All posts under category "Statistics / Stat.CO"
Wallace has proposed a new class of pseudo-random generators for normal variates. These generators do not require a stream of uniform pseudo-random numbers, except for initialisation. The inner loops are essentially matrix-vector multiplications and are very suitable for implementation on vector pro
This paper discusses the potential of graphics processing units (GPUs) in high-dimensional optimization problems. A single GPU card with hundreds of arithmetic cores can be inserted in a personal computer and dramatically accelerates many statistical algorithms. To exploit these devices fully, optim
This paper proposes consistent and asymptotically Gaussian estimators for the drift, the diffusion coefficient and the Hurst exponent of the discretely observed fractional Ornstein-Uhlenbeck process. For the estimation of the drift, the results are obtained only in the case when 1/2 < H < 3/4. This
We merge in this note our two discussions about the Read Paper 'Particle Markov chain Monte Carlo' (Andrieu, Doucet, and Holenstein, 2010) presented on October 16th 2009 at the Royal Statistical Society, appearing in the Journal of the Royal Statistical Society Series B. We also present a more detai
This paper describes four methods for estimating autocorrelation time and evaluates these methods with a test set of seven series. Fitting an autoregressive process appears to be the most accurate method of the four. An R package is provided for extending the comparison to more methods and test seri
In this paper, we propose a general approach for improving the efficiency of computing distribution functions. The idea is to truncate the domain of summation or integration.
Motivated by a computer experiment for the design of a rocket booster, this paper explores nonstationary modeling methodologies that couple stationary Gaussian processes with treed partitioning. Partitioning is a simple but effective method for dealing with nonstationarity. The methodological develo
This paper gives a method for computing distributions associated with patterns in the state sequence of a hidden Markov model, conditional on observing all or part of the observation sequence. Probabilities are computed for very general classes of patterns (competing patterns and generalized later p
We consider the problem of optimizing a real-valued continuous function $f$ using a Bayesian approach, where the evaluations of $f$ are chosen sequentially by combining prior information about $f$, which is described by a random process model, and past evaluation results. The main difficulty with th
The standard textbook method for estimating the probability of a biased coin from finite tosses implicitly assumes the sample sizes are large and gives incorrect results for small samples. We describe the exact solution, which is correct for any sample size.
In this paper, we develop an approach for optimizing the explicit binomial confidence interval recently derived by Chen et al. The optimization reduces conservativeness while guaranteeing prescribed coverage probability.
We present the extention and application of a new unsupervised statistical learning technique--the Partition Decoupling Method--to gene expression data. Because it has the ability to reveal non-linear and non-convex geometries present in the data, the PDM is an improvement over typical gene expressi
Stochastic simulation is widely used to study complex systems composed of various interconnected subprocesses, such as input processes, routing and control logic, optimization routines, and data-driven decision modules. In practice, these subprocesses may be inherently unknown or too computationally
Maximum likelihood estimations for the parameters of extreme value distributions are discussed in this paper using fixed point iteration. The commonly used numerical approach for addressing this problem is the Newton-Raphson approach which requires differentiation unlike the fixed point iteration wh
In this paper we present a new approach to control variates for improving computational efficiency of Ensemble Monte Carlo. We present the approach using simulation of paths of a time-dependent nonlinear stochastic equation. The core idea is to extract information at one or more nominal model parame
Let H be a Haar distributed random matrix on the group of pxp real orthogonal matrices. Partition H into four blocks: (1) the (1,1) element, (2)the rest of the first row, (3) the rest of the first column, and (4)the remaining (p-1)x(p-1) matrix. The marginal distribution of (1) is well known. In thi
For the vast majority of genome wide association studies (GWAS) published so far, statistical analysis was performed by testing markers individually. In this article we present some elementary statistical considerations which clearly show that in case of complex traits the approach based on multiple
This paper considers the topic of finding prior distributions when a major component of the statistical model depends on a nonlinear function. Using results on how to construct uniform distributions in general metric spaces, we propose a prior distribution that is uniform in the space of functional
Recently, Andrieu, Doucet and Holenstein (2010) introduced a general framework for using particle filters (PFs) to construct proposal kernels for Markov chain Monte Carlo (MCMC) methods. This framework, termed Particle Markov chain Monte Carlo (PMCMC), was shown to provide powerful methods for joint
Tutorial chapter on the Online EM algorithm to appear in the volume 'Mixtures' edited by Kerrie Mengersen, Mike Titterington and Christian P. Robert.
A simple closed-form approximation for the median of the beta distribution Beta(a, b) is introduced: (a-1/3)/(a+b-2/3) for (a,b) both larger than 1 has a relative error of less than 4%, rapidly decreasing to zero as both shape parameters increase.
This paper proposes a new randomized strategy for adaptive MCMC using Bayesian optimization. This approach applies to non-differentiable objective functions and trades off exploration and exploitation to reduce the number of potentially costly objective function evaluations. We demonstrate the strat
Gaussian Markov random fields (GMRFs) are frequently used as computationally efficient models in spatial statistics. Unfortunately, it has traditionally been difficult to link GMRFs with the more traditional Gaussian random field models as the Markov property is difficult to deploy in continuous spa
The present paper proposes an adaptive biasing potential for the computation of free energy landscapes. It is motivated by statistical learning arguments and unifies the tasks of biasing the molecular dynamics to escape free energy wells and estimating the free energy function, under the same object
Simulated tempering (ST) is an established Markov chain Monte Carlo (MCMC) method for sampling from a multimodal density $pi(theta)$. Typically, ST involves introducing an auxiliary variable $k$ taking values in a finite subset of $[0,1]$ and indexing a set of tempered distributions, say $pi_k(theta
One of the most popular class of tests for independence between two random variables is the general class of rank statistics which are invariant under permutations. This class contains Spearman's coefficient of rank correlation statistic, Fisher-Yates statistic, weighted Mann statistic and others. U
We describe von Neumann's elegant idea for sampling from the exponential distribution, Forsythe's generalization for sampling from a probability distribution whose density has the form exp(-G(x)), where G(x) is easy to compute (e.g. a polynomial), and my refinement of these ideas to give an efficien
In this note we provide explicit expressions and expansions for a special function which appears in nonparametric estimation of log-densities. This function returns the integral of a log-linear function on a simplex of arbitrary dimension. In particular it is used in the R-package 'LogCondDEAD' by C
In this paper, we consider estimating sparse inverse covariance of a Gaussian graphical model whose conditional independence is assumed to be partially known. Similarly as in [5], we formulate it as an $l_1$-norm penalized maximum likelihood estimation problem. Further, we propose an algorithm frame
This paper presents an improved result on the negative-binomial Monte Carlo technique analyzed in a previous paper for the estimation of an unknown probability p. Specifically, the confidence level associated to a relative interval [p/mu_2, pmu_1], with mu_1, mu_2 > 1, is proved to exceed its asympt
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