Search results for "Markovin ketjut"

Importance sampling type estimators based on approximate marginal Markov chain Monte Carlo

2020

We consider importance sampling (IS) type weighted estimators based on Markov chain Monte Carlo (MCMC) targeting an approximate marginal of the target distribution. In the context of Bayesian latent variable models, the MCMC typically operates on the hyperparameters, and the subsequent weighting may be based on IS or sequential Monte Carlo (SMC), but allows for multilevel techniques as well. The IS approach provides a natural alternative to delayed acceptance (DA) pseudo-marginal/particle MCMC, and has many advantages over DA, including a straightforward parallelisation and additional flexibility in MCMC implementation. We detail minimal conditions which ensure strong consistency of the sug…

On the convergence of unconstrained adaptive Markov chain Monte Carlo algorithms

2010

Importance sampling correction versus standard averages of reversible MCMCs in terms of the asymptotic variance

2017

We establish an ordering criterion for the asymptotic variances of two consistent Markov chain Monte Carlo (MCMC) estimators: an importance sampling (IS) estimator, based on an approximate reversible chain and subsequent IS weighting, and a standard MCMC estimator, based on an exact reversible chain. Essentially, we relax the criterion of the Peskun type covariance ordering by considering two different invariant probabilities, and obtain, in place of a strict ordering of asymptotic variances, a bound of the asymptotic variance of IS by that of the direct MCMC. Simple examples show that IS can have arbitrarily better or worse asymptotic variance than Metropolis-Hastings and delayed-acceptanc…

bssm: Bayesian Inference of Non-linear and Non-Gaussian State Space Models in R

2021

We present an R package bssm for Bayesian non-linear/non-Gaussian state space modelling. Unlike the existing packages, bssm allows for easy-to-use approximate inference based on Gaussian approximations such as the Laplace approximation and the extended Kalman filter. The package accommodates also discretely observed latent diffusion processes. The inference is based on fully automatic, adaptive Markov chain Monte Carlo (MCMC) on the hyperparameters, with optional importance sampling post-correction to eliminate any approximation bias. The package implements also a direct pseudo-marginal MCMC and a delayed acceptance pseudo-marginal MCMC using intermediate approximations. The package offers …

Cluster priors in the Bayesian modelling of fMRI data

2001

A New Method to Reconstruct Quantitative Food Webs and Nutrient Flows from Isotope Tracer Addition Experiments

2020

Understanding how nutrients flow through food webs is central in ecosystem ecology. Tracer addition experiments are powerful tools to reconstruct nutrient flows by adding an isotopically enriched element into an ecosystem and tracking its fate through time. Historically, the design and analysis of tracer studies have varied widely, ranging from descriptive studies to modeling approaches of varying complexity. Increasingly, isotope tracer data are being used to compare ecosystems and analyze experimental manipulations. Currently, a formal statistical framework for analyzing such experiments is lacking, making it impossible to calculate the estimation errors associated with the model fit, the…

Statistical analysis of life sequence data

2016

Combining Sequence Analysis and Hidden Markov Models in the Analysis of Complex Life Sequence Data

2018

Life course data often consists of multiple parallel sequences, one for each life domain of interest. Multichannel sequence analysis has been used for computing pairwise dissimilarities and finding clusters in this type of multichannel (or multidimensional) sequence data. Describing and visualizing such data is, however, often challenging. We propose an approach for compressing, interpreting, and visualizing the information within multichannel sequences by finding (1) groups of similar trajectories and (2) similar phases within trajectories belonging to the same group. For these tasks we combine multichannel sequence analysis and hidden Markov modelling. We illustrate this approach with an …

Bayesian semiparametric long memory models for discretized event data

2020

We introduce a new class of semiparametric latent variable models for long memory discretized event data. The proposed methodology is motivated by a study of bird vocalizations in the Amazon rain forest; the timings of vocalizations exhibit self-similarity and long range dependence. This rules out Poisson process based models where the rate function itself is not long range dependent. The proposed class of FRActional Probit (FRAP) models is based on thresholding, a latent process. This latent process is modeled by a smooth Gaussian process and a fractional Brownian motion by assuming an additive structure. We develop a Bayesian approach to inference using Markov chain Monte Carlo and show g…