Efficient MCMC for Binomial Logit Models

Fussl, Agnes; Frühwirth‐Schnatter, Sylvia; Frühwirth, R.

doi:10.1145/2414416.2414419

Cited by 11 publications

(27 citation statements)

References 24 publications

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“…Their sampler uses a t 6 proposal, while ours uses a normal proposal. The suite of routines in the binomlogit package (Fussl, 2012) implement the techniques discussed in Fussl et al (2013). One routine provided by the binomlogit package coincides with the technique described in Frühwirth-Schnatter and Frühwirth (2010) for the case of binary logistic regression.…”

Section: S32 Methodsmentioning

confidence: 99%

“…Strictly speaking, this is not logistic regression; it is binary regression using a Student-t cumulative distribution function as the inverse link function. dRUMAuxMix: Work by Fussl et al (2013) that extends the technique of Frühwirth-Schnatter and Frühwirth (2010). A convenient representation is found that relies on a discrete mixture of normals approximation for posterior inference that works for binomial logistic regression.…”

Section: S32 Methodsmentioning

confidence: 99%

“…A convenient representation is found that relies on a discrete mixture of normals approximation for posterior inference that works for binomial logistic regression. From the R package binomlogit (Fussl, 2012). dRUMIndMH: Similar to dRUMAuxMix, but instead of using a discrete mixture of normals, use a single normal to approximate the error term and correct using MetropolisHastings.…”

Section: S32 Methodsmentioning

confidence: 99%

“…The dRUM representation is superior to the random utility approach explored in Frühwirth-Schnatter and Frühwirth (2007). Further work by Fussl et al (2013) improves the approach for binomial logistic models. In this extension, one must use a table of different weights and variances representing different normal mixtures, to approximate a finite collection of type-III logistic distributions, and interpolate within this table to approximate the entire family.…”

Section: Existing Data-augmentation Schemesmentioning

confidence: 98%

“…For negative-binomial regression, Frühwirth-Schnatter et al (2009) employ the discretemixture/table-interpolation approach, like that used by Fussl et al (2013), to produce a tractable data augmentation scheme. In some instances, the Pólya-Gamma approach outperforms this method; in others, it does not.…”

Section: Existing Data-augmentation Schemesmentioning

confidence: 99%

See 4 more Smart Citations

Bayesian Inference for Logistic Models Using Pólya–Gamma Latent Variables

Polson

Scott

Windle

2013

Journal of the American Statistical Association

750

1,070

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We propose a new data-augmentation strategy for fully Bayesian inference in models with binomial likelihoods. The approach appeals to a new class of Pólya-Gamma distributions, which are constructed in detail. A variety of examples are presented to show the versatility of the method, including logistic regression, negative binomial regression, nonlinear mixed-effects models, and spatial models for count data. In each case, our data-augmentation strategy leads to simple, effective methods for posterior inference that: (1) circumvent the need for analytic approximations, numerical integration, or Metropolis-Hastings; and (2) outperform other known data-augmentation strategies, both in ease of use and in computational efficiency. All methods, including an efficient sampler for the Pólya-Gamma distribution, are implemented in the R package BayesLogit.In the technical supplement appended to the end of the paper, we provide further details regarding the generation of Pólya-Gamma random variables; the empirical benchmarks reported in the main manuscript; and the extension of the basic dataaugmentation framework to contingency tables and multinomial outcomes.

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Section: S32 Methodsmentioning

confidence: 99%

Section: S32 Methodsmentioning

confidence: 99%

Section: S32 Methodsmentioning

confidence: 99%

Section: Existing Data-augmentation Schemesmentioning

confidence: 98%

Section: Existing Data-augmentation Schemesmentioning

confidence: 99%

See 3 more Smart Citations

Bayesian Inference for Logistic Models Using Pólya–Gamma Latent Variables

Polson

Scott

Windle

2013

Journal of the American Statistical Association

750

1,070

View full text Add to dashboard Cite

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Forecasting under model uncertainty: Non‐homogeneous hidden Markov models with Pòlya‐Gamma data augmentation

Koki

Meligkotsidou

Vrontos

2020

Journal of Forecasting

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We consider two-state Non-Homogeneous Hidden Markov Models (NHHMMs) for forecasting univariate time series. Given a set of predictors, the time series are modeled via predictive regressions with state dependent coefficients and timevarying transition probabilities that depend on the predictors via a logistic function. In a hidden Markov setting, inference for logistic regression coefficients becomes complicated and in some cases impossible due to convergence issues. In this paper, we aim to address this problem using a new latent variable scheme that utilizes the Pólya-Gamma class of distributions. We allow for model uncertainty regarding the predictors that affect the series both linearly -in the mean -and non-linearly -in the transition matrix. Predictor selection and inference on the model parameters are based on a MCMC scheme with reversible jump steps. Single-step and multiple-steps-ahead predictions are obtained by the most probable model, median probability model or a Bayesian Model Averaging approach. Using simulation experiments, we illustrate the performance of our algorithm in various setups, in terms of mixing properties, model selection and predictive ability. An empirical study on realized volatility data shows that our methodology gives improved forecasts compared to benchmark models.

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Genomic prediction of dichotomous traits with Bayesian logistic models

Technow

Melchinger

2013

Theor Appl Genet

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Bayesian methods are a popular choice for genomic prediction of genotypic values. The methodology is well established for traits with approximately Gaussian phenotypic distribution. However, numerous important traits are of dichotomous nature and the phenotypic counts observed follow a Binomial distribution. The standard Gaussian generalized linear models (GLM) are not statistically valid for this type of data. Therefore, we implemented Binomial GLM with logit link function for the BayesB and Bayesian GBLUP genomic prediction methods. We compared these models with their standard Gaussian counterparts using two experimental data sets from plant breeding, one on female fertility in wheat and one on haploid induction in maize, as well as a simulated data set. With the aid of the simulated data referring to a bi-parental population of doubled haploid lines, we further investigated the influence of training set size (N), number of independent Bernoulli trials for trait evaluation (n i ) and genetic architecture of the trait on genomic prediction accuracies and abilities in general and on the relative performance of our models. For BayesB, we in addition implemented finite mixture Binomial GLM to account for overdispersion. We found that prediction accuracies increased with increasing N and n i . For the simulated and experimental data sets, we found Binomial GLM to be superior to Gaussian models for small n i , but that for large n i Gaussian models might be used as ad hoc approximations. We further show with simulated and real data sets that accounting for overdispersion in Binomial data can markedly increase the prediction accuracy.

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Efficient MCMC for Binomial Logit Models

Cited by 11 publications

References 24 publications

Bayesian Inference for Logistic Models Using Pólya–Gamma Latent Variables

Bayesian Inference for Logistic Models Using Pólya–Gamma Latent Variables

Forecasting under model uncertainty: Non‐homogeneous hidden Markov models with Pòlya‐Gamma data augmentation

Genomic prediction of dichotomous traits with Bayesian logistic models

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