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Stimulus reconstruction or decoding methods provide an important tool for understanding how sensory and motor information is represented in neural activity. We address Bayesian decoding methods based on an encoding generalized linear model (GLM) [1, 2] that accurately describes how stimuli are transformed into the spike trains of a group of neurons. The log-concave GLM likelihood is combined wi...

One prevailing assumption in reflection seismology is that the observed trace can be described as a convolution of a source wavelet with the Earth’s reflectivity plus some noise. In a conventional deconvolution approach one thus estimates a linear deconvolution filter to retrieve the reflectivity series from the observed data. This amounts to taking linear combinations of noisy observations and...

In dynamic statistical modeling situations, observations arise sequentially, causing the model to expand by progressive incorporation of new data items and new unknown parameters. For example, in clinical monitoring, new patient-speci c parameters are introduced with each new patient. Markov chain Monte Carlo (MCMC) might be used for posterior inference, but would need to be redone at each expa...

It is a pleasure to present this discussion of Chopin and Jacob (2010), which has been influenced by reading in parallel the recent paper by Chopin, Lelièvre and Stoltz (2010). This gives more detail on free-energy biasing, and applies it in the context of Markov chain Monte Carlo, and is also illustrated by applications to mixture modelling. My discussion focuses on the general ideas of free e...

We review and discuss some recent progress on the theory of Markov chain Monte Carlo applications, particularly oriented to applications in statistics. We attempt to assess the relevance of this theory for practical applications.

There are two conceptually distinct tasks in Markov chain Monte Carlo (MCMC): a sampler is designed for simulating a Markov chain and then an estimator is constructed on the Markov chain for computing integrals and expectations. In this article, we aim to address the second task by extending the likelihood approach of Kong et al. for Monte Carlo integration. We consider a general Markov chain s...

Existing Markov Chain Monte Carlo (MCMC) methods are either based on generalpurpose and domain-agnostic schemes, which can lead to slow convergence, or problem-specific proposals hand-crafted by an expert. In this paper, we propose ANICE-MC, a novel method to automatically design efficient Markov chain kernels tailored for a specific domain. First, we propose an efficient likelihood-free advers...

We present a Monte Carlo integration method, antithetic Markov chain sampling (AMCS), that incorporates local Markov transitions in an underlying importance sampler. Like sequential Monte Carlo sampling, the proposed method uses a sequence of Markov transitions to guide the sampling toward influential regions of the integrand (modes). However, AMCS differs in the type of transitions that may be...