Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userImproving Grid Based Bayesian Methods
58
0
0.0
(
0
)
Added by
Chaitanya Joshi Dr.
Publication date
2016
fields
Mathematical Statistics
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
In some cases, computational benefit can be gained by exploring the hyper parameter space using a deterministic set of grid points instead of a Markov chain. We view this as a numerical integration problem and make three unique contributions. First, we explore the space using low discrepancy point sets instead of a grid. This allows for accurate estimation of marginals of any shape at a much lower computational cost than a grid based approach and thus makes it possible to extend the computational benefit to a hyper parameter space with higher dimensionality (10 or more). Second, we propose a new, quick and easy method to estimate the marginal using a least squares polynomial and prove the conditions under which this polynomial will converge to the true marginal. Our results are valid for a wide range of point sets including grids, random points and low discrepancy points. Third, we show that further accuracy and efficiency can be gained by taking into consideration the functional decomposition of the integrand and illustrate how this can be done using anchored f-ANOVA on weighted spaces.
rate research
Read More
In this paper, we introduce efficient ensemble Markov Chain Monte Carlo (MCMC) sampling methods for Bayesian computations in the univariate stochastic volatility model. We compare the performance of our ensemble MCMC methods with an improved version of a recent sampler of Kastner and Fruwirth-Schnatter (2014). We show that ensemble samplers are more efficient than this state of the art sampler by a factor of about 3.1, on a data set simulated from the stochastic volatility model. This performance gain is achieved without the ensemble MCMC sampler relying on the assumption that the latent process is linear and Gaussian, unlike the sampler of Kastner and Fruwirth-Schnatter.
This paper introduces a new way to calculate distance-based statistics, particularly when the data are multivariate. The main idea is to pre-calculate the optimal projection directions given the variable dimension, and to project multidimensional variables onto these pre-specified projection directions; by subsequently utilizing the fast algorithm that is developed in Huo and Szekely [2016] for the univariate variables, the computational complexity can be improved from $O(m^2)$ to $O(n m cdot mbox{log}(m))$, where $n$ is the number of projection directions and $m$ is the sample size. When $n ll m/log(m)$, computational savings can be achieved. The key challenge is how to find the optimal pre-specified projection directions. This can be obtained by minimizing the worse-case difference between the true distance and the approximated distance, which can be formulated as a nonconvex optimization problem in a general setting. In this paper, we show that the exact solution of the nonconvex optimization problem can be derived in two special cases: the dimension of the data is equal to either $2$ or the number of projection directions. In the generic settings, we propose an algorithm to find some approximate solutions. Simulations confirm the advantage of our method, in comparison with the pure Monte Carlo approach, in which the directions are randomly selected rather than pre-calculated.
Phylodynamics focuses on the problem of reconstructing past population size dynamics from current genetic samples taken from the population of interest. This technique has been extensively used in many areas of biology, but is particularly useful for studying the spread of quickly evolving infectious diseases agents, e.g., influenza virus. Phylodynamics inference uses a coalescent model that defines a probability density for the genealogy of randomly sampled individuals from the population. When we assume that such a genealogy is known, the coalescent model, equipped with a Gaussian process prior on population size trajectory, allows for nonparametric Bayesian estimation of population size dynamics. While this approach is quite powerful, large data sets collected during infectious disease surveillance challenge the state-of-the-art of Bayesian phylodynamics and demand computationally more efficient inference framework. To satisfy this demand, we provide a computationally efficient Bayesian inference framework based on Hamiltonian Monte Carlo for coalescent process models. Moreover, we show that by splitting the Hamiltonian function we can further improve the efficiency of this approach. Using several simulated and real datasets, we show that our method provides accurate estimates of population size dynamics and is substantially faster than alternative methods based on elliptical slice sampler and Metropolis-adjusted Langevin algorithm.
In this work we test the most widely used methods for fitting the composition fraction in data, namely maximum likelihood, $chi^2$, mean value of the distributions and mean value of the posterior probability function. We discuss the discrimination power of the four methods in different scenarios: signal to noise discrimination; two signals; and distributions of Xmax for mixed primary mass composition. We introduce a distance parameter, which can be used to estimate, as a rule of thumb, the precision of the discrimination. Finally, we conclude that the most reliable methods in all the studied scenarios are the maximum likelihood and the mean value of the posterior probability function.
Bayesian inference for nonlinear diffusions, observed at discrete times, is a challenging task that has prompted the development of a number of algorithms, mainly within the computational statistics community. We propose a new direction, and accompanying methodology, borrowing ideas from statistical physics and computational chemistry, for inferring the posterior distribution of latent diffusion paths and model parameters, given observations of the process. Joint configurations of the underlying process noise and of parameters, mapping onto diffusion paths consistent with observations, form an implicitly defined manifold. Then, by making use of a constrained Hamiltonian Monte Carlo algorithm on the embedded manifold, we are able to perform computationally efficient inference for an extensive class of discretely observed diffusion models. Critically, in contrast with other approaches proposed in the literature, our methodology is highly automated, requiring minimal user intervention and applying alike in a range of settings, including: elliptic or hypo-elliptic systems; observations with or without noise; linear or non-linear observation operators. Exploiting Markovianity, we propose a variant of the method with complexity that scales linearly in the resolution of path discretisation and the number of observation times.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
