Adaptive Incremental Mixture Markov Chain Monte Carlo

Maire, Florian; Friel, Nial; Mira, Antonietta; Raftery, Adrian E.

doi:10.1080/10618600.2019.1598872

Cited by 6 publications

(7 citation statements)

References 42 publications

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“…However, if parameters are interdependent, MCMC algorithm samples manifolds of alternative solutions, resulting in large standard errors of the overfitted parameters. We successfully addressed this issue by a modified version of Maire’s algorithm [ 56 ]. Central to this approach is the idea that the proposal distribution adapts to the target by locally adding a mixture component when the discrepancy between the proposal mixture and the target is deemed to be too large.…”

Section: Discussionmentioning

confidence: 99%

“…Here the proposal distribution is learned along the process using the full information cumulated so far. We implemented the adaptive MCMC version with Gaussian proposal distribution described in [ 60 ] as well as adaptive incremental Mixture MCMC [ 56 ] called AIMM, which we modified slightly. Strictly speaking, these methods are not really Markov chains, because proposal distribution of the next step depends on all preceding states

rather than only the previous one.…”

Section: Figure A1mentioning

confidence: 99%

“…If

stays in the r -th cluster, it updates the r -th covariance matrix in a similar way as in Haario’s algorithm [ 60 ], Equation (A26). We here modified the conditions for new cluster formation compared to [ 56 ] as follows. In our algorithm, a new cluster is formed when one of the following conditions hold: The Mahalanobis distance of

to the cluster from which it was generated is less than 0.025 or larger than 0.975.…”

Section: Figure A1mentioning

confidence: 99%

See 2 more Smart Citations

On the Parametrization of Epidemiologic Models—Lessons from Modelling COVID-19 Epidemic

Kheifetz¹,

Kirsten²,

Scholz

2022

Viruses

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Numerous prediction models of SARS-CoV-2 pandemic were proposed in the past. Unknown parameters of these models are often estimated based on observational data. However, lag in case-reporting, changing testing policy or incompleteness of data lead to biased estimates. Moreover, parametrization is time-dependent due to changing age-structures, emerging virus variants, non-pharmaceutical interventions, and vaccination programs. To cover these aspects, we propose a principled approach to parametrize a SIR-type epidemiologic model by embedding it as a hidden layer into an input-output non-linear dynamical system (IO-NLDS). Observable data are coupled to hidden states of the model by appropriate data models considering possible biases of the data. This includes data issues such as known delays or biases in reporting. We estimate model parameters including their time-dependence by a Bayesian knowledge synthesis process considering parameter ranges derived from external studies as prior information. We applied this approach on a specific SIR-type model and data of Germany and Saxony demonstrating good prediction performances. Our approach can estimate and compare the relative effectiveness of non-pharmaceutical interventions and provide scenarios of the future course of the epidemic under specified conditions. It can be translated to other data sets, i.e., other countries and other SIR-type models.

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Section: Discussionmentioning

confidence: 99%

rather than only the previous one.…”

Section: Figure A1mentioning

confidence: 99%

“…If

to the cluster from which it was generated is less than 0.025 or larger than 0.975.…”

Section: Figure A1mentioning

confidence: 99%

See 1 more Smart Citation

On the Parametrization of Epidemiologic Models—Lessons from Modelling COVID-19 Epidemic

Kheifetz¹,

Kirsten²,

Scholz

2022

Viruses

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“…Nevertheless, we have been able to analyze certain behaviors of proposals based on kernel density estimators. A version of this procedure (to use kernel density estimators as a proposal in independent Metropolis-Hastings) was previously pursued in Maire et al (2019); however, they do not appear to have looked at the question of when the addition of a new component into the mixture is beneficial, which is the topic under consideration in the sequel.…”

Section: H Adaptation Of a Kernel Density Proposal Distributionmentioning

confidence: 99%

Adaptation of the Independent Metropolis-Hastings Sampler with Normalizing Flow Proposals

Brofos¹,

Gabrié²,

Brubaker³

et al. 2021

Preprint

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Markov Chain Monte Carlo (MCMC) methods are a powerful tool for computation with complex probability distributions. However the performance of such methods is critically dependant on properly tuned parameters, most of which are difficult if not impossible to know a priori for a given target distribution. Adaptive MCMC methods aim to address this by allowing the parameters to be updated during sampling based on previous samples from the chain at the expense of requiring a new theoretical analysis to ensure convergence. In this work we extend the convergence theory of adaptive MCMC methods to a new class of methods built on a powerful class of parametric density estimators known as normalizing flows. In particular, we consider an independent Metropolis-Hastings sampler where the proposal distribution is represented by a normalizing flow whose parameters are updated using stochastic gradient descent. We explore the practical performance of this procedure on both synthetic settings and in the analysis of a physical field system and compare it against both adaptive and non-adaptive MCMC methods.

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“…In view of the shortcomings of previous works, this paper proposes a downhole track line detection model based on CGAN. We use the method of adversarial learning to solve the problem of artificially designing complex loss functions and introduce Monte Carlo search [14] technology into the generator network. Monte Carlo searches have been widely used in text generation tasks.…”

Section: Introductionmentioning

confidence: 99%

Downhole Track Detection via Multi-dimensional Conditional Generative Adversarial Nets

Wei

Yang

et al. 2024

IEEE Access

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Frequent mine disasters cause a large number of casualties and property losses. Autonomous driving is a fundamental measure for solving this problem, and track detection is one of the key technologies for computer vision to achieve downhole automatic driving. The track detection result based on the existing models lacks the semantic detail of the tracks and relies too much on visual postprocessing technology. Therefore, this paper proposes a track detection model based on the multi-dimensional conditional generative adversarial network. First, the generator is decomposed into global and local parts using a multigranularity structure. Second, a multi-scale shared convolution structure is introduced into the discriminator to further guide the generator. In addition, this paper proposes a penalty mechanism based on Monte Carlo search to enhance the semantic constraints in the image generation process. Compared with the state-of-theart semantic segmentation algorithms, extensive experiments on the downhole scene dataset demonstrate proposed model achieved the best results in terms of pixel accuracy, intersection-over-union (IOU) and the track detection accuracy. This paper provides a new idea for track line detection. In the future, the model can also beapplied to other segmentation problems as well. Code and data will be shared.

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Adaptive Incremental Mixture Markov Chain Monte Carlo

Cited by 6 publications

References 42 publications

On the Parametrization of Epidemiologic Models—Lessons from Modelling COVID-19 Epidemic

On the Parametrization of Epidemiologic Models—Lessons from Modelling COVID-19 Epidemic

Adaptation of the Independent Metropolis-Hastings Sampler with Normalizing Flow Proposals

Downhole Track Detection via Multi-dimensional Conditional Generative Adversarial Nets

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