Using this implementation, we investigated the effectiveness of different adaptive MCMC algorithms, burn-in, initialization, and thinning. Using an efficient GPU-based implementation, we showed that run times can be removed as a prohibitive constraint for the sampling of diffusion multi-compartment models. Here we investigate the performance of the MCMC algorithm variations over multiple popular diffusion microstructure models, to examine whether a single, well performing variation could be applied efficiently and robustly to many models. In addition, sampling often takes at least an order of magnitude, more time than non-linear optimization. MCMC sampling is currently not routinely applied in dMRI microstructure modeling, as it requires adjustment and tuning, specific to each model, particularly in the choice of proposal distributions, burn-in length, thinning, and the number of samples to store. Whereas, the MLE provides only a point estimate of the fitted model parameters, the MCMC recovers the entire posterior distribution of the model parameters given in the data, providing additional information such as parameter uncertainty and correlations. Biophysical multi-compartment models require a parameter estimation, typically performed using either the Maximum Likelihood Estimation (MLE) or the Markov Chain Monte Carlo (MCMC) sampling. In diffusion MRI analysis, advances in biophysical multi-compartment modeling have gained popularity over the conventional Diffusion Tensor Imaging (DTI), because they can obtain a greater specificity in relating the dMRI signal to underlying cellular microstructure. Department of Cognitive Neuroscience, Faculty of Psychology & Neuroscience, Maastricht University, Maastricht, Netherlands.The problem- independent bound for this proxy matches its recent minimax lower bound in terms of $n$ up to a $\log n$ factor. We give similar, but somewhat sharper bounds on a proxy of the regret. For sub-Gaussian arm distributions, we provide bounds on the total regret: a distribution-dependent bound of order $\text)$ that does not. We compare its performance to an ideal sample allocation that knows the standard deviations of the arms. We propose an UCB-type strategy that samples the arms according to an upper bound on their estimated standard deviations. The learner is allowed to sample the variable $n$ times, but it can decide on-line which stratum to sample next. The goal is to estimate the integral mean, that is a weighted average of the mean values of the arms. We model this problem in a $K$-armed bandit, where the arms represent the $K$ strata. We consider the problem of stratified sampling for Monte Carlo integration of a random variable. Adaptive Strategy for Stratified Monte Carlo SamplingĪlexandra Carpentier, Remi Munos, András Antos 16(68):2231−2271, 2015.
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