146,737 research outputs found
The statistical distribution of magnetotelluric apparent resistivity and phase
Author Posting. © The Authors, 2007. This article is posted here by permission of John Wiley & Sons for personal use, not for redistribution. The definitive version was published in Geophysical Journal International 171 (2007): 127-132, doi:10.1111/j.1365-246X.2007.03523.x.The marginal distributions for the magnetotelluric (MT) magnitude squared response function (and hence apparent resistivity) and phase are derived from the bivariate complex normal distribution that describes the distribution of response function estimates when the GaussâMarkov theorem is satisfied and the regression random errors are normally distributed. The distribution of the magnitude squared response function is shown to be non-central chi-squared with 2 degrees of freedom, with the non-centrality parameter given by the squared magnitude of the true MT response. The standard estimate for the magnitude squared response function is biased, with the bias proportional to the variance and hence important when the uncertainty is large. The distribution reduces to the exponential when the expected value of the MT response function is zero. The distribution for the phase is also obtained in closed form. It reduces to the uniform distribution when the squared magnitude of the true MT response function is zero or its variance is very large. The phase distribution is symmetric and becomes increasingly concentrated as the variance decreases, although it is shorter-tailed than the Gaussian. The standard estimate for phase is unbiased. Confidence limits are derived from the distributions for magnitude squared response function and phase. Using a data set taken from the 2003 Kaapvaal transect, it is shown that the bias in the apparent resistivity is small and that confidence intervals obtained using the non-parametric delta method are very close to the true values obtained from the distributions. Thus, it appears that the computationally simple delta approximation provides accurate estimates for the confidence intervals, provided that the MT response function is obtained using an estimator that bounds the influence of extreme data.This work was supported by NSF grant EAR0309584
Addressing Function Approximation Error in Actor-Critic Methods
In value-based reinforcement learning methods such as deep Q-learning,
function approximation errors are known to lead to overestimated value
estimates and suboptimal policies. We show that this problem persists in an
actor-critic setting and propose novel mechanisms to minimize its effects on
both the actor and the critic. Our algorithm builds on Double Q-learning, by
taking the minimum value between a pair of critics to limit overestimation. We
draw the connection between target networks and overestimation bias, and
suggest delaying policy updates to reduce per-update error and further improve
performance. We evaluate our method on the suite of OpenAI gym tasks,
outperforming the state of the art in every environment tested.Comment: Accepted at ICML 201
Global consensus Monte Carlo
To conduct Bayesian inference with large data sets, it is often convenient or
necessary to distribute the data across multiple machines. We consider a
likelihood function expressed as a product of terms, each associated with a
subset of the data. Inspired by global variable consensus optimisation, we
introduce an instrumental hierarchical model associating auxiliary statistical
parameters with each term, which are conditionally independent given the
top-level parameters. One of these top-level parameters controls the
unconditional strength of association between the auxiliary parameters. This
model leads to a distributed MCMC algorithm on an extended state space yielding
approximations of posterior expectations. A trade-off between computational
tractability and fidelity to the original model can be controlled by changing
the association strength in the instrumental model. We further propose the use
of a SMC sampler with a sequence of association strengths, allowing both the
automatic determination of appropriate strengths and for a bias correction
technique to be applied. In contrast to similar distributed Monte Carlo
algorithms, this approach requires few distributional assumptions. The
performance of the algorithms is illustrated with a number of simulated
examples
A novel estimator of the polarization amplitude from normally distributed Stokes parameters
We propose a novel estimator of the polarization amplitude from a single
measurement of its normally distributed Stokes components. Based on the
properties of the Rice distribution and dubbed 'MAS' (Modified ASymptotic), it
meets several desirable criteria:(i) its values lie in the whole positive
region; (ii) its distribution is continuous; (iii) it transforms smoothly with
the signal-to-noise ratio (SNR) from a Rayleigh-like shape to a Gaussian one;
(iv) it is unbiased and reaches its components' variance as soon as the SNR
exceeds 2; (v) it is analytic and can therefore be used on large data-sets. We
also revisit the construction of its associated confidence intervals and show
how the Feldman-Cousins prescription efficiently solves the issue of classical
intervals lying entirely in the unphysical negative domain. Such intervals can
be used to identify statistically significant polarized regions and conversely
build masks for polarization data. We then consider the case of a general
covariance matrix and perform a generalization of the estimator that
preserves its asymptotic properties. We show that its bias does not depend on
the true polarization angle, and provide an analytic estimate of its variance.
The estimator value, together with its variance, provide a powerful
point-estimate of the true polarization amplitude that follows an unbiased
Gaussian distribution for a SNR as low as 2. These results can be applied to
the much more general case of transforming any normally distributed random
variable from Cartesian to polar coordinates.Comment: Accepted by MNRA
Bias in Estimating Multivariate and Univariate Diffusions
Published in Journal of Econometrics, 2011, https://doi.org/10.1016/j.jeconom.2010.12.006</p
On estimation of entropy and mutual information of continuous distributions
Mutual information is used in a procedure to estimate time-delays between recordings of electroencephalogram (EEG) signals originating from epileptic animals and patients. We present a simple and reliable histogram-based method to estimate mutual information. The accuracies of this mutual information estimator and of a similar entropy estimator are discussed. The bias and variance calculations presented can also be applied to discrete valued systems. Finally, we present some simulation results, which are compared with earlier work
Estimating Euler equations
In this paper we consider conditions under which the estimation of a log-linearized Euler equation for
consumption yields consistent estimates of preference parameters. When utility is isoelastic and a
sample covering a long time period is available, consistent estimates are obtained from the loglinearized
Euler equation when the innovations to the conditional variance of consumption growth are
uncorrelated with the instruments typically used in estimation.
We perform a Montecarlo experiment, consisting in solving and simulating a simple life cycle model
under uncertainty, and show that in most situations, the estimates obtained from the log-linearized
equation are not systematically biased. This is true even when we introduce heteroscedasticity in the
process generating income.
The only exception is when discount rates are very high (e.g. 47% per year). This problem arises
because consumers are nearly always close to the maximum borrowing limit: the estimation bias is
unrelated to the linearization and estimates using nonlinear GMM are as bad. Across all our situations,
estimation using a log-linearized Euler equation does better than nonlinear GMM despite the absence
of measurement error.
Finally, we plot life cycle profiles for the variance of consumption growth, which, except when the
discount factor is very high, is remarkably flat. This implies that claims that demographic variables in
log-linearized Euler equations capture changes in the variance of consumption growth are unwarranted
A review of R-packages for random-intercept probit regression in small clusters
Generalized Linear Mixed Models (GLMMs) are widely used to model clustered categorical outcomes. To tackle the intractable integration over the random effects distributions, several approximation approaches have been developed for likelihood-based inference. As these seldom yield satisfactory results when analyzing binary outcomes from small clusters, estimation within the Structural Equation Modeling (SEM) framework is proposed as an alternative. We compare the performance of R-packages for random-intercept probit regression relying on: the Laplace approximation, adaptive Gaussian quadrature (AGQ), Penalized Quasi-Likelihood (PQL), an MCMC-implementation, and integrated nested Laplace approximation within the GLMM-framework, and a robust diagonally weighted least squares estimation within the SEM-framework. In terms of bias for the fixed and random effect estimators, SEM usually performs best for cluster size two, while AGQ prevails in terms of precision (mainly because of SEM's robust standard errors). As the cluster size increases, however, AGQ becomes the best choice for both bias and precision
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