7,958 research outputs found
Relative fixed-width stopping rules for Markov chain Monte Carlo simulations
Markov chain Monte Carlo (MCMC) simulations are commonly employed for
estimating features of a target distribution, particularly for Bayesian
inference. A fundamental challenge is determining when these simulations should
stop. We consider a sequential stopping rule that terminates the simulation
when the width of a confidence interval is sufficiently small relative to the
size of the target parameter. Specifically, we propose relative magnitude and
relative standard deviation stopping rules in the context of MCMC. In each
setting, we develop sufficient conditions for asymptotic validity, that is
conditions to ensure the simulation will terminate with probability one and the
resulting confidence intervals will have the proper coverage probability. Our
results are applicable in a wide variety of MCMC estimation settings, such as
expectation, quantile, or simultaneous multivariate estimation. Finally, we
investigate the finite sample properties through a variety of examples and
provide some recommendations to practitioners.Comment: 24 page
You can go your own way: effectiveness of participant-driven versus experimenter-driven processing strategies in memory training and transfer
Cognitive training programs that instruct specific strategies frequently
show limited transfer. Open-ended approaches can achieve greater transfer, but may fail to benefit many older adults due to age deficits in self-initiated processing. We examined whether a compromise that encourages effort at encoding without an experimenter-prescribed strategy might yield better results. Older adults completed memory training under conditions that either (1) mandated a specific strategy to increase deep, associative encoding, (2) attempted to suppress such encoding by mandating rote rehearsal, or (3) encouraged time and effort toward encoding but allowed for strategy choice. The experimenter-enforced associative encoding strategy succeeded in creating integrated representations of studied items, but training-task progress was related to pre-existing ability. Independent of condition assignment, self-reported deep encoding was associated with positive training and transfer effects, suggesting that the most beneficial outcomes occur when environmental support guiding effort is provided but participants generate their own strategies
Exact sampling for intractable probability distributions via a Bernoulli factory
Many applications in the field of statistics require Markov chain Monte Carlo
methods. Determining appropriate starting values and run lengths can be both
analytically and empirically challenging. A desire to overcome these problems
has led to the development of exact, or perfect, sampling algorithms which
convert a Markov chain into an algorithm that produces i.i.d. samples from the
stationary distribution. Unfortunately, very few of these algorithms have been
developed for the distributions that arise in statistical applications, which
typically have uncountable support. Here we study an exact sampling algorithm
using a geometrically ergodic Markov chain on a general state space. Our work
provides a significant reduction to the number of input draws necessary for the
Bernoulli factory, which enables exact sampling via a rejection sampling
approach. We illustrate the algorithm on a univariate Metropolis-Hastings
sampler and a bivariate Gibbs sampler, which provide a proof of concept and
insight into hyper-parameter selection. Finally, we illustrate the algorithm on
a Bayesian version of the one-way random effects model with data from a styrene
exposure study.Comment: 28 pages, 2 figure
Batch means and spectral variance estimators in Markov chain Monte Carlo
Calculating a Monte Carlo standard error (MCSE) is an important step in the
statistical analysis of the simulation output obtained from a Markov chain
Monte Carlo experiment. An MCSE is usually based on an estimate of the variance
of the asymptotic normal distribution. We consider spectral and batch means
methods for estimating this variance. In particular, we establish conditions
which guarantee that these estimators are strongly consistent as the simulation
effort increases. In addition, for the batch means and overlapping batch means
methods we establish conditions ensuring consistency in the mean-square sense
which in turn allows us to calculate the optimal batch size up to a constant of
proportionality. Finally, we examine the empirical finite-sample properties of
spectral variance and batch means estimators and provide recommendations for
practitioners.Comment: Published in at http://dx.doi.org/10.1214/09-AOS735 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Get the gist? The effects of processing depth on false recognition in short-term and long-term memory
Gist-based processing has been proposed to account for robust false memories in the converging-associates task. The deep-encoding processes known to enhance verbatim memory also strengthen gist memory and increase distortions of long-term memory (LTM). Recent research has demonstrated that compelling false memory illusions are relatively delay-invariant, also occurring under canonical short-term memory (STM) conditions. To investigate the contributions of gist to false memory at short and long delays, processing depth was manipulated as participants encoded lists of four semantically related words and were probed immediately, following a filled 3- to 4-s retention interval, or approximately 20 min later, in a surprise recognition test. In two experiments, the encoding manipulation dissociated STM and LTM on the frequency, but not the phenomenology, of false memory. Deep encoding at STM increases false recognition rates at LTM, but confidence ratings and remember/know judgments are similar across delays and do not differ as a function of processing depth. These results suggest that some shared and some unique processes underlie false memory illusions at short and long delays
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