Estimating Discrete Markov Models From Various Incomplete Data Schemes

The parameters of a discrete stationary Markov model are transition probabilities between states. Traditionally, data consist in sequences of observed states for a given number of individuals over the whole observation period. In such a case, the estimation of transition probabilities is straightforwardly made by counting one-step moves from a given state to another. In many real-life problems, however, the inference is much more difficult as state sequences are not fully observed, namely the state of each individual is known only for some given values of the time variable. A review of the problem is given, focusing on Monte Carlo Markov Chain (MCMC) algorithms to perform Bayesian inference and evaluate posterior distributions of the transition probabilities in this missing-data framework. Leaning on the dependence between the rows of the transition matrix, an adaptive MCMC mechanism accelerating the classical Metropolis-Hastings algorithm is then proposed and empirically studied.Comment: 26 pages - preprint accepted in 20th February 2012 for publication in Computational Statistics and Data Analysis (please cite the journal's paper

Simulation based Bayesian econometric inference: principles and some recent computational advances

In this paper we discuss several aspects of simulation based Bayesian econometric inference. We start at an elementary level on basic concepts of Bayesian analysis; evaluating integrals by simulation methods is a crucial ingredient in Bayesian inference. Next, the most popular and well-known simulation techniques are discussed, the MetropolisHastings algorithm and Gibbs sampling (being the most popular Markov chain Monte Carlo methods) and importance sampling. After that, we discuss two recently developed sampling methods: adaptive radial based direction sampling [ARDS], which makes use of a transformation to radial coordinates, and neural network sampling, which makes use of a neural network approximation to the posterior distribution of interest. Both methods are especially useful in cases where the posterior distribution is not well-behaved, in the sense of having highly non-elliptical shapes. The simulation techniques are illustrated in several example models, such as a model for the real US GNP and models for binary data of a US recession indicator.

Simulation based bayesian econometric inference: principles and some recent computational advances.

In this paper we discuss several aspects of simulation basedBayesian econometric inference. We start at an elementary level on basic concepts of Bayesian analysis; evaluatingintegrals by simulation methods is a crucial ingredientin Bayesian inference. Next, the most popular and well-knownsimulation techniques are discussed, the Metropolis-Hastingsalgorithm and Gibbs sampling (being the most popular Markovchain Monte Carlo methods) and importance sampling. After that, we discuss two recently developed samplingmethods: adaptive radial based direction sampling [ARDS],which makes use of a transformation to radial coordinates,and neural network sampling, which makes use of a neural network approximation to the posterior distribution ofinterest. Both methods are especially useful in cases wherethe posterior distribution is not well-behaved, in the senseof having highly non-elliptical shapes. The simulationtechniques are illustrated in several example models, suchas a model for the real US GNP and models for binary data ofa US recession indicator.

Gaussian process hyper-parameter estimation using parallel asymptotically independent Markov sampling

Gaussian process emulators of computationally expensive computer codes provide fast statistical approximations to model physical processes. The training of these surrogates depends on the set of design points chosen to run the simulator. Due to computational cost, such training set is bound to be limited and quantifying the resulting uncertainty in the hyper-parameters of the emulator by uni-modal distributions is likely to induce bias. In order to quantify this uncertainty, this paper proposes a computationally efficient sampler based on an extension of Asymptotically Independent Markov Sampling, a recently developed algorithm for Bayesian inference. Structural uncertainty of the emulator is obtained as a by-product of the Bayesian treatment of the hyper-parameters. Additionally, the user can choose to perform stochastic optimisation to sample from a neighbourhood of the Maximum a Posteriori estimate, even in the presence of multimodality. Model uncertainty is also acknowledged through numerical stabilisation measures by including a nugget term in the formulation of the probability model. The efficiency of the proposed sampler is illustrated in examples where multi-modal distributions are encountered. For the purpose of reproducibility, further development, and use in other applications the code used to generate the examples is freely available for download at https://github.com/agarbuno/paims_codesComment: Computational Statistics \& Data Analysis, Volume 103, November 201

Rejection-Cascade of Gaussians: Real-time adaptive background subtraction framework

Background-Foreground classification is a well-studied problem in computer vision. Due to the pixel-wise nature of modeling and processing in the algorithm, it is usually difficult to satisfy real-time constraints. There is a trade-off between the speed (because of model complexity) and accuracy. Inspired by the rejection cascade of Viola-Jones classifier, we decompose the Gaussian Mixture Model (GMM) into an adaptive cascade of Gaussians(CoG). We achieve a good improvement in speed without compromising the accuracy with respect to the baseline GMM model. We demonstrate a speed-up factor of 4-5x and 17 percent average improvement in accuracy over Wallflowers surveillance datasets. The CoG is then demonstrated to over the latent space representation of images of a convolutional variational autoencoder(VAE). We provide initial results over CDW-2014 dataset, which could speed up background subtraction for deep architectures.Comment: Accepted for National Conference on Computer Vision, Pattern Recognition, Image Processing and Graphics (NCVPRIPG 2019