scholarly journals Automatic Tempered Posterior Distributions for Bayesian Inversion Problems

Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 784
Author(s):  
Luca Martino ◽  
Fernando Llorente ◽  
Ernesto Cuberlo ◽  
Javier López-Santiago ◽  
Joaquín Míguez
Keyword(s):  
Iterative Procedure ◽  
Numerical Experiments ◽  
Scale Parameter ◽  
Bayesian Inversion ◽  
Model Parameters ◽  
Noise Power ◽  
Posterior Distributions ◽  
Current Estimate ◽  
Maximum Likelihood Approach ◽  
Likelihood Approach

We propose a novel adaptive importance sampling scheme for Bayesian inversion problems where the inference of the variables of interest and the power of the data noise are carried out using distinct (but interacting) methods. More specifically, we consider a Bayesian analysis for the variables of interest (i.e., the parameters of the model to invert), whereas we employ a maximum likelihood approach for the estimation of the noise power. The whole technique is implemented by means of an iterative procedure with alternating sampling and optimization steps. Moreover, the noise power is also used as a tempered parameter for the posterior distribution of the the variables of interest. Therefore, a sequence of tempered posterior densities is generated, where the tempered parameter is automatically selected according to the current estimate of the noise power. A complete Bayesian study over the model parameters and the scale parameter can also be performed. Numerical experiments show the benefits of the proposed approach.

scholarly journals Inverse modeling of hydrologic parameters using surface flux and runoff observations in the Community Land Model

2013 ◽  
Vol 17 (12) ◽  
pp. 4995-5011 ◽  
Author(s):  
Y. Sun ◽  
Z. Hou ◽  
M. Huang ◽  
F. Tian ◽  
L. Ruby Leung
Keyword(s):  
Inverse Modeling ◽  
Bayesian Model Averaging ◽  
Surface Flux ◽  
Sensitivity Analyses ◽  
Soil Conditions ◽  
Bayesian Inversion ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Posterior Distributions ◽  
Community Land Model

Abstract. This study demonstrates the possibility of inverting hydrologic parameters using surface flux and runoff observations in version 4 of the Community Land Model (CLM4). Previous studies showed that surface flux and runoff calculations are sensitive to major hydrologic parameters in CLM4 over different watersheds, and illustrated the necessity and possibility of parameter calibration. Both deterministic least-square fitting and stochastic Markov-chain Monte Carlo (MCMC)-Bayesian inversion approaches are evaluated by applying them to CLM4 at selected sites with different climate and soil conditions. The unknowns to be estimated include surface and subsurface runoff generation parameters and vadose zone soil water parameters. We find that using model parameters calibrated by the sampling-based stochastic inversion approaches provides significant improvements in the model simulations compared to using default CLM4 parameter values, and that as more information comes in, the predictive intervals (ranges of posterior distributions) of the calibrated parameters become narrower. In general, parameters that are identified to be significant through sensitivity analyses and statistical tests are better calibrated than those with weak or nonlinear impacts on flux or runoff observations. Temporal resolution of observations has larger impacts on the results of inverse modeling using heat flux data than runoff data. Soil and vegetation cover have important impacts on parameter sensitivities, leading to different patterns of posterior distributions of parameters at different sites. Overall, the MCMC-Bayesian inversion approach effectively and reliably improves the simulation of CLM under different climates and environmental conditions. Bayesian model averaging of the posterior estimates with different reference acceptance probabilities can smooth the posterior distribution and provide more reliable parameter estimates, but at the expense of wider uncertainty bounds.

scholarly journals Estimation of latent network flows in bike-sharing systems

2020 ◽  
pp. 1471082X2097191
Author(s):  
Marc Schneble ◽  
Göran Kauermann
Keyword(s):  
Network Flow ◽  
Network Flows ◽  
Estimation Error ◽  
Weather Conditions ◽  
Model Parameters ◽  
Maximum Likelihood Approach ◽  
Bike Sharing ◽  
Mixed Regression ◽  
Likelihood Approach ◽  
Modelling Approach

Estimation of latent network flows is a common problem in statistical network analysis. The typical setting is that we know the margins of the network, that is, in- and outdegrees, but the flows are unobserved. In this article, we develop a mixed regression model to estimate network flows in a bike-sharing network if only the hourly differences of in- and outdegrees at bike stations are known. We also include exogenous covariates such as weather conditions. Two different parameterizations of the model are considered to estimate (a) the whole network flow and (b) the network margins only. The estimation of the model parameters is proposed via an iterative penalized maximum likelihood approach. This is exemplified by modelling network flows in the Vienna bike-sharing system. In order to evaluate our modelling approach, we conduct our analyses exploiting different distributional assumptions while we also respect the provider's interventions appropriately for keeping the estimation error low. Furthermore, a simulation study is conducted to show the performance of the model. For practical purposes, it is crucial to predict when and at which station there is a lack or an excess of bikes. For this application, our model shows to be well suited by providing quite accurate predictions.

scholarly journals Genetic parameters for test-day model with random regressions for production traits of Czech Holstein cattle

2011 ◽  
Vol 50 (No. 4) ◽  
pp. 142-154 ◽  
Author(s):  
L. Zavadilová ◽  
J. Jamrozik ◽  
Schaeffer LR
Keyword(s):  
Milk Fat ◽  
Sampling Method ◽  
Random Regression ◽  
Model Parameters ◽  
Residual Variance ◽  
Posterior Distributions ◽  
Production Traits ◽  
Multiple Trait ◽  
Holstein Breed ◽  
Random Regression Model

Multiple-lactation random regression model was applied to test-day records of milk, fat and protein yields in the first three lactations of the Czech Holstein breed. Data included 9 583 cows, 89 584, 44 207 and 11 266 test-day records in the first, second and third lactation, respectively. Milk, fat and protein in the first three lactations were analysed separately and in a multiple-trait analysis. Linear model included herd-test date, fixed regressions within age-season class and two random effects: animal genetic and permanent environment modelled by regressions. Gibbs sampling method was used to generate samples from marginal posterior distributions of the model parameters. The single- and multiple-trait models provided similar results. Genetic and permanent environmental variances and heritability for particular days in milk were high at the beginning and at the end of lactation. The residual variance decreased throughout the lactation. The resulting heritability ranged from 0.13 to 0.52 and increased with parity.  

Emotion detection in infants² cries based on a maximum likelihood approach

2006 ◽  
Author(s):  
S. Matsunaga ◽  
S. Sakaguchi ◽  
M. Yamashita ◽  
S. Miyahara ◽  
S. Nishitani ◽  
...  
Keyword(s):  
Maximum Likelihood ◽  
Emotion Detection ◽  
Maximum Likelihood Approach ◽  
Likelihood Approach
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