Ergonomic and Reliable Bayesian Inference with Adaptive Markov Chain Monte Carlo

Vihola, Matti

doi:10.1002/9781118445112.stat08286

Cited by 12 publications

(12 citation statements)

References 37 publications

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“…The (A)AI-CPF applied with M (θ) 2:T and G (θ) 1:T may be used as a replacement of the CPF steps in a PG. Another adaptation, independent of the AAI-CPF, may be used for the hyperparameter updates; see for instance the discussion in [28].…”

Section: Methods For Diffuse Initialisation Of Conditional Particle F...mentioning

confidence: 99%

“…Line 2 involves an update of θ (j−1) to θ (j) using transition probabilities K ζ θ ( • | x 1:T ) which leave π(θ | x 1:T ) invariant, and Line 3 is (optional) adaptation. This could, for instance, correspond to the robust adaptive Metropolis algorithm (RAM) as suggested in [28]. Lines 4 and 5 implement the AAI-CPF.…”

Section: Methods For Diffuse Initialisation Of Conditional Particle F...mentioning

confidence: 99%

“…The DPG-BS is a standard particle Gibbs algorithm, where the first latent state x 1 is regarded as a 'parameter', that is, the algorithm alternates between the update of x 1 conditional on x 2:T using a random-walk Metropolis-within-Gibbs step, and the update of the latent state variables x 2:T conditional on x 1 using the CPF-BS. We also adapt the Metropolis-within-Gibbs proposal distribution Q DPG of the DPG-BS, using the RAM algorithm [27]; see also the discussion in [28]. For further details regarding our implementation of the DPG-BS, see Appendix B.…”

Section: 2mentioning

confidence: 99%

“…We used the AAI-PG (Algorithm 9) with the FDI-CPF with the ASWAM adaptation, and a RAM adaptation [27,28] for σ and p, (i.e. in the lines 2-3 of Algorithm 9).…”

Section: 3mentioning

confidence: 99%

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Conditional particle filters with diffuse initial distributions

Karppinen¹,

Vihola²

2020

Preprint

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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 on-line 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.

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Section: Methods For Diffuse Initialisation Of Conditional Particle F...mentioning

confidence: 99%

Section: Methods For Diffuse Initialisation Of Conditional Particle F...mentioning

confidence: 99%

Section: 2mentioning

confidence: 99%

“…We used the AAI-PG (Algorithm 9) with the FDI-CPF with the ASWAM adaptation, and a RAM adaptation [27,28] for σ and p, (i.e. in the lines 2-3 of Algorithm 9).…”

Section: 3mentioning

confidence: 99%

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Conditional particle filters with diffuse initial distributions

Karppinen¹,

Vihola²

2020

Preprint

Self Cite

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“…Combining the likelihood (8) with the prior p(β, θ I , θ Z ) yields the approximate posterior distribution. To sample from this distribution, we use Robust Adaptive Metropolis algorithm (Vihola 2012(Vihola , 2020, which uses a Gaussian random-walk proposal distribution, whose covariance is updated adaptively. The limiting proposal covariance matches the shape of the posterior, such that an average acceptance rate of 0.234 is attained, following the theoretical findings presented e.g.…”

Section: Mcmcmentioning

confidence: 99%

Hierarchical log Gaussian Cox process for regeneration in uneven-aged forests

et al. 2021

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We propose a hierarchical log Gaussian Cox process (LGCP) for point patterns, where a set of points $$\varvec{x}$$ x affects another set of points $$\varvec{y}$$ y but not vice versa. We use the model to investigate the effect of large trees on the locations of seedlings. In the model, every point in $$\varvec{x}$$ x has a parametric influence kernel or signal, which together form an influence field. Conditionally on the parameters, the influence field acts as a spatial covariate in the intensity of the model, and the intensity itself is a non-linear function of the parameters. Points outside the observation window may affect the influence field inside the window. We propose an edge correction to account for this missing data. The parameters of the model are estimated in a Bayesian framework using Markov chain Monte Carlo where a Laplace approximation is used for the Gaussian field of the LGCP model. The proposed model is used to analyze the effect of large trees on the success of regeneration in uneven-aged forest stands in Finland.

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Markov-Chain Monte Carlo

Jiang

2021

Springer Texts in Statistics

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Due to the high dimensionality or multimodality that is common in modern astronomy, sampling Bayesian posteriors can be challenging. Several publicly available codes based on different sampling algorithms can solve these complex models, but the execution of the code is not always efficient or fast enough. The article introduces a C language general-purpose code, Nii-C a) (Jin 2024), that implements a framework of Automatic Parallel Tempering Markov Chain Monte Carlo. Automatic in this context means that the parameters that ensure an efficient parallel tempering process can be set by a control system during the inital stages of a sampling process. The auto-tuned parameters consist of two parts, the temperature ladders of all parallel tempering Markov chains and the proposal distributions for all model parameters across all parallel tempering chains. In order to reduce dependencies in the compilation process and increase the code's execution speed, Nii-C code is constructed entirely in the C language and parallelised using the Message-Passing Interface protocol to optimise the efficiency of parallel sampling. These implementations facilitate rapid convergence in the sampling of highdimensional and multi-modal distributions, as well as expeditious code execution time. The Nii-C code can be used in various research areas to trace complex distributions due to its high sampling efficiency and quick execution speed. This article presents a few applications of the Nii-C code.

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Ergonomic and Reliable Bayesian Inference with Adaptive Markov Chain Monte Carlo

Cited by 12 publications

References 37 publications

Conditional particle filters with diffuse initial distributions

Conditional particle filters with diffuse initial distributions

Hierarchical log Gaussian Cox process for regeneration in uneven-aged forests

Markov-Chain Monte Carlo

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