Optimal Proposal Distributions and Adaptive MCMC

Fan, Ye; Sisson, Scott A.

doi:10.1201/b10905-5

Cited by 170 publications

(147 citation statements)

References 41 publications

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“…These results are consistent with existing literature on tuning proposal distributions [23]. It is possible that other methods of "data-driven" tuning which incorporate overall variance in the MSIM may be necessary to further improve acceptance rates in the RJMCMC scheme [24].…”

Section: Discussionsupporting

confidence: 81%

Mixtures of Self-Modelling Regressions

K¹

2014

J Biomet Biostat

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A shape invariant model for functions f 1 ,…,f n specifies that each individual function f i can be related to a common shape function g through the relation f i (x)=a i g(c i x + d i ) + b i . We consider a flexible mixture model that allows multiple shape functions g 1 ,…,g K , where each f i is a shape invariant transformation of one of those g k . We derive an MCMC algorithm for fitting the model using Bayesian Adaptive Regression Splines (BARS), propose a strategy to improve its mixing properties and utilize existing model selection criteria in semiparametric mixtures to select the number of distinct shape functions. We discuss some of the computational difficulties that arise. The method is illustrated using synaptic transmission data, where the groups of functions may indicate different active zones in a synapse.

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Section: Discussionsupporting

confidence: 81%

Mixtures of Self-Modelling Regressions

K¹

2014

J Biomet Biostat

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“…The burn-in period was also used to calibrate the proposal distribution used by the Metropolis-Hastings algorithm to select potential new states for the Markov chain because a good choice of proposal distribution can make a large difference in the efficiency of the sampler. We used an adaptive proposal distribution: Setting the covariance of the Gaussian proposal distribution to be a constant multiple of the covariance of the already collected samples, plus a small additive diagonal factor to ensure the covariance matrix did not collapse to zero (Rosenthal, 2011). Convergence of the sampler was evalu- ated by comparing the variance between and within the two runs of the sampler using thê R p statistic (Brooks & Gelman, 1998).…”

Section: Value Functionmentioning

confidence: 99%

Weighing Outcomes by Time or Against Time? Evaluation Rules in Intertemporal Choice

2014

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Models of intertemporal choice draw on three evaluation rules, which we compare in the restricted domain of choices between smaller sooner and larger later monetary outcomes. The hyperbolic discounting model proposes an alternative-based rule, in which options are evaluated separately. The interval discounting model proposes a hybrid rule, in which the outcomes are evaluated separately, but the delays to those outcomes are evaluated in comparison with one another. The tradeoff model proposes an attribute-based rule, in which both outcomes and delays are evaluated in comparison with one another: People consider both the intervals between the outcomes and the compensations received or paid over those intervals. We compare highly general parametric functional forms of these models by means of a Bayesian analysis, a method of analysis not previously used in intertemporal choice. We find that the hyperbolic discounting model is outperformed by the interval discounting model, which, in turn, is outperformed by the tradeoff model. Our cognitive modeling is among the first to offer quantitative evidence against the conventional view that people make intertemporal choices by discounting the value of future outcomes, and in favor of the view that they directly compare options along the time and outcome attributes.

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“…Variances of proposal distributions are automatically adjusted in an adaptive stage before the main stage of MCMC so that the acceptance proportions of proposed samples are between 0.3 and 0.5 (Rosenthal, 2011). Initial values of…”

Section: Continuous Itemsmentioning

confidence: 99%

A Direct Bayesian Estimation of Reliability

Okamoto

2013

Behaviormetrika

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Bayesian estimation of reliability by MCMC is proposed as an alternative to coefficient alpha, regarded as a classic method of estimating reliability. However, coefficient alpha is derived from a structural factor model, various kinds of which are used in modern data analysis, e.g., SEM, sometimes used to analyze reliability. SEM emphasizes covariances to analyze categorical items that are estimated by polychoric correlations. The methods proposed in this study directly apply the MCMC algorithm to individual examinees responses. Thus, covariances are not estimated but implicitly represented by factor models. For categorical items, models for continuous items are modified and applied based on an ordinal probit regression. The performances of the proposed models and algorithms are investigated by simulations and successful results are obtained.

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Optimal Proposal Distributions and Adaptive MCMC

Abstract: Abstract. We review recent work concerning optimal proposal scalings for Metropolis-Hastings MCMC algorithms, and adaptive MCMC algorithms for trying to improve the algorithm on the fly.

Cited by 170 publications

References 41 publications

Mixtures of Self-Modelling Regressions

Mixtures of Self-Modelling Regressions

Weighing Outcomes by Time or Against Time? Evaluation Rules in Intertemporal Choice

A Direct Bayesian Estimation of Reliability

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