Correction to: Function estimation with locally adaptive dynamic models

Lang, Stefan; Fronk, Eva-Maria; Fahrmeir, Ludwig

doi:10.1007/bf02753919

Cited by 9 publications

(23 citation statements)

References 1 publication

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“…The approach extends recent work by Lang et al (2002) for Gaussian responses. Our approach uses a two-stage prior for the unknown regression function.…”

Section: Introductionsupporting

confidence: 64%

“…We start with the stochastic dependent variant. Following Lang et al (2002) we set τ 2 s = exp(h s ). For the parameters h s we add a second smoothness prior in the form of first or second order random walks for…”

Section: Prior Modelsmentioning

confidence: 99%

“…It turns out, that updating of the variance parameters vector h j in one step is not feasible because of too small acceptance rates. As a remedy the parameter vector h j must be further divided into smaller blocks (usually of size 10-20), see Lang et al (2002) for details on updating the variance parameters.…”

Section: Bayesian Inference Via Mcmcmentioning

confidence: 99%

“…From a computational point of view we prefer probit models because updates of the full conditionals of the latent utilities are (slightly) faster compared to logit models or the t-link. The advantage of augmenting the posterior by the latent variables is that the full conditionals for functions f j become Gaussian, allowing the usage of the sampling schemes developed for Gaussian responses in Lang et al (2002) with only minor changes. Updating of f j , h j and σ 2 j , j = 1, .…”

Section: Bayesian Inference Via Mcmcmentioning

confidence: 99%

“…. , p, can be done exactly as described in Lang et al (2002) using the current values of the latent utilities as (pseudo) responses.…”

Section: Bayesian Inference Via Mcmcmentioning

confidence: 99%

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Locally Adaptive Function Estimation for Binary Regression Models

Jerak

Lang

2005

Biom. J.

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In this paper we present a nonparametric Bayesian approach for fitting unsmooth or highly oscillating functions in regression models with binary responses. The approach extends previous work by Lang et al. (2002) for Gaussian responses. Nonlinear functions are modelled by first or second order random walk priors with locally varying variances or smoothing parameters. Estimation is fully Bayesian and uses latent utility representations of binary regression models for efficient block sampling from the full conditionals of nonlinear functions.

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“…The approach extends recent work by Lang et al (2002) for Gaussian responses. Our approach uses a two-stage prior for the unknown regression function.…”

Section: Introductionsupporting

confidence: 64%

Section: Prior Modelsmentioning

confidence: 99%

Section: Bayesian Inference Via Mcmcmentioning

confidence: 99%

Section: Bayesian Inference Via Mcmcmentioning

confidence: 99%

“…. , p, can be done exactly as described in Lang et al (2002) using the current values of the latent utilities as (pseudo) responses.…”

Section: Bayesian Inference Via Mcmcmentioning

confidence: 99%

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Locally Adaptive Function Estimation for Binary Regression Models

Jerak

Lang

2005

Biom. J.

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Bayesian age–period–cohort models with versatile interactions and long‐term predictions: mortality and population in Finland 1878–2050

Havulinna

2013

Statistics in Medicine

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Age-period-cohort (APC) models are widely used for studying time trends of disease incidence or mortality. Model identifiability has become less of a problem with Bayesian APC models. These models are usually based on random walk (RW1, RW2) smoothing priors. For long and complex time series and for long predicted periods, these models as such may not be adequate. We present two extensions for the APC models. First, we introduce flexible interactions between the age, period and cohort effects based on a two-dimensional conditional autoregressive smoothing prior on the age/period plane. Our second extension uses autoregressive integrated (ARI) models to provide reasonable long-term predictions. To illustrate the utility of our model framework, we provide stochastic predictions for the Finnish male and female population, in 2010-2050. For that, we first study and forecast all-cause male and female mortality in Finland, 1878-2050, showing that using an interaction term is needed for fitting and interpreting the observed data. We then provide population predictions using a cohort component model, which also requires predictions for fertility and migration. As our main conclusion, ARI models have better properties for predictions than the simple RW models do, but mixing these prediction models with RW1 or RW2 smoothing priors for observed periods leads to a model that is not fully consistent. Further research with our model framework will concentrate on using a more consistent model for smoothing and prediction, such as autoregressive integrated moving average models with state-space methods or Gaussian process priors.

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Priors for Bayesian adaptive spline smoothing

Speckman

Sun

2011

Ann Inst Stat Math

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Adaptive smoothing has been proposed for curve-fitting problems where the underlying function is spatially inhomogeneous. Two Bayesian adaptive smoothing models, Bayesian adaptive smoothing splines on a lattice and Bayesian adaptive P-splines, are studied in this paper. Estimation is fully Bayesian and carried out by efficient Gibbs sampling. Choice of prior is critical in any Bayesian non-parametric regression method. We use objective priors on the first level parameters where feasible, specifically independent Jeffreys priors (right Haar priors) on the implied base linear model and error variance, and we derive sufficient conditions on higher level components to ensure that the posterior is proper. Through simulation, we demonstrate that the common practice of approximating improper priors by proper but diffuse priors may lead to invalid inference, and we show how appropriate choices of proper but only weakly informative priors yields satisfactory inference.

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Correction to: Function estimation with locally adaptive dynamic models

Cited by 9 publications

References 1 publication

Locally Adaptive Function Estimation for Binary Regression Models

Locally Adaptive Function Estimation for Binary Regression Models

Bayesian age–period–cohort models with versatile interactions and long‐term predictions: mortality and population in Finland 1878–2050

Priors for Bayesian adaptive spline smoothing

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