Nonparametric Convergence Assessment for MCMC Model Selection

Brooks, Stephen; Giudici, Paolo; Philippe, Anne

doi:10.1198/1061860031347

Cited by 73 publications

(81 citation statements)

References 38 publications

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“…Otherwise the test shows no significant evidence against the null hypothesis and the chains are considered to be homogeneous. We take a similar approach as in (Brooks et al 2003) in that a drop below the threshold α for a few iterations in the beginning or middle of the chain does not cause the chain pair to get rejected. Rejection requires the significance value to be below α for a larger number of consecutive iterations (see Sect.…”

Section: Convergence Assessmentsmentioning

confidence: 99%

“…The actual convergence diagnostic is implemented using a goodness of fit test. Of the two alternative methods introduced in (Brooks et al 2003) we choose to use the chi-squared test since that generally provides a more conservative diagnostic than the corresponding Kolmogorov-Smirnov test. Let …”

Section: Convergence Assessmentsmentioning

confidence: 99%

“…A way around is to combine similar models and monitor the behavior of groups of models. As suggested by Brooks et al (2003), each model M i is labeled by the number of edges, ν(M i ), that it possesses and models with the same number of edges are grouped. This model indicator should reflect the complexity of the model.…”

Section: Convergence Assessmentsmentioning

confidence: 99%

“…Following the reasoning in (Brooks et al 2003), an estimate of the thinning parameter for sub-sampling the j th chain is obtained as λ j = log p log ρ j , where p is the accepted error level (of independency) and ρ j is an estimate of the convergence rate. In the following, we use p = 0.01.…”

Section: Convergence Assessmentsmentioning

confidence: 99%

“…Therefore, it is suggested that two or more diagnostics are applied together. In this study we use a non-parametric convergence assessment method that has been developed particularly for model selection problems (Brooks et al 2003) and a general purpose method that compares the estimated posterior probabilities of the network connections from two independent simulations (see, e.g., Husmeier 2005). Both Brooks et al's and Husmeier's diagnostics assume that one has several (J ≥ 2) independent chains, which we also assume here.…”

Section: Convergence Assessmentsmentioning

confidence: 99%

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Learning the structure of dynamic Bayesian networks from time series and steady state measurements

Lähdesmäki

Shmulevich

2008

Mach Learn

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Dynamic Bayesian networks (DBN) are a class of graphical models that has become a standard tool for modeling various stochastic time-varying phenomena. In many applications, the primary goal is to infer the network structure from measurement data. Several efficient learning methods have been introduced for the inference of DBNs from time series measurements. Sometimes, however, it is either impossible or impractical to collect time series data, in which case, a common practice is to model the non-time series observations using static Bayesian networks (BN). Such an approach is obviously sub-optimal if the goal is to gain insight into the underlying dynamical model. Here, we introduce Bayesian methods for the inference of DBNs from steady state measurements. We also consider learning the structure of DBNs from a combination of time series and steady state measurements. We introduce two different methods: one that is based on an approximation and another one that provides exact computation. Simulation results demonstrate that dynamic network structures can be learned to an extent from steady state measurements alone and that inference from a combination of steady state and time series data has the potential to improve learning performance relative to the inference from time series data alone. Keywords

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Section: Convergence Assessmentsmentioning

confidence: 99%

Section: Convergence Assessmentsmentioning

confidence: 99%

Section: Convergence Assessmentsmentioning

confidence: 99%

Section: Convergence Assessmentsmentioning

confidence: 99%

Section: Convergence Assessmentsmentioning

confidence: 99%

See 3 more Smart Citations

Learning the structure of dynamic Bayesian networks from time series and steady state measurements

Lähdesmäki

Shmulevich

2008

Mach Learn

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Is there a link between geomagnetic reversal frequency and paleointensity? A Bayesian approach

et al. 2014

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Over the last 25 years, several studies have tested for a link between geomagnetic field intensity and reversal frequency. However, despite a large increase in the number of absolute paleointensity determinations, and improved methods for obtaining such data, two competing models have arisen. Here we employ a new tool for objectively analyzing paleomagnetic time series to investigate the possibility of a link between reversal frequency and paleointensity. Transdimensional Markov chain Monte Carlo techniques are applied to a quality-filtered version of the global paleointensity (PINT) database for the last 202 Myr to model long-term paleointensity behavior. A large ensemble of models is sampled, from which a final representative mean model is extracted. The resulting paleointensity model confirms published conclusions that the single-silicate crystal method gives significantly different results from more conventional whole rock paleointensity methods; this makes it difficult to jointly model the two data types in the same analysis. When the much larger whole rock data set is considered, a stable paleointensity of 5.46 ± 0.28 × 10 22 A/m 2 for the last 202 Myr is consistent with the 95% confidence interval of the paleointensity model. Statistical tests indicate no significant correlation between reversal frequency and field intensity at the 0.05 level. However, this result is likely due to the characteristics of the PINT database rather than being a genuine, physically representative conclusion. Given the paucity of data and general state of the global paleointensity database, concerted efforts to increase the number of high-quality, well-dated paleointensity data are required before conclusions about a link between geomagnetic field intensity and reversal frequency can be confidently drawn.

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2012

Computational Statistics

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Nonparametric Convergence Assessment for MCMC Model Selection

Cited by 73 publications

References 38 publications

Learning the structure of dynamic Bayesian networks from time series and steady state measurements

Learning the structure of dynamic Bayesian networks from time series and steady state measurements

Is there a link between geomagnetic reversal frequency and paleointensity? A Bayesian approach

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