Understanding the Hastings Algorithm

Minh, David D. L.; Minh, Do Le

doi:10.1080/03610918.2013.777455

Cited by 24 publications

(10 citation statements)

References 13 publications

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“…Parameters were updated by sequential Gibbs sampling. In sequential Gibbs sampling, one parameter is updated at a time using the Metropolis-Hastings algorithm [ 40 , 41 ]: For each single parameter, a proposal is drawn from a normal distribution centered at the current value, and a scale of unity for Δ H , Δ G , and Δ H 0 , or the initial guess value for σ , [ L ] s , and [ R ] 0 ; The trial move is accepted or rejected according to the Metropolis criterion. If it is accepted, the next value in the Markov chain is the trial move.…”

Section: Methodsmentioning

confidence: 99%

Bayesian analysis of isothermal titration calorimetry for binding thermodynamics

Nguyen¹,

Rustenburg²,

Krimmer³

et al. 2018

PLoS ONE

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Isothermal titration calorimetry (ITC) is the only technique able to determine both the enthalpy and entropy of noncovalent association in a single experiment. The standard data analysis method based on nonlinear regression, however, provides unrealistically small uncertainty estimates due to its neglect of dominant sources of error. Here, we present a Bayesian framework for sampling from the posterior distribution of all thermodynamic parameters and other quantities of interest from one or more ITC experiments, allowing uncertainties and correlations to be quantitatively assessed. For a series of ITC measurements on metal:chelator and protein:ligand systems, the Bayesian approach yields uncertainties which represent the variability from experiment to experiment more accurately than the standard data analysis. In some datasets, the median enthalpy of binding is shifted by as much as 1.5 kcal/mol. A Python implementation suitable for analysis of data generated by MicroCal instruments (and adaptable to other calorimeters) is freely available online.

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Section: Methodsmentioning

confidence: 99%

Bayesian analysis of isothermal titration calorimetry for binding thermodynamics

Nguyen¹,

Rustenburg²,

Krimmer³

et al. 2018

PLoS ONE

Self Cite

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show abstract

“…A well-known class of methods is based on Markov chain Monte Carlo (MCMC), where the aim is to define an iterative process whose stationary distribution coincides with the target distribution, which in Bayesian inversion is the posterior. MCMC techniques come in many variants, and one common variant is MCMC sampling with Metropolis-Hastings dynamics (Minh and Le Minh 2015), which generates a Markov chain with equilibrium distribution that coincides with the posterior in the limit. Other variants use Gibbs sampling, which reduces the autocorrelation between samples.…”

Section: Computational Feasibilitymentioning

confidence: 99%

Solving inverse problems using data-driven models

et al. 2019

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Recent research in inverse problems seeks to develop a mathematically coherent foundation for combining data-driven models, and in particular those based on deep learning, with domain-specific knowledge contained in physical–analytical models. The focus is on solving ill-posed inverse problems that are at the core of many challenging applications in the natural sciences, medicine and life sciences, as well as in engineering and industrial applications. This survey paper aims to give an account of some of the main contributions in data-driven inverse problems.

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“…We perform the analysis with the software BAT v1.1.0-DEV [21], which internally uses CUBA [31] v4.2 for the integration of multi-dimensional probabilities and the Metropolis-Hastings algorithm [32] for the fit. The computation time depends on the number of samples drawn from the considered probability distribution.…”

Section: Fit Proceduresmentioning

confidence: 99%

CUORE sensitivity to $$0\nu \beta \beta $$ decay

et al. 2017

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We report a study of the CUORE sensitivity to neutrinoless double beta (0νββ) decay. We used a Bayesian analysis based on a toy Monte Carlo (MC) approach to extract the exclusion sensitivity to the 0νββ decay half-life (T 0ν 1/2 ) at 90% credibility interval (CI) -i.e. the interval containing the true value of T 0ν 1/2 with 90% probability -and the 3 σ discovery sensitivity. We consider various background levels and energy resolutions, and describe the influence of the data division in subsets with different background levels. If the background level and the energy resolution meet the expectation, CUORE will reach a 90% CI exclusion sensitivity of 2 · 10 25 year with 3 months, and 9 · 10 25 year with 5 years of live time. Under the same conditions, the discovery sensitivity after 3 months and 5 years will be 7 · 10 24 year and 4 · 10 25 year, respectively.

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Understanding the Hastings Algorithm

Cited by 24 publications

References 13 publications

Bayesian analysis of isothermal titration calorimetry for binding thermodynamics

Bayesian analysis of isothermal titration calorimetry for binding thermodynamics

Solving inverse problems using data-driven models

CUORE sensitivity to $$0\nu \beta \beta $$ decay

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