scholarly journals Bayesian Multiple Emitter Fitting using Reversible Jump Markov Chain Monte Carlo

2019 ◽  
Author(s):  
Mohamadreza Fazel ◽  
Michael J. Wester ◽  
Hanieh Mazloom-Farsibaf ◽  
Marjolein B. M. Meddens ◽  
Alexandra Eklund ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Single Molecule ◽  
Posterior Probability ◽  
Super Resolution ◽  
Image Data ◽  
Reversible Jump ◽  
Posterior Probability Distribution ◽  
Resolution Imaging

In single molecule localization-based super-resolution imaging, high labeling density or the desire for greater data collection speed can lead to clusters of overlapping emitter images in the raw super-resolution image data. We describe a Bayesian inference approach to multiple-emitter fitting that uses Reversible Jump Markov Chain Monte Carlo to identify and localize the emitters in dense regions of data. This formalism can take advantage of any prior information, such as emitter intensity and density. The output is both a posterior probability distribution of emitter locations that includes uncertainty in the number of emitters and the background structure, and a set of coordinates and uncertainties from the most probable model.

scholarly journals Bayesian Multiple Emitter Fitting using Reversible Jump Markov Chain Monte Carlo

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Mohamadreza Fazel ◽  
Michael J. Wester ◽  
Hanieh Mazloom-Farsibaf ◽  
Marjolein B. M. Meddens ◽  
Alexandra S. Eklund ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Single Molecule ◽  
Posterior Probability ◽  
Super Resolution ◽  
Image Data ◽  
Reversible Jump ◽  
Posterior Probability Distribution ◽  
Resolution Imaging

Abstract In single molecule localization-based super-resolution imaging, high labeling density or the desire for greater data collection speed can lead to clusters of overlapping emitter images in the raw super-resolution image data. We describe a Bayesian inference approach to multiple-emitter fitting that uses Reversible Jump Markov Chain Monte Carlo to identify and localize the emitters in dense regions of data. This formalism can take advantage of any prior information, such as emitter intensity and density. The output is both a posterior probability distribution of emitter locations that includes uncertainty in the number of emitters and the background structure, and a set of coordinates and uncertainties from the most probable model.

scholarly journals Nonlinear Parameter Estimation: Comparison of an Ensemble Kalman Smoother with a Markov Chain Monte Carlo Algorithm

2012 ◽  
Vol 140 (6) ◽  
pp. 1957-1974 ◽  
Author(s):  
Derek J. Posselt ◽  
Craig H. Bishop
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Parameter Uncertainty ◽  
Posterior Probability ◽  
Monte Carlo Algorithm ◽  
Parameter Estimates ◽  
Posterior Probability Distribution ◽  
Kalman Smoother ◽  
Non Gaussian

Abstract This paper explores the temporal evolution of cloud microphysical parameter uncertainty using an idealized 1D model of deep convection. Model parameter uncertainty is quantified using a Markov chain Monte Carlo (MCMC) algorithm. A new form of the ensemble transform Kalman smoother (ETKS) appropriate for the case where the number of ensemble members exceeds the number of observations is then used to obtain estimates of model uncertainty associated with variability in model physics parameters. Robustness of the parameter estimates and ensemble parameter distributions derived from ETKS is assessed via comparison with MCMC. Nonlinearity in the relationship between parameters and model output gives rise to a non-Gaussian posterior probability distribution for the parameters that exhibits skewness early and multimodality late in the simulation. The transition from unimodal to multimodal posterior probability density function (PDF) reflects the transition from convective to stratiform rainfall. ETKS-based estimates of the posterior mean are shown to be robust, as long as the posterior PDF has a single mode. Once multimodality manifests in the solution, the MCMC posterior parameter means and variances differ markedly from those from the ETKS. However, it is also shown that if the ETKS is given a multimode prior ensemble, multimodality is preserved in the ETKS posterior analysis. These results suggest that the primary limitation of the ETKS is not the inability to deal with multimodal, non-Gaussian priors. Rather it is the inability of the ETKS to represent posterior perturbations as nonlinear functions of prior perturbations that causes the most profound difference between MCMC posterior PDFs and ETKS posterior PDFs.

scholarly journals Joining forces of Bayesian and frequentist methodology: a study for inference in the presence of non-identifiability

2013 ◽  
Vol 371 (1984) ◽  
pp. 20110544 ◽  
Author(s):  
Andreas Raue ◽  
Clemens Kreutz ◽  
Fabian Joachim Theis ◽  
Jens Timmer
Keyword(s):  
Experimental Data ◽  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Probability Distribution ◽  
Cell Biology ◽  
Posterior Probability ◽  
Monte Carlo Sampling ◽  
Posterior Probability Distribution ◽  
Model Predictions

Increasingly complex applications involve large datasets in combination with nonlinear and high-dimensional mathematical models. In this context, statistical inference is a challenging issue that calls for pragmatic approaches that take advantage of both Bayesian and frequentist methods. The elegance of Bayesian methodology is founded in the propagation of information content provided by experimental data and prior assumptions to the posterior probability distribution of model predictions. However, for complex applications, experimental data and prior assumptions potentially constrain the posterior probability distribution insufficiently. In these situations, Bayesian Markov chain Monte Carlo sampling can be infeasible. From a frequentist point of view, insufficient experimental data and prior assumptions can be interpreted as non-identifiability. The profile-likelihood approach offers to detect and to resolve non-identifiability by experimental design iteratively. Therefore, it allows one to better constrain the posterior probability distribution until Markov chain Monte Carlo sampling can be used securely. Using an application from cell biology, we compare both methods and show that a successive application of the two methods facilitates a realistic assessment of uncertainty in model predictions.

A novel approach to model the land mobile satellite channel through reversible jump markov chain monte carlo technique

2008 ◽  
Vol 7 (2) ◽  
pp. 532-542 ◽  
Author(s):  
Clemence Alasseur ◽  
Sandro Scalise ◽  
Lionel Husson ◽  
Harald Ernst
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Monte Carlo Technique ◽  
Reversible Jump ◽  
Novel Approach ◽  
Mobile Satellite

Velocity log upscaling based on reversible jump Markov chain Monte Carlo simulated annealing

Geophysics ◽  
2016 ◽  
Vol 81 (5) ◽  
pp. R293-R305 ◽  
Author(s):  
Sireesh Dadi ◽  
Richard Gibson ◽  
Kainan Wang
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Simulated Annealing ◽  
Markov Chain Monte Carlo ◽  
Random Perturbation ◽  
Current Model ◽  
Sampling Technique ◽  
Maximum Deviation ◽  
Reversible Jump ◽  
Layer Boundary

Upscaling log measurements acquired at high frequencies and correlating them with corresponding low-frequency values from surface seismic and vertical seismic profile data is a challenging task. We have applied a sampling technique called the reversible jump Markov chain Monte Carlo (RJMCMC) method to this problem. A key property of our approach is that it treats the number of unknowns itself as a parameter to be determined. Specifically, we have considered upscaling as an inverse problem in which we considered the number of coarse layers, layer boundary depths, and material properties as the unknowns. The method applies Bayesian inversion, with RJMCMC sampling and uses simulated annealing to guide the optimization. At each iteration, the algorithm will randomly move a boundary in the current model, add a new boundary, or delete an existing boundary. In each case, a random perturbation is applied to Backus-average values. We have developed examples showing that the mismatch between seismograms computed from the upscaled model and log velocities improves by 89% compared to the case in which the algorithm is allowed to move boundaries only. The layer boundary distributions after running the RJMCMC algorithm can represent sharp and gradual changes in lithology. The maximum deviation of upscaled velocities from Backus-average values is less than 10% with most of the values close to zero.

scholarly journals Estimation of trace gas fluxes with objectively determined basis functions using reversible-jump Markov chain Monte Carlo

2016 ◽  
Vol 9 (9) ◽  
pp. 3213-3229 ◽  
Author(s):  
Mark F. Lunt ◽  
Matt Rigby ◽  
Anita L. Ganesan ◽  
Alistair J. Manning
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Parameter Space ◽  
Spatial Domain ◽  
Monte Carlo Algorithm ◽  
Trace Gas ◽  
Reversible Jump ◽  
Pseudo Data ◽  
Atmospheric Trace Gas

Abstract. Atmospheric trace gas inversions often attempt to attribute fluxes to a high-dimensional grid using observations. To make this problem computationally feasible, and to reduce the degree of under-determination, some form of dimension reduction is usually performed. Here, we present an objective method for reducing the spatial dimension of the parameter space in atmospheric trace gas inversions. In addition to solving for a set of unknowns that govern emissions of a trace gas, we set out a framework that considers the number of unknowns to itself be an unknown. We rely on the well-established reversible-jump Markov chain Monte Carlo algorithm to use the data to determine the dimension of the parameter space. This framework provides a single-step process that solves for both the resolution of the inversion grid, as well as the magnitude of fluxes from this grid. Therefore, the uncertainty that surrounds the choice of aggregation is accounted for in the posterior parameter distribution. The posterior distribution of this transdimensional Markov chain provides a naturally smoothed solution, formed from an ensemble of coarser partitions of the spatial domain. We describe the form of the reversible-jump algorithm and how it may be applied to trace gas inversions. We build the system into a hierarchical Bayesian framework in which other unknown factors, such as the magnitude of the model uncertainty, can also be explored. A pseudo-data example is used to show the usefulness of this approach when compared to a subjectively chosen partitioning of a spatial domain. An inversion using real data is also shown to illustrate the scales at which the data allow for methane emissions over north-west Europe to be resolved.

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