Bayesian Parameter Inference Research Articles

Multiobjective Approach for Pipe Replacement Based on Bayesian Inference of Break Model Parameters

A planning strategy is presented that aims at establishing the optimal replacement schedule for a water distribution network. Two performance indicators are defined. The first accounts for structural state (total cost defined as the sum of pipe replacement cost and the expected cost of pipe break repairs) and the second for hydraulic performance (minimization of the pressure deficit). A multiobjective objective function is defined based on these two indicators and a genetic algorithm optimization technique is used to identify optimal solutions (Pareto front). Three management strategies are considered to choose a replacement schedule among those making up the Pareto front: (1) a prostructural strategy that only considers the structural indicator; (2) a prohydraulic strategy that integrates both structural and hydraulic indicators; and (3) a budgetary constraint strategy which assumes a predefined budget for replacement expenditures. The proposed planning strategy was tested on two hypothetical networks. S...

Bayesian inference and life testing plans for generalized exponential distribution

Recently generalized exponential distribution has received considerable attentions. In this paper, we deal with the Bayesian inference of the unknown parameters of the progressively censored generalized exponential distribution. It is assumed that the scale and the shape parameters have independent gamma priors. The Bayes estimates of the unknown parameters cannot be obtained in the closed form. Lindley’s approximation and importance sampling technique have been suggested to compute the approximate Bayes estimates. Markov Chain Monte Carlo method has been used to compute the approximate Bayes estimates and also to construct the highest posterior density credible intervals. We also provide different criteria to compare two different sampling schemes and hence to find the optimal sampling schemes. It is observed that finding the optimum censoring procedure is a computationally expensive process. And we have recommended to use the sub-optimal censoring procedure, which can be obtained very easily. Monte Carlo simulations are performed to compare the performances of the different methods and one data analysis has been performed for illustrative purposes.

A Bayesian joint probability modeling approach for seasonal forecasting of streamflows at multiple sites

Seasonal forecasting of streamflows can be highly valuable for water resources management. In this paper, a Bayesian joint probability (BJP) modeling approach for seasonal forecasting of streamflows at multiple sites is presented. A Box‐Cox transformed multivariate normal distribution is proposed to model the joint distribution of future streamflows and their predictors such as antecedent streamflows and El Niño‐Southern Oscillation indices and other climate indicators. Bayesian inference of model parameters and uncertainties is implemented using Markov chain Monte Carlo sampling, leading to joint probabilistic forecasts of streamflows at multiple sites. The model provides a parametric structure for quantifying relationships between variables, including intersite correlations. The Box‐Cox transformed multivariate normal distribution has considerable flexibility for modeling a wide range of predictors and predictands. The Bayesian inference formulated allows the use of data that contain nonconcurrent and missing records. The model flexibility and data‐handling ability means that the BJP modeling approach is potentially of wide practical application. The paper also presents a number of statistical measures and graphical methods for verification of probabilistic forecasts of continuous variables. Results for streamflows at three river gauges in the Murrumbidgee River catchment in southeast Australia show that the BJP modeling approach has good forecast quality and that the fitted model is consistent with observed data.

Modeling Exopeptidase Activity from LC-MS Data

Recent studies demonstrate that the peptides in the serum of cancer patients that are generated (ex vivo) as a result of tumor protease activity can be used for the detection and classification of cancer. In this paper, we propose the first formal approach to modeling exopeptidase activity from liquid chromatography-mass spectrometry (LC-MS) samples. We design a statistical model of peptidome degradation and a Metropolis-Hastings algorithm for Bayesian inference of model parameters. The model is successfully validated on a real LC-MS dataset. Our findings support the hypotheses about disease-specific exopeptidase activity, which can lead to new diagnostic approach in clinical proteomics.

Bayesian inference of genetic parameters on litter size and gestation length in Hungarian Landrace and Hungarian Large White pigs

Genetic parameters of number of piglets born alive (NBA) and gestation length (GL) were analyzed for 39798 Hungarian Landrace (HLA, 141397 records) and 70356 Hungarian Large White (HLW, 246961 records) sows. Bivariate repeatability animal models were used, applying a Bayesian statistics. Estimated and heritabilitie repeatabilities (within brackets), were low for NBA, 0.07 (0.14) for HLA and 0.08 (0.17) for HLW, but somewhat higher for GL, 0.18 (0.27) for HLA and 0.26 (0.35) for HLW. Estimated genetic correlations between NBA and GL were low, -0.08 for HLA and -0.05 for HLW.

Bayesian Inference and Life Testing Plan for the Weibull Distribution in Presence of Progressive Censoring

This article deals with the Bayesian inference of unknown parameters of the progressively censored Weibull distribution. It is well known that for a Weibull distribution, while computing the Bayes estimates, the continuous conjugate joint prior distribution of the shape and scale parameters does not exist. In this article it is assumed that the shape parameter has a log-concave prior density function, and for the given shape parameter, the scale parameter has a conjugate prior distribution. As expected, when the shape parameter is unknown, the closed-form expressions of the Bayes estimators cannot be obtained. We use Lindley's approximation to compute the Bayes estimates and the Gibbs sampling procedure to calculate the credible intervals. For given priors, we also provide a methodology to compare two different censoring schemes and thus find the optimal Bayesian censoring scheme. Monte Carlo simulations are performed to observe the behavior of the proposed methods, and a data analysis is onducted for illustrative purposes.

Bayesian inference of kinematic earthquake rupture parameters through fitting of strong motion data

SUMMARY Due to uncertainties in data and in forward modelling, the inherent limitations in data coverage and the non-linearity of the governing equation, earthquake source imaging is a problem with multiple solutions. The multiplicity of solutions can be conveniently expressed using a Bayesian approach, which allow to state inferences on model parameters in terms of probability density functions. The estimation of the posterior state of information, expressing the combination of the a priori knowledge on model parameters with the information contained in the data, is achieved in two steps. First, we explore the model space using an evolutionary algorithm to identify good data fitting regions. Secondly, using a neighbourhood algorithm and considering the entire ensemble of models found during the search stage, we compute a geometric approximation of the true posterior that is used to generate a second ensemble of models from which Bayesian inference can be performed. We apply this methodology to infer kinematic parameters of a synthetic fault rupture through fitting of strong motion data. We show how multiple rupture models are able to reproduce the observed waveforms within the same level of fit, suggesting therefore that the solution of the inversion cannot be expressed in terms of a single model but rather as a set of models which show certain statistical properties. For all model parameters we compute the posterior marginal distribution. We show how for some parameters the posterior do not follow a Gaussian distribution rendering the usual characterization in terms of mean value and standard deviation not correct. We compare the posterior marginal distributions with the ‘raw’ marginal distributions computed from the ensemble of models generated by the evolutionary algorithm. We show how they are systematically different proving therefore that the search algorithm we adopt cannot be directly used to estimate uncertainties. We also analyse the stability of our inferences comparing the posterior marginals computed by different independent ensembles. The solutions provided by independent explorations are similar but not identical because each ensemble searches the model space differently resulting in different reconstructed posteriors. Our study illustrates how uncertainty estimates derive from the topology of the objective function, and how accurate and reliable resolution analysis is limited by the intrinsic difficulty of mapping the ‘true’ structure of the objective function.

Bayesian Inference of Scale Parameters in Exponential Family Using Conditionally Specified Priors

This article considers a unified Bayesian approach for comparing scale parameters in an exponential family, assuming other parameters such as location or shape, are known. Particular cases include the normal, gamma, Weibull, exponential, Poisson, and binomial distributions. Convenient conjugate priors are found in joint distribution conditionally specified. Hyperparameter elicitation techniques are discussed. The results are illustrated in the comparison of scales of two normals and two Weibull densities.

Bayesian Inference of Scale Parameters in Exponential Family Using Conditionally Specified Priors

This article considers a unified Bayesian approach for comparing scale parameters in an exponential family, assuming other parameters such as location or shape, are known. Particular cases include the normal, gamma, Weibull, exponential, Poisson, and binomial distributions. Convenient conjugate priors are found in joint distribution conditionally specified. Hyperparameter elicitation techniques are discussed. The results are illustrated in the comparison of scales of two normals and two Weibull densities.

Exact bayesian inference for normal hierarchical models

This paper provides an algorithm for generating independent draws from the exact joint posterior distribution of the parameters of a univariate Normal hierarchical model. Suppose one observes data on J groups: . At level-1 of the model where are known constants (e.g.,group sample sizes),and . At level-2, where: are known q×1 covariate vectors. The unknown varameters are the J group means, the q × 1 level-2 regression coefficient γ and the level-1 and level-2 variance components, σ2 and A Given the two variance components, the conditional posterior distributions of the and of γ are closed-form Normals, assuming a q-dimensional Normal or Uniform prior on γ The algorithm of this paper yields independent samples from , having specified vague prior distributions for A, and σ2This enables exact Bayesian inference for all model parameters. The algorithm is implemented as an SPlus program,TLNise, available from www.swarthmore.edu/NatSci/peversol/tlnise.htm.

On estimation and prediction for temporally correlated longitudinal data

Abstract In this paper, from a Bayesian point of view, we consider estimation of parameters and prediction of future values for the longitudinal model proposed by Diggle (1988. Biometrics 44, 959–971). This model, called the repeated measures linear model, incorporates group mean, variability among individuals, serial correlation within an individual, and measurement error. Two different priors are employed by the Bayesian approach, one is the noninformative prior and the other is composed of inverse gamma distributions. Given the noninformative prior, it is shown that the resulting approximate estimates of the regression coefficients are the same as those derived by the restricted maximum likelihood estimation. Markov chain Monte Carlo methods are also used to obtain more accurate Bayesian inference for parameters as well as prediction of future values. For parameter estimation and prediction of future values, the advantages of the Bayesian approach over the maximum likelihood method and the restricted maximum likelihood method are demonstrated by both real and simulated data.

Semiparametric Bayesian inference for regression models

This paper presents a method for Bayesian inference for the regression parameters in a linear model with independent and identically distributed errors that does not require the specification of a parametric family of densities for the error distribution. This method first selects a nonparametric kernel density estimate of the error distribution which is unimodal and based on the least-squares residuals. Once the error distribution is selected, the Metropolis algorithm is used to obtain the marginal posterior distribution of the regression parameters. The methodology is illustrated with data sets, and its performance relative to standard Bayesian techniques is evaluated using simulation results.

Bayesian inference of genetic parameters and selection response for litter size components in pigs.

Three contemporary lines were formed from the progeny of 50 French Large White sows. In the first line, gilts were selected for ovulation rate at puberty. In the second line, they were selected for prenatal survival of the first two parities, corrected for ovulation rate. The control constituted the third line. Ovulation rate at puberty was analyzed using an animal model with a batch effect. Prenatal survival was analyzed with a repeatability animal model that included batch and parity effects. Flat priors were used to represent vague previous knowledge about parity and batch effects. Additive and residual effects were represented assuming that they were a priori normally distributed. Variance components were assumed to follow either uniform or inverted chi-square distributions, a priori. The use of different priors did not affect the results substantially. Heritabilities for ovulation rate ranged from 0.32 to 0.39, and from 0.11 to 0.16 for prenatal survival, depending on the prior used. The mean of the marginal posterior distribution of response to four generations of selection ranged from 0.38 to 0.40 ova per generation, and from 1.1 to 1.3% of the mean survival rate for average survival per generation.

Random differential equations as models of ecosystems— III. bayesian inference for parameters

The usefulness of the Bayesian inference for specifying and updating the parameters of the models of ecological systems based on long-term investigations has been examined. Our analyses indicate that in these systems this inferential procedure provides a rational basis for specifying the parameters and other input quantities of the model. Thus a modeling approach based on random differential equations, the principle of maximum entropy, and Bayesian inference is more useful than the deterministic modeling for applied problems in ecology and resource management.