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10,800 | Construction of Bayesian Deformable Models via Stochastic Approximation Algorithm: A Convergence Study | stat.CO | The problem of the definition and the estimation of generative models based
on deformable templates from raw data is of particular importance for modelling
non aligned data affected by various types of geometrical variability. This is
especially true in shape modelling in the computer vision community or in
probabilist... | statistics |
10,801 | The random Tukey depth | stat.CO | The computation of the Tukey depth, also called halfspace depth, is very
demanding, even in low dimensional spaces, because it requires the
consideration of all possible one-dimensional projections. In this paper we
propose a random depth which approximates the Tukey depth. It only takes into
account a finite number of... | statistics |
10,802 | Deconvolution by simulation | stat.CO | Given samples (x_1,...,x_m) and (z_1,...,z_n) which we believe are
independent realizations of random variables X and Z respectively, where we
further believe that Z=X+Y with Y independent of X, the problem is to estimate
the distribution of Y. We present a new method for doing this, involving
simulation. Experiments s... | statistics |
10,803 | Parallel marginalization Monte Carlo with applications to conditional path sampling | stat.CO | Monte Carlo sampling methods often suffer from long correlation times.
Consequently, these methods must be run for many steps to generate an
independent sample. In this paper a method is proposed to overcome this
difficulty. The method utilizes information from rapidly equilibrating coarse
Markov chains that sample mar... | statistics |
10,804 | On The Density Estimation by Super-Parametric Method | stat.CO | The super-parametric density estimators and its related algorism were
suggested by Y. -S. Tsai et al [7]. The number of parameters is unlimited in
the super- parametric estimators and it is a general theory in sense of
unifying or connecting nonparametric and parametric estimators. Before applying
to numerical examples... | statistics |
10,805 | Adaptive Importance Sampling in General Mixture Classes | stat.CO | In this paper, we propose an adaptive algorithm that iteratively updates both
the weights and component parameters of a mixture importance sampling density
so as to optimise the importance sampling performances, as measured by an
entropy criterion. The method is shown to be applicable to a wide class of
importance samp... | statistics |
10,806 | Particle Filters for Multiscale Diffusions | stat.CO | We consider multiscale stochastic systems that are partially observed at
discrete points of the slow time scale. We introduce a particle filter that
takes advantage of the multiscale structure of the system to efficiently
approximate the optimal filter. | statistics |
10,807 | An Elegant Method for Generating Multivariate Poisson Random Variable | stat.CO | Generating multivariate Poisson data is essential in many applications.
Current simulation methods suffer from limitations ranging from computational
complexity to restrictions on the structure of the correlation matrix. We
propose a computationally efficient and conceptually appealing method for
generating multivariat... | statistics |
10,808 | Population-Based Reversible Jump Markov Chain Monte Carlo | stat.CO | In this paper we present an extension of population-based Markov chain Monte
Carlo (MCMC) to the trans-dimensional case. One of the main challenges in
MCMC-based inference is that of simulating from high and trans-dimensional
target measures. In such cases, MCMC methods may not adequately traverse the
support of the ta... | statistics |
10,809 | A statistical analysis of probabilistic counting algorithms | stat.CO | This paper considers the problem of cardinality estimation in data stream
applications. We present a statistical analysis of probabilistic counting
algorithms, focusing on two techniques that use pseudo-random variates to form
low-dimensional data sketches. We apply conventional statistical methods to
compare probabili... | statistics |
10,810 | Efficient l_{alpha} Distance Approximation for High Dimensional Data Using alpha-Stable Projection | stat.CO | In recent years, large high-dimensional data sets have become commonplace in
a wide range of applications in science and commerce. Techniques for dimension
reduction are of primary concern in statistical analysis. Projection methods
play an important role. We investigate the use of projection algorithms that
exploit pr... | statistics |
10,811 | On variance stabilisation by double Rao-Blackwellisation | stat.CO | Population Monte Carlo has been introduced as a sequential importance
sampling technique to overcome poor fit of the importance function. In this
paper, we compare the performances of the original Population Monte Carlo
algorithm with a modified version that eliminates the influence of the
transition particle via a dou... | statistics |
10,812 | The adjusted Viterbi training for hidden Markov models | stat.CO | The EM procedure is a principal tool for parameter estimation in the hidden
Markov models. However, applications replace EM by Viterbi extraction, or
training (VT). VT is computationally less intensive, more stable and has more
of an intuitive appeal, but VT estimation is biased and does not satisfy the
following fixed... | statistics |
10,813 | A practical procedure to find matching priors for frequentist inference | stat.CO | In the manuscript, we present a practical way to find the matching priors
proposed by Welch & Peers (1963) and Peers (1965). We investigate the use of
saddlepoint approximations combined with matching priors and obtain p-values of
the test of an interest parameter in the presence of nuisance parameter. The
advantage of... | statistics |
10,814 | Confidence regions for the multinomial parameter with small sample size | stat.CO | Consider the observation of n iid realizations of an experiment with d>1
possible outcomes, which corresponds to a single observation of a multinomial
distribution M(n,p) where p is an unknown discrete distribution on {1,...,d}.
In many applications, the construction of a confidence region for p when n is
small is cruc... | statistics |
10,815 | Adaptive approximate Bayesian computation | stat.CO | Sequential techniques can enhance the efficiency of the approximate Bayesian
computation algorithm, as in Sisson et al.'s (2007) partial rejection control
version. While this method is based upon the theoretical works of Del Moral et
al. (2006), the application to approximate Bayesian computation results in a
bias in t... | statistics |
10,816 | A note on the ABC-PRC algorithm of Sissons et al. (2007) | stat.CO | This note describes the results of some tests of the ABC-PRC algorithm of
Sissons et al. (PNAS, 2007), and demonstrates with a toy example that the
method does not converge on the true posterior distribution. | statistics |
10,817 | Marginal Likelihood Integrals for Mixtures of Independence Models | stat.CO | Inference in Bayesian statistics involves the evaluation of marginal
likelihood integrals. We present algebraic algorithms for computing such
integrals exactly for discrete data of small sample size. Our methods apply to
both uniform priors and Dirichlet priors. The underlying statistical models are
mixtures of indepen... | statistics |
10,818 | Case-deletion importance sampling estimators: Central limit theorems and related results | stat.CO | Case-deleted analysis is a popular method for evaluating the influence of a
subset of cases on inference. The use of Monte Carlo estimation strategies in
complicated Bayesian settings leads naturally to the use of importance sampling
techniques to assess the divergence between full-data and case-deleted
posteriors and ... | statistics |
10,819 | A randomized algorithm for principal component analysis | stat.CO | Principal component analysis (PCA) requires the computation of a low-rank
approximation to a matrix containing the data being analyzed. In many
applications of PCA, the best possible accuracy of any rank-deficient
approximation is at most a few digits (measured in the spectral norm, relative
to the spectral norm of the... | statistics |
10,820 | Improved Sequential Stopping Rule for Monte Carlo Simulation | stat.CO | 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, p\mu_1], with \mu_1, \mu_2 > 1, is proved to exceed its
asymptotic value for a... | statistics |
10,821 | Smooth supersaturated models | stat.CO | In areas such as kernel smoothing and non-parametric regression there is
emphasis on smooth interpolation and smooth statistical models. Splines are
known to have optimal smoothness properties in one and higher dimensions. It is
shown, with special attention to polynomial models, that smooth interpolators
can be constr... | statistics |
10,822 | Generalised linear mixed model analysis via sequential Monte Carlo sampling | stat.CO | We present a sequential Monte Carlo sampler algorithm for the Bayesian
analysis of generalised linear mixed models (GLMMs). These models support a
variety of interesting regression-type analyses, but performing inference is
often extremely difficult, even when using the Bayesian approach combined with
Markov chain Mont... | statistics |
10,823 | An Algorithm for Unconstrained Quadratically Penalized Convex Optimization | stat.CO | A descent algorithm, "Quasi-Quadratic Minimization with Memory" (QQMM), is
proposed for unconstrained minimization of the sum, $F$, of a non-negative
convex function, $V$, and a quadratic form. Such problems come up in
regularized estimation in machine learning and statistics. In addition to
values of $F$, QQMM require... | statistics |
10,824 | Grapham: Graphical Models with Adaptive Random Walk Metropolis Algorithms | stat.CO | Recently developed adaptive Markov chain Monte Carlo (MCMC) methods have been
applied successfully to many problems in Bayesian statistics. Grapham is a new
open source implementation covering several such methods, with emphasis on
graphical models for directed acyclic graphs. The implemented algorithms
include the sem... | statistics |
10,825 | A Fast Algorithm for Robust Regression with Penalised Trimmed Squares | stat.CO | The presence of groups containing high leverage outliers makes linear
regression a difficult problem due to the masking effect. The available high
breakdown estimators based on Least Trimmed Squares often do not succeed in
detecting masked high leverage outliers in finite samples.
An alternative to the LTS estimator,... | statistics |
10,826 | On the Permutation Distribution of Independence Tests | stat.CO | 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. Under
the null hypoth... | statistics |
10,827 | A Gibbs Sampling Alternative to Reversible Jump MCMC | stat.CO | This note presents a simple and elegant sampler which could be used as an
alternative to the reversible jump MCMC methodology. | statistics |
10,828 | A Mixture-Based Approach to Regional Adaptation for MCMC | stat.CO | Recent advances in adaptive Markov chain Monte Carlo (AMCMC) include the need
for regional adaptation in situations when the optimal transition kernel is
different across different regions of the sample space. Motivated by these
findings, we propose a mixture-based approach to determine the partition needed
for regiona... | statistics |
10,829 | Least-Squares Joint Diagonalization of a matrix set by a congruence transformation | stat.CO | The approximate joint diagonalization (AJD) is an important analytic tool at
the base of numerous independent component analysis (ICA) and other blind
source separation (BSS) methods, thus finding more and more applications in
medical imaging analysis. In this work we present a new AJD algorithm named
SDIAG (Spheric Di... | statistics |
10,830 | Generalized Rejection Sampling Schemes and Applications in Signal Processing | stat.CO | Bayesian methods and their implementations by means of sophisticated Monte
Carlo techniques, such as Markov chain Monte Carlo (MCMC) and particle filters,
have become very popular in signal processing over the last years. However, in
many problems of practical interest these techniques demand procedures for
sampling fr... | statistics |
10,831 | Computation of confidence intervals in regression utilizing uncertain prior information | stat.CO | We consider a linear regression model with regression parameter beta
=(beta_1, ..., beta_p) and independent and identically N(0, sigma^2)distributed
errors. Suppose that the parameter of interest is theta = a^T beta where a is a
specified vector. Define the parameter tau = c^T beta - t where the vector c
and the number... | statistics |
10,832 | On the utility of graphics cards to perform massively parallel simulation of advanced Monte Carlo methods | stat.CO | We present a case-study on the utility of graphics cards to perform massively
parallel simulation of advanced Monte Carlo methods. Graphics cards, containing
multiple Graphics Processing Units (GPUs), are self-contained parallel
computational devices that can be housed in conventional desktop and laptop
computers. For ... | statistics |
10,833 | A Dynamic Programming Approach for Approximate Uniform Generation of Binary Matrices with Specified Margins | stat.CO | Consider the collection of all binary matrices having a specific sequence of
row and column sums and consider sampling binary matrices uniformly from this
collection. Practical algorithms for exact uniform sampling are not known, but
there are practical algorithms for approximate uniform sampling. Here it is
shown how ... | statistics |
10,834 | Reduction algorithm for the NPMLE for the distribution function of bivariate interval censored data | stat.CO | We study computational aspects of the nonparametric maximum likelihood
estimator (NPMLE) for the distribution function of bivariate interval censored
data. The computation of the NPMLE consists of two steps: a parameter reduction
step and an optimization step. In this paper we focus on the reduction step. We
introduce ... | statistics |
10,835 | Information geometry for testing pseudorandom number generators | stat.CO | The information geometry of the 2-manifold of gamma probability density
functions provides a framework in which pseudorandom number generators may be
evaluated using a neighbourhood of the curve of exponential density functions.
The process is illustrated using the pseudorandom number generator in
Mathematica. This met... | statistics |
10,836 | Statistical estimation requires unbounded memory | stat.CO | We investigate the existence of bounded-memory consistent estimators of
various statistical functionals. This question is resolved in the negative in a
rather strong sense. We propose various bounded-memory approximations, using
techniques from automata theory and stochastic processes. Some questions of
potential inter... | statistics |
10,837 | A Numerical Approach to Performance Analysis of Quickest Change-Point Detection Procedures | stat.CO | For the most popular sequential change detection rules such as CUSUM, EWMA,
and the Shiryaev-Roberts test, we develop integral equations and a concise
numerical method to compute a number of performance metrics, including average
detection delay and average time to false alarm. We pay special attention to
the Shiryaev-... | statistics |
10,838 | Simulating Events of Unknown Probabilities via Reverse Time Martingales | stat.CO | Assume that one aims to simulate an event of unknown probability $s\in (0,1)$
which is uniquely determined, however only its approximations can be obtained
using a finite computational effort. Such settings are often encountered in
statistical simulations. We consider two specific examples. First, the exact
simulation ... | statistics |
10,839 | Computational methods for Bayesian model choice | stat.CO | In this note, we shortly survey some recent approaches on the approximation
of the Bayes factor used in Bayesian hypothesis testing and in Bayesian model
choice. In particular, we reassess importance sampling, harmonic mean sampling,
and nested sampling from a unified perspective. | statistics |
10,840 | Numerical Comparison of Cusum and Shiryaev-Roberts Procedures for Detecting Changes in Distributions | stat.CO | The CUSUM procedure is known to be optimal for detecting a change in
distribution under a minimax scenario, whereas the Shiryaev-Roberts procedure
is optimal for detecting a change that occurs at a distant time horizon. As a
simpler alternative to the conventional Monte Carlo approach, we propose a
numerical method for... | statistics |
10,841 | Monte Carlo Methods in Statistics | stat.CO | Monte Carlo methods are now an essential part of the statistician's toolbox,
to the point of being more familiar to graduate students than the measure
theoretic notions upon which they are based! We recall in this note some of the
advances made in the design of Monte Carlo techniques towards their use in
Statistics, re... | statistics |
10,842 | Probability matrices, non-negative rank, and parameterizations of mixture models | stat.CO | In this paper we parameterize non-negative matrices of sum one and rank at
most two. More precisely, we give a family of parameterizations using the least
possible number of parameters. We also show how these parameterizations relate
to a class of statistical models, known in Probability and Statistics as
mixture model... | statistics |
10,843 | Likelihood-free Bayesian inference for alpha-stable models | stat.CO | $\alpha$-stable distributions are utilised as models for heavy-tailed noise
in many areas of statistics, finance and signal processing engineering.
However, in general, neither univariate nor multivariate $\alpha$-stable
models admit closed form densities which can be evaluated pointwise. This
complicates the inferen... | statistics |
10,844 | Adaptive Gibbs samplers | stat.CO | We consider various versions of adaptive Gibbs and Metropolis within-Gibbs
samplers, which update their selection probabilities (and perhaps also their
proposal distributions) on the fly during a run, by learning as they go in an
attempt to optimise the algorithm. We present a cautionary example of how even
a simple-se... | statistics |
10,845 | Measures of Analysis of Time Series (MATS): A MATLAB Toolkit for Computation of Multiple Measures on Time Series Data Bases | stat.CO | In many applications, such as physiology and finance, large time series data
bases are to be analyzed requiring the computation of linear, nonlinear and
other measures. Such measures have been developed and implemented in commercial
and freeware softwares rather selectively and independently. The Measures of
Analysis o... | statistics |
10,846 | Covariance-Adaptive Slice Sampling | stat.CO | We describe two slice sampling methods for taking multivariate steps using
the crumb framework. These methods use the gradients at rejected proposals to
adapt to the local curvature of the log-density surface, a technique that can
produce much better proposals when parameters are highly correlated. We
evaluate our meth... | statistics |
10,847 | Graphics Processing Units and High-Dimensional Optimization | stat.CO | 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,
optimization algorithms s... | statistics |
10,848 | Computational Methods in Bayesian Statistics | stat.CO | This paper focuses on utilizing two different Bayesian methods to deal with a
variety of toy problems which occur in data analysis. In particular we
implement the Variational Bayesian and Nested Sampling methods to tackle the
problems of polynomial selection and Gaussian Mixture Models, comparing the
algorithms in term... | statistics |
10,849 | Ideal-Theoretic Strategies for Asymptotic Approximation of Marginal Likelihood Integrals | stat.CO | The accurate asymptotic evaluation of marginal likelihood integrals is a
fundamental problem in Bayesian statistics. Following the approach introduced
by Watanabe, we translate this into a problem of computational algebraic
geometry, namely, to determine the real log canonical threshold of a polynomial
ideal, and we pr... | statistics |
10,850 | An empirical Bayes procedure for the selection of Gaussian graphical models | stat.CO | A new methodology for model determination in decomposable graphical Gaussian
models is developed. The Bayesian paradigm is used and, for each given graph, a
hyper inverse Wishart prior distribution on the covariance matrix is
considered. This prior distribution depends on hyper-parameters. It is
well-known that the mod... | statistics |
10,851 | Maximin design on non hypercube domain and kernel interpolation | stat.CO | In the paradigm of computer experiments, the choice of an experimental design
is an important issue. When no information is available about the black-box
function to be approximated, an exploratory design have to be used. In this
context, two dispersion criteria are usually considered: the minimax and the
maximin ones.... | statistics |
10,852 | A pruned dynamic programming algorithm to recover the best segmentations with $1$ to $K_{max}$ change-points | stat.CO | A common computational problem in multiple change-point models is to recover
the segmentations with $1$ to $K_{max}$ change-points of minimal cost with
respect to some loss function. Here we present an algorithm to prune the set of
candidate change-points which is based on a functional representation of the
cost of seg... | statistics |
10,853 | Optimally Robust Kalman Filtering at Work: AO-, IO-, and Simultaneously IO- and AO- Robust Filters | stat.CO | We take up optimality results for robust Kalman filtering from
Ruckdeschel[2001,2010] where robustness is understood in a distributional
sense, i.e.; we enlarge the distribution assumptions made in the ideal model by
suitable neighborhoods, allowing for outliers which in our context may be
system-endogenous/propagating... | statistics |
10,854 | Exact posterior distributions over the segmentation space and model selection for multiple change-point detection problems | stat.CO | In segmentation problems, inference on change-point position and model
selection are two difficult issues due to the discrete nature of change-points.
In a Bayesian context, we derive exact, non-asymptotic, explicit and tractable
formulae for the posterior distribution of variables such as the number of
change-points o... | statistics |
10,855 | An Adaptive Sequential Monte Carlo Sampler | stat.CO | Sequential Monte Carlo (SMC) methods are not only a popular tool in the
analysis of state space models, but offer an alternative to MCMC in situations
where Bayesian inference must proceed via simulation. This paper introduces a
new SMC method that uses adaptive MCMC kernels for particle dynamics. The
proposed algorith... | statistics |
10,856 | Efficient computation of the cdf of the maximal difference between Brownian bridge and its concave majorant | stat.CO | In this paper, we describe two computational methods for calculating the
cumulative distribution function and the upper quantiles of the maximal
difference between a Brownian bridge and its concave majorant. The first method
has two different variants that are both based on a Monte Carlo approach,
whereas the second us... | statistics |
10,857 | Sequential Monte Carlo Methods for Option Pricing | stat.CO | In the following paper we provide a review and development of sequential
Monte Carlo (SMC) methods for option pricing. SMC are a class of Monte
Carlo-based algorithms, that are designed to approximate expectations w.r.t a
sequence of related probability measures. These approaches have been used,
successfully, for a wid... | statistics |
10,858 | A simple and efficient algorithm for fused lasso signal approximator with convex loss function | stat.CO | We consider the augmented Lagrangian method (ALM) as a solver for the fused
lasso signal approximator (FLSA) problem. The ALM is a dual method in which
squares of the constraint functions are added as penalties to the Lagrangian.
In order to apply this method to FLSA, two types of auxiliary variables are
introduced to ... | statistics |
10,859 | A note on target distribution ambiguity of likelihood-free samplers | stat.CO | Methods for Bayesian simulation in the presence of computationally
intractable likelihood functions are of growing interest. Termed
likelihood-free samplers, standard simulation algorithms such as Markov chain
Monte Carlo have been adapted for this setting. In this article, by presenting
generalisations of existing alg... | statistics |
10,860 | General Purpose Convolution Algorithm in S4-Classes by means of FFT | stat.CO | Object orientation provides a flexible framework for the implementation of
the convolution of arbitrary distributions of real-valued random variables.
We discuss an algorithm which is based on the discrete Fourier transformation
(DFT) and its fast computability via the fast Fourier transformation (FFT). It
directly a... | statistics |
10,861 | Free energy Sequential Monte Carlo, application to mixture modelling | stat.CO | We introduce a new class of Sequential Monte Carlo (SMC) methods, which we
call free energy SMC. This class is inspired by free energy methods, which
originate from Physics, and where one samples from a biased distribution such
that a given function $\xi(\theta)$ of the state $\theta$ is forced to be
uniformly distribu... | statistics |
10,862 | Approximating quantiles in very large datasets | stat.CO | Very large datasets are often encountered in climatology, either from a
multiplicity of observations over time and space or outputs from deterministic
models (sometimes in petabytes= 1 million gigabytes). Loading a large data
vector and sorting it, is impossible sometimes due to memory limitations or
computing power. W... | statistics |
10,863 | Cases for the nugget in modeling computer experiments | stat.CO | Most surrogate models for computer experiments are interpolators, and the
most common interpolator is a Gaussian process (GP) that deliberately omits a
small-scale (measurement) error term called the nugget. The explanation is that
computer experiments are, by definition, "deterministic", and so there is no
measurement... | statistics |
10,864 | Multiplicative random walk Metropolis-Hastings on the real line | stat.CO | In this article we propose multiplication based random walk Metropolis
Hastings (MH) algorithm on the real line. We call it the random dive MH (RDMH)
algorithm. This algorithm, even if simple to apply, was not studied earlier in
Markov chain Monte Carlo literature. The associated kernel is shown to have
standard proper... | statistics |
10,865 | Rate estimation in partially observed Markov jump processes with measurement errors | stat.CO | We present a simulation methodology for Bayesian estimation of rate
parameters in Markov jump processes arising for example in stochastic kinetic
models. To handle the problem of missing components and measurement errors in
observed data, we embed the Markov jump process into the framework of a general
state space mode... | statistics |
10,866 | Bayesian Tracking of Emerging Epidemics Using Ensemble Optimal Statistical Interpolation (EnOSI) | stat.CO | We explore the use of the optimal statistical interpolation (OSI) data
assimilation method for the statistical tracking of emerging epidemics and to
study the spatial dynamics of a disease. The epidemic models that we used for
this study are spatial variants of the common susceptible-infectious-removed
(S-I-R) compartm... | statistics |
10,867 | The Time Machine: A Simulation Approach for Stochastic Trees | stat.CO | In the following paper we consider a simulation technique for stochastic
trees. One of the most important areas in computational genetics is the
calculation and subsequent maximization of the likelihood function associated
to such models. This typically consists of using importance sampling (IS) and
sequential Monte Ca... | statistics |
10,868 | Tuning Tempered Transitions | stat.CO | The method of tempered transitions was proposed by Neal (1996) for tackling
the difficulties arising when using Markov chain Monte Carlo to sample from
multimodal distributions. In common with methods such as simulated tempering
and Metropolis-coupled MCMC, the key idea is to utilise a series of
successively easier to ... | statistics |
10,869 | A Bregman Extension of quasi-Newton updates II: Convergence and Robustness Properties | stat.CO | We propose an extension of quasi-Newton methods, and investigate the
convergence and the robustness properties of the proposed update formulae for
the approximate Hessian matrix. Fletcher has studied a variational problem
which derives the approximate Hessian update formula of the quasi-Newton
methods. We point out tha... | statistics |
10,870 | A Bregman Extension of quasi-Newton updates I: An Information Geometrical framework | stat.CO | We study quasi-Newton methods from the viewpoint of information geometry
induced associated with Bregman divergences. Fletcher has studied a variational
problem which derives the approximate Hessian update formula of the
quasi-Newton methods. We point out that the variational problem is identical to
optimization of the... | statistics |
10,871 | Maximum Likelihood Estimation of Nonnegative Trigonometric Sum Models Using a Newton-like Algorithm on Manifolds | stat.CO | In Fern\'andez-Dur\'an (2004), a new family of circular distributions based
on nonnegative trigonometric sums (NNTS models) is developed. Because the
parameter space of this family is the surface of the hypersphere, an efficient
Newton-like algorithm on manifolds is generated in order to obtain the maximum
likelihood e... | statistics |
10,872 | A Comparison of Methods for Computing Autocorrelation Time | stat.CO | 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
series. | statistics |
10,873 | Discussions on "Riemann manifold Langevin and Hamiltonian Monte Carlo methods" | stat.CO | This is a collection of discussions of `Riemann manifold Langevin and
Hamiltonian Monte Carlo methods" by Girolami and Calderhead, to appear in the
Journal of the Royal Statistical Society, Series B. | statistics |
10,874 | Interacting Multiple Try Algorithms with Different Proposal Distributions | stat.CO | We propose a new class of interacting Markov chain Monte Carlo (MCMC)
algorithms designed for increasing the efficiency of a modified multiple-try
Metropolis (MTM) algorithm. The extension with respect to the existing MCMC
literature is twofold. The sampler proposed extends the basic MTM algorithm by
allowing different... | statistics |
10,875 | Online Expectation-Maximisation | stat.CO | Tutorial chapter on the Online EM algorithm to appear in the volume
'Mixtures' edited by Kerrie Mengersen, Mike Titterington and Christian P.
Robert. | statistics |
10,876 | Metropolising forward particle filtering backward sampling and Rao-Blackwellisation of Metropolised particle smoothers | stat.CO | Smoothing in state-space models amounts to computing the conditional
distribution of the latent state trajectory, given observations, or
expectations of functionals of the state trajectory with respect to this
distributions. For models that are not linear Gaussian or possess finite state
space, smoothing distributions ... | statistics |
10,877 | Efficient Bayesian Inference for Switching State-Space Models using Discrete Particle Markov Chain Monte Carlo Methods | stat.CO | Switching state-space models (SSSM) are a very popular class of time series
models that have found many applications in statistics, econometrics and
advanced signal processing. Bayesian inference for these models typically
relies on Markov chain Monte Carlo (MCMC) techniques. However, even
sophisticated MCMC methods de... | statistics |
10,878 | Simulation-based Bayesian analysis for multiple changepoints | stat.CO | This paper presents a Markov chain Monte Carlo method to generate approximate
posterior samples in retrospective multiple changepoint problems where the
number of changes is not known in advance. The method uses conjugate models
whereby the marginal likelihood for the data between consecutive changepoints
is tractable.... | statistics |
10,879 | Block clustering with collapsed latent block models | stat.CO | We introduce a Bayesian extension of the latent block model for model-based
block clustering of data matrices. Our approach considers a block model where
block parameters may be integrated out. The result is a posterior defined over
the number of clusters in rows and columns and cluster memberships. The number
of row a... | statistics |
10,880 | Robust adaptive Metropolis algorithm with coerced acceptance rate | stat.CO | The adaptive Metropolis (AM) algorithm of Haario, Saksman and Tamminen
[Bernoulli 7 (2001) 223-242] uses the estimated covariance of the target
distribution in the proposal distribution. This paper introduces a new robust
adaptive Metropolis algorithm estimating the shape of the target distribution
and simultaneously c... | statistics |
10,881 | Graphical Comparison of MCMC Performance | stat.CO | This paper presents a graphical method for comparing performance of Markov
Chain Monte Carlo methods. Most researchers present comparisons of MCMC methods
using tables of figures of merit; this paper presents a graphical alternative.
It first discusses the computation of autocorrelation time, then uses this to
construc... | statistics |
10,882 | An Alternating Direction Method for Finding Dantzig Selectors | stat.CO | In this paper, we study the alternating direction method for finding the
Dantzig selectors, which are first introduced in [8]. In particular, at each
iteration we apply the nonmonotone gradient method proposed in [17] to
approximately solve one subproblem of this method. We compare our approach with
a first-order metho... | statistics |
10,883 | Slice Sampling with Adaptive Multivariate Steps: The Shrinking-Rank Method | stat.CO | The shrinking rank method is a variation of slice sampling that is efficient
at sampling from multivariate distributions with highly correlated parameters.
It requires that the gradient of the log-density be computable. At each
individual step, it approximates the current slice with a Gaussian occupying a
shrinking-dim... | statistics |
10,884 | Approximate simulation-free Bayesian inference for multiple changepoint models with dependence within segments | stat.CO | This paper proposes approaches for the analysis of multiple changepoint
models when dependency in the data is modelled through a hierarchical Gaussian
Markov random field. Integrated nested Laplace approximations are used to
approximate data quantities, and an approximate filtering recursions approach
is proposed for s... | statistics |
10,885 | A coordinate-wise optimization algorithm for the Fused Lasso | stat.CO | L1 -penalized regression methods such as the Lasso (Tibshirani 1996) that
achieve both variable selection and shrinkage have been very popular. An
extension of this method is the Fused Lasso (Tibshirani and Wang 2007), which
allows for the incorporation of external information into the model. In this
article, we develo... | statistics |
10,886 | Two Proposals for Robust PCA using Semidefinite Programming | stat.CO | The performance of principal component analysis (PCA) suffers badly in the
presence of outliers. This paper proposes two novel approaches for robust PCA
based on semidefinite programming. The first method, maximum mean absolute
deviation rounding (MDR), seeks directions of large spread in the data while
damping the eff... | statistics |
10,887 | Zero Variance Markov Chain Monte Carlo for Bayesian Estimators | stat.CO | Interest is in evaluating, by Markov chain Monte Carlo (MCMC) simulation, the
expected value of a function with respect to a, possibly unnormalized,
probability distribution. A general purpose variance reduction technique for
the MCMC estimator, based on the zero-variance principle introduced in the
physics literature,... | statistics |
10,888 | MCMC Using Ensembles of States for Problems with Fast and Slow Variables such as Gaussian Process Regression | stat.CO | I introduce a Markov chain Monte Carlo (MCMC) scheme in which sampling from a
distribution with density pi(x) is done using updates operating on an
"ensemble" of states. The current state x is first stochastically mapped to an
ensemble, x^{(1)},...,x^{(K)}. This ensemble is then updated using MCMC updates
that leave in... | statistics |
10,889 | Approximate Bayesian Computational methods | stat.CO | Also known as likelihood-free methods, approximate Bayesian computational
(ABC) methods have appeared in the past ten years as the most satisfactory
approach to untractable likelihood problems, first in genetics then in a
broader spectrum of applications. However, these methods suffer to some degree
from calibration di... | statistics |
10,890 | Marginal Likelihood Computation via Arrogance Sampling | stat.CO | This paper describes a method for estimating the marginal likelihood or Bayes
factors of Bayesian models using non-parametric importance sampling ("arrogance
sampling"). This method can also be used to compute the normalizing constant of
probability distributions. Because the required inputs are samples from the
distri... | statistics |
10,891 | SMC^2: an efficient algorithm for sequential analysis of state-space models | stat.CO | We consider the generic problem of performing sequential Bayesian inference
in a state-space model with observation process y, state process x and fixed
parameter theta. An idealized approach would be to apply the iterated batch
importance sampling (IBIS) algorithm of Chopin (2002). This is a sequential
Monte Carlo alg... | statistics |
10,892 | Nonasymptotic bounds on the mean square error for MCMC estimates via renewal techniques | stat.CO | The Nummellin's split chain construction allows to decompose a Markov chain
Monte Carlo (MCMC) trajectory into i.i.d. "excursions". RegenerativeMCMC
algorithms based on this technique use a random number of samples. They have
been proposed as a promising alternative to usual fixed length simulation [25,
33, 14]. In thi... | statistics |
10,893 | Perfect Simulation for Mixtures with Known and Unknown Number of components | stat.CO | We propose and develop a novel and effective perfect sampling methodology for
simulating from posteriors corresponding to mixtures with either known (fixed)
or unknown number of components. For the latter we consider the Dirichlet
process-based mixture model developed by these authors, and show that our ideas
are appli... | statistics |
10,894 | Approximating Probability Densities by Iterated Laplace Approximations | stat.CO | The Laplace approximation is an old, but frequently used method to
approximate integrals for Bayesian calculations. In this paper we develop an
extension of the Laplace approximation, by applying it iteratively to the
residual, i.e., the difference between the current approximation and the true
function. The final appr... | statistics |
10,895 | A Path Algorithm for Constrained Estimation | stat.CO | Many least squares problems involve affine equality and inequality
constraints. Although there are variety of methods for solving such problems,
most statisticians find constrained estimation challenging. The current paper
proposes a new path following algorithm for quadratic programming based on
exact penalization. Si... | statistics |
10,896 | On the Stability of Sequential Monte Carlo Methods in High Dimensions | stat.CO | We investigate the stability of a Sequential Monte Carlo (SMC) method applied
to the problem of sampling from a target distribution on $\mathbb{R}^d$ for
large $d$. It is well known that using a single importance sampling step one
produces an approximation for the target that deteriorates as the dimension $d$
increases... | statistics |
10,897 | Automatic Step Size Selection in Random Walk Metropolis Algorithms | stat.CO | Practitioners of Markov chain Monte Carlo (MCMC) may hesitate to use random
walk Metropolis-Hastings algorithms, especially variable-at-a-time algorithms
with many parameters, because these algorithms require users to select values
of tuning parameters (step sizes). These algorithms perform poorly if the step
sizes are... | statistics |
10,898 | Sampling decomposable graphs using a Markov chain on junction trees | stat.CO | Full Bayesian computational inference for model determination in undirected
graphical models is currently restricted to decomposable graphs, except for
problems of very small scale. In this paper we develop new, more efficient
methodology for such inference, by making two contributions to the
computational geometry of ... | statistics |
10,899 | Bounding rare event probabilities in computer experiments | stat.CO | We are interested in bounding probabilities of rare events in the context of
computer experiments. These rare events depend on the output of a physical
model with random input variables. Since the model is only known through an
expensive black box function, standard efficient Monte Carlo methods designed
for rare event... | statistics |
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