well as, image restoration methods for that context. Often, the transformation of an image from a two-dimensional format to a one-dimensional sequence occurs via Hilbert-Peano scan (HPS), whereas in the proposed model, the second component of the observed process takes over this role to exceed the situation of pixel missing information after transformation for a to be segmented image. To reconstruct the hidden process, we used the MPM decision criterion after estimating the model's parameters with two algorithms: Stochastic expectation maximization (SEM) and iterative conditional estimation (ICE). In this study, experimental, numerical, and visual results are shown to demonstrate the superiority of the proposed model over the classical PMC for unsupervised restorations.</p>

A fully Bayesian approach to a general nonlinear ordinal regression model for ROC- curve analysis is presented. Samples from the marginal posterior distributions of the model parameters are obtained by a Markov-chain Monte Carlo (MCMC) technique— Gibbs sampling. These samples facilitate the calculation of point estimates and cred ible regions as well as inferences for the associated areas under the ROC curves. The analysis of an example using freely available software shows that the use of nonin formative vague prior distributions for all model parameters yields posterior summary statistics very similar to the conventional maximum-likelihood estimates. Clinically im portant advantages of this Bayesian approach are: the possible inclusion of prior knowl edge and beliefs into the ROC analysis (via the prior distributions), the possible cal culation of the posterior predictive distribution of a future patient outcome, and the potential to address questions such as: "What is the probability that a certain diagnostic test is better in one setting than in another?" Key words: ROC curve; diagnostic test; ordinal regression; Bayesian methods; MCMC; Gibbs sampling; maximum likelihood (Med Decis Making 1998;18:436-443)

Bayesian analysis of hierarchically structured data with random intercept and heterogeneous within-group (Level-1) variance is presented. Inferences about all parameters, including the Level-1 variance and intercept for each group, are based on their marginal posterior distributions approximated via the Gibbs sampler Analysis of artificial data with varying degrees of heterogeneity and varying Level-2 sample sizes illustrates the likely benefits of using a Bayesian approach to model heterogeneity of variance (Bayes/Het). Results are compared to those based on now-standard restricted maximum likelihood with homogeneous Level-1 variance (RML/Hom). Bayes/Het provides sensible interval estimates for Level-1 variances and their heterogeneity, and, relatedly, for each group’s intercept. RML/Hom inferences about Level-2 regression coefficients appear surprisingly robust to heterogeneity, and conditions under which such robustness can be expected are discussed. Application is illustrated in a reanalysis of High School and Beyond data. It appears informative and practically feasible to obtain approximate marginal posterior distributions for all Level-1 and Level-2 parameters when analyzing large- or small-scale survey data. A key advantage of the Bayes approach is that inferences about any parameter appropriately reflect uncertainty about all remaining parameters.

Generative Bayesian Computation (GBC) methods are developed to provide an efficient computational solution for maximum expected utility (MEU). We propose a density-free generative method based on quantiles that naturally calculates expected utility as a marginal of posterior quantiles. Our approach uses a deep quantile neural estimator to directly simulate distributional utilities. Generative methods only assume the ability to simulate from the model and parameters and as such are likelihood-free. A large training dataset is generated from parameters, data and a base distribution. Then, a supervised learning problem is solved as a non-parametric regression of generative utilities on outputs and base distribution. We propose the use of deep quantile neural networks. Our method has a number of computational advantages, primarily being density-free and an efficient estimator of expected utility. A link with the dual theory of expected utility and risk taking is also described. To illustrate our methodology, we solve an optimal portfolio allocation problem with Bayesian learning and power utility (also known as the fractional Kelly criterion). Finally, we conclude with directions for future research.

Purpose: This study aims to investigate the ultimate fractural strength and marginal integrity of a three-unit implant-supported fixed partial denture (FPD) framework fabricated of polyetherketoneketone (PEKK) after simulated five-year clinical aging. Materials and Methods: Twelve FPD frameworks were milled (n = 6 per group). All experimental frameworks were cemented on identical stainless-steel abutment models and subjected to five years of clinically simulated thermomechanical aging. The vertical marginal gap values were analyzed using a scanning electron microscope before and after being subjected to each aging condition. A universal testing machine was used to evaluate the ultimate fracture load. Results: A significant increase in marginal gap values of the PEKK group was observed after five years of simulation aging (p < 0.001), while no significant difference was seen in the titanium group (p = 0.071). After thermocycling, the PEKK group showed a higher statistically significant mean marginal gap value (84.99 + 44.28 μm) than before (81.75 + 44.53 μm). The titanium group exhibited superior mechanical strength, with a fracture load significantly higher than that of the PEKK group (3050 + 385.30 and 1359.14 + 205.49 N, respectively). Conclusions: Thermocycling affects the marginal gap discrepancy of PEKK restoration. However, the mean vertical marginal gap values in PEKK and titanium groups after a five-year clinical aging simulation were clinically acceptable. The ultimate fracture load values were higher than the maximum bite force reported in the posterior region. Thus, PEKK could serve as a suitable alternative material to metal in the framework of fixed dental prostheses.

OBJECTIVE: This study aims to compare the topography patterns and parameters in eyes with pellucid marginal degeneration (PMD) and eyes with keratoconus (KC). MATERIAL AND METHODS: This study is a retrospective and comparative study. Twenty-nine eyes of 15 patients with PMD and 46 eyes of 25 patients with keratoconus (KC) underwent examination. Topographic patterns of axial curvature, anterior and posterior elevation maps, and pachymetric maps obtained by the Scheimpflug camera were categorized. RESULTS: In eyes with PMD, the crab-claw pattern (93.1% of all axial curvature map patterns) was the most prevalent. The most common patterns in eyes with KC were inferior (41.3%) and central (39.1%) steepening patterns. In eyes with PMD, the asymmetric island pattern (96.6%) was the most prevalent pattern in elevation maps. Asymmetric incomplete ridge pattern (54.3%), center island (17.4%), and asymmetric regular ridge pattern (15.2%) were the most common elevation map patterns in eyes with KC. Among pachymetric map patterns, the decentred oval pattern was most frequent in eyes with PMD, paracentral oval pattern (54.3%), and decentred round pattern (34.8%) in eyes with KC. The result of the receiver operating characteristics (ROC) graphs showed that the anterior and posterior asphericity (Q) values had the maximum area under the ROC curve (0.98 and 0.93 respectively) in discriminating PMD and KC. CONCLUSIONS: The crab-claw pattern for the axial curvature map, asymmetric island pattern for the anterior and posterior elevation map, and decentred oval pattern for the pachymetric map were frequently observed in eyes with PMD. Asphericity values of the cornea may be clinically relevant parameters for effectively discriminating PMD from KC.

L’objectif de cette thèse est de proposer un Alphabet Structural (AS) permettant une caractérisation fine et précise des structures tridimensionnelles (3D) des protéines, à l’aide des chaînes de Markov cachées (HMM) qui permettent de prendre en compte la logique issue de l’enchaînement des fragments structuraux en intégrant l’augmentation des conformations 3D des structures protéiques désormais disponibles dans la banque de données de la Protein Data Bank (PDB). Nous proposons dans cette thèse un nouvel alphabet, améliorant l’alphabet structural HMM-SA27,appelé SAFlex (Structural Alphabet Flexibility), dans le but de prendre en compte l’incertitude des données (données manquantes dans les fichiers PDB) et la redondance des structures protéiques. Le nouvel alphabet structural SAFlex obtenu propose donc un nouveau modèle d’encodage rigoureux et robuste. Cet encodage permet de prendre en compte l’incertitude des données en proposant trois options d’encodages : le Maximum a posteriori (MAP), la distribution marginale a posteriori (POST)et le nombre effectif de lettres à chaque position donnée (NEFF). SAFlex fournit également un encodage consensus à partir de différentes réplications (chaînes multiples, monomères et homomères) d’une même protéine. Il permet ainsi la détection de la variabilité structurale entre celles-ci. Les avancées méthodologiques ainsi que l’obtention de l’alphabet SAFlex constituent les contributions principales de ce travail de thèse. Nous présentons aussi le nouveau parser de la PDB (SAFlex-PDB) et nous démontrons que notre parser a un intérêt aussi bien sur le plan qualitatif (détection de diverses erreurs)que quantitatif (rapidité et parallélisation) en le comparant avec deux autres parsers très connus dans le domaine (Biopython et BioJava). Nous proposons également à la communauté scientifique un site web mettant en ligne ce nouvel alphabet structural SAFlex. Ce site web représente la contribution concrète de cette thèse alors que le parser SAFlex-PDB représente une contribution importante pour le fonctionnement du site web proposé. Cette caractérisation précise des conformations 3D et la prise en compte de la redondance des informations 3D disponibles, fournies par SAFlex, a en effet un impact très important pour la modélisation de la conformation et de la variabilité des structures 3D, des boucles protéiques et des régions d’interface avec différents partenaires, impliqués dans la fonction des protéines<br>The purpose of this PhD is to provide a Structural Alphabet (SA) for more accurate characterization of protein three-dimensional (3D) structures as well as integrating the increasing protein 3D structure information currently available in the Protein Data Bank (PDB). The SA also takes into consideration the logic behind the structural fragments sequence by using the hidden Markov Model (HMM). In this PhD, we describe a new structural alphabet, improving the existing HMM-SA27 structural alphabet, called SAFlex (Structural Alphabet Flexibility), in order to take into account the uncertainty of data (missing data in PDB files) and the redundancy of protein structures. The new SAFlex structural alphabet obtained therefore offers a new, rigorous and robust encoding model. This encoding takes into account the encoding uncertainty by providing three encoding options: the maximum a posteriori (MAP), the marginal posterior distribution (POST), and the effective number of letters at each given position (NEFF). SAFlex also provides and builds a consensus encoding from different replicates (multiple chains, monomers and several homomers) of a single protein. It thus allows the detection of structural variability between different chains. The methodological advances and the achievement of the SAFlex alphabet are the main contributions of this PhD. We also present the new PDB parser(SAFlex-PDB) and we demonstrate that our parser is therefore interesting both qualitative (detection of various errors) and quantitative terms (program optimization and parallelization) by comparing it with two other parsers well-known in the area of Bioinformatics (Biopython and BioJava). The SAFlex structural alphabet is being made available to the scientific community by providing a website. The SAFlex web server represents the concrete contribution of this PhD while the SAFlex-PDB parser represents an important contribution to the proper function of the proposed website. Here, we describe the functions and the interfaces of the SAFlex web server. The SAFlex can be used in various fashions for a protein tertiary structure of a given PDB format file; it can be used for encoding the 3D structure, identifying and predicting missing data. Hence, it is the only alphabet able to encode and predict the missing data in a 3D protein structure to date. Finally, these improvements; are promising to explore increasing protein redundancy data and obtain useful quantification of their flexibility

Abstract We propose a formal mathematical approach to assimilate LES data into values of RANS model parameters combined with some prior knowledge of the expected RANS parameter values. This is achieved using Bayesian inference to determine parameter values that maximize their posterior probability and is known as maximum a posteriori (MAP) estimation. We apply this approach to a premixed turbulent methane-air round jet flame using unburnt mixture equivalence ratio and bulk flow velocity as design parameters. The k-ε model is used for turbulence closure and the eddy dissipation concept (EDC) model is used to model combustion. Three dimesional LES data for six design cases are computed and upto three of these are used for MAP estimation. The likelihood of RANS solutions is evaluated using flow field statistics from LES at training data points. The results show significant improvement in agreement between LES and RANS solutions, computed using MAP estimate parameters for species mass fraction and temperature fields at design points not in the training set. Marginal improvement is observed for velocity fields. This is most likely due to the absence of production terms in the RANS model that capture the three-dimensional nature of the flow being modelled. The marginal likelihood of the RANS model when assimilating both k-ε and EDC model parameters is significantly higher than the case that leaves out the EDC model parameters. This suggests that the former approach is more likely to yield reliable RANS parameters. These results demonstrate the viability of MAP estimation as a means to improving the reliability of turbulent reacting flow RANS simulations for engineering design and optimization applications.