<scp>B</scp>ayesian Forecasting

West, Mike

doi:10.1002/0471667196.ess0600.pub2

Cited by 5 publications

(5 citation statements)

References 62 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…These results imply that our method provides a framework for more precisely estimating the CV of α tGH by smoothing the α tGH and eliminating temporal noise and cross-covariance dependencies. These results are consistent with studies that have shown when temporal correlation is ignored, estimators are often biased and variances are poorly estimated (West, 1996).…”

Section: Discussionsupporting

confidence: 92%

Diagnosing Glaucoma Progression With Visual Field Data Using a Spatiotemporal Boundary Detection Method

Berchuck

Mwanza

Warren

2019

Journal of the American Statistical Association

View full text Add to dashboard Cite

Diagnosing glaucoma progression is critical for limiting irreversible vision loss. A common method for assessing glaucoma progression uses a longitudinal series of visual fields (VF) acquired at regular intervals. VF data are characterized by a complex spatiotemporal structure due to the data generating process and ocular anatomy. Thus, advanced statistical methods are needed to make clinical determinations regarding progression status. We introduce a spatiotemporal boundary detection model that allows the underlying anatomy of the optic disc to dictate the spatial structure of the VF data across time. We show that our new method provides novel insight into vision loss that improves diagnosis of glaucoma progression using data from the Vein Pulsation Study Trial in Glaucoma and the Lions Eye Institute trial registry. Simulations are presented, showing the proposed methodology is preferred over existing spatial methods for VF data. Supplementary materials for this article are available online and the method is implemented in the R package womblR.

show abstract

Section: Discussionsupporting

confidence: 92%

Diagnosing Glaucoma Progression With Visual Field Data Using a Spatiotemporal Boundary Detection Method

Berchuck

Mwanza

Warren

2019

Journal of the American Statistical Association

View full text Add to dashboard Cite

show abstract

“…Forecasting the future of a dynamical system based on past noisy measurements and a system of dynamic equations is crucial for many scientific applications [40]. The most well-known of these applications is arguably weather forecasting [11].…”

Section: Bayesian Variational Forecastermentioning

confidence: 99%

Forward Amortized Inference for Likelihood-Free Variational Marginalization

Ambrogioni,

Güçlü,

Berezutskaya

et al. 2018

Preprint

View full text Add to dashboard Cite

In this paper, we introduce a new form of amortized variational inference by using the forward KL divergence in a joint-contrastive variational loss. The resulting forward amortized variational inference is a likelihood-free method as its gradient can be sampled without bias and without requiring any evaluation of either the model joint distribution or its derivatives. We prove that our new variational loss is optimized by the exact posterior marginals in the fully factorized mean-field approximation, a property that is not shared with the more conventional reverse KL inference. Furthermore, we show that forward amortized inference can be easily marginalized over large families of latent variables in order to obtain a marginalized variational posterior. We consider two examples of variational marginalization. In our first example we train a Bayesian forecaster for predicting a simplified chaotic model of atmospheric convection. In the second example we train an amortized variational approximation of a Bayesian optimal classifier by marginalizing over the model space. The result is a powerful meta-classification network that can solve arbitrary classification problems without further training.

show abstract

“…The pair of sequences x n and y n yield a discrete-time, Markov state space model [27] conditional on the choice of parameters θ. The model is specified by the prior probability distribution of the state x 0 , which we denote as K 0 (dx 0 ), the dynamics of the state sequence x n , which is given by the Markov kernel…”

Section: Numerical Integration and State Space Modelmentioning

confidence: 99%

An iterative importance sampler for Bayesian parameter estimation in stochastic models of multicellular clocks

Mariño,

Miguez,

Zaikin

2015

Preprint

View full text Add to dashboard Cite

We investigate a stochastic version of the synthetic multicellular clock model proposed by Garcia-Ojalvo, Elowitz and Strogatz. By introducing dynamical noise in the model and assuming that the partial observations of the system can be contaminated by additive noise, we enable a principled mechanism to represent experimental uncertainties in the synthesis of the multicellular system and pave the way for the design of probabilistic methods for the estimation of any unknowns in the model. Within this setup, we investigate the use of an iterative importance sampling scheme, termed nonlinear population Monte Carlo (NPMC), for the Bayesian estimation of the model parameters. The algorithm yields a stochastic approximation of the posterior probability distribution of the unknown parameters given the available data (partial and possibly noisy observations). We prove a new theoretical result for this algorithm, which indicates that the approximations converge almost surely to the actual distributions, even when the weights in the importance sampling scheme cannot be computed exactly. We also provide a detailed numerical assessment of the stochastic multicellular model and the accuracy of the proposed NPMC algorithm, including a comparison with the popular particle Metropolis-Hastings algorithm of Andrieu et al., 2010, applied to the same model and an approximate Bayesian computation sequential Monte Carlo method introduced by Mariño et al., 2013.

show abstract

Bayesian Forecasting

Cited by 5 publications

References 62 publications

Diagnosing Glaucoma Progression With Visual Field Data Using a Spatiotemporal Boundary Detection Method

Diagnosing Glaucoma Progression With Visual Field Data Using a Spatiotemporal Boundary Detection Method

Forward Amortized Inference for Likelihood-Free Variational Marginalization

An iterative importance sampler for Bayesian parameter estimation in stochastic models of multicellular clocks

Contact Info

Product

Resources

About