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Conditional particle filters with diffuse initial distributions.

ABSTRACT: Conditional particle filters (CPFs) are powerful smoothing algorithms for general nonlinear/non-Gaussian hidden Markov models. However, CPFs can be inefficient or difficult to apply with diffuse initial distributions, which are common in statistical applications. We propose a simple but generally applicable auxiliary variable method, which can be used together with the CPF in order to perform efficient inference with diffuse initial distributions. The method only requires simulatable Markov transitions that are reversible with respect to the initial distribution, which can be improper. We focus in particular on random walk type transitions which are reversible with respect to a uniform initial distribution (on some domain), and autoregressive kernels for Gaussian initial distributions. We propose to use online adaptations within the methods. In the case of random walk transition, our adaptations use the estimated covariance and acceptance rate adaptation, and we detail their theoretical validity. We tested our methods with a linear Gaussian random walk model, a stochastic volatility model, and a stochastic epidemic compartment model with time-varying transmission rate. The experimental findings demonstrate that our method works reliably with little user specification and can be substantially better mixing than a direct particle Gibbs algorithm that treats initial states as parameters.

Supplementary information

The online version contains supplementary material available at 10.1007/s11222-020-09975-1.

SUBMITTER: Karppinen S

PROVIDER: S-EPMC7926083 | biostudies-literature | 2021

REPOSITORIES: biostudies-literature

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Conditional particle filters with diffuse initial distributions.

Karppinen Santeri S Vihola Matti M

Statistics and computing 20210303 3

Conditional particle filters (CPFs) are powerful smoothing algorithms for general nonlinear/non-Gaussian hidden Markov models. However, CPFs can be inefficient or difficult to apply with diffuse initial distributions, which are common in statistical applications. We propose a simple but generally applicable auxiliary variable method, which can be used together with the CPF in order to perform efficient inference with diffuse initial distributions. The method only requires simulatable Markov tran ...[more]

PMID: 33679010

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Project description:Abstract Understanding the drivers of trait selection is critical for resolving community assembly processes. Here, we test the importance of environmental filtering and trait covariance for structuring the functional traits of understory herbaceous communities distributed along a natural environmental resource gradient that varied in soil moisture, temperature, and nitrogen availability, produced by different topographic positions in the southern Appalachian Mountains. To uncover potential differences in community?level trait responses to the resource gradient, we quantified the averages and variances of both abundance?weighted and unweighted values for six functional traits (vegetative height, leaf area, specific leaf area, leaf dry matter content, leaf nitrogen, and leaf ?13C) using 15 individuals of each of the 108 species of understory herbs found at two sites in the southern Appalachians of western North Carolina, USA. Environmental variables were better predictors of weighted than unweighted community?level average trait values for all but height and leaf N, indicating strong environmental filtering of plant abundance. Community?level variance patterns also showed increased convergence of abundance?weighted traits as resource limitation became more severe. Functional trait covariance patterns based on weighted averages were uniform across the gradient, whereas coordination based on unweighted averages was inconsistent and varied with environmental context. In line with these results, structural equation modeling revealed that unweighted community?average traits responded directly to local environmental variation, whereas weighted community?average traits responded indirectly to local environmental variation through trait coordination. Our finding that trait coordination is more important for explaining the distribution of weighted than unweighted average trait values along the gradient indicates that environmental filtering acts on multiple traits simultaneously, with abundant species possessing more favorable combinations of traits for maximizing fitness in a given environment. Understanding the drivers of trait selection is critical for resolving community assembly processes. Our finding that trait coordination is more important for explaining the distribution of weighted than unweighted average trait values along the gradient indicates that environmental filtering acts on multiple traits simultaneously, with abundant species possessing more favorable combinations of traits for maximizing fitness in a given environment.

Dataset Information

Conditional particle filters with diffuse initial distributions.

Supplementary information

Publications

Conditional particle filters with diffuse initial distributions.

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