553 research outputs found
Bayesian Item Response Modeling in R with brms and Stan
Item Response Theory (IRT) is widely applied in the human sciences to model
persons' responses on a set of items measuring one or more latent constructs.
While several R packages have been developed that implement IRT models, they
tend to be restricted to respective prespecified classes of models. Further,
most implementations are frequentist while the availability of Bayesian methods
remains comparably limited. We demonstrate how to use the R package brms
together with the probabilistic programming language Stan to specify and fit a
wide range of Bayesian IRT models using flexible and intuitive multilevel
formula syntax. Further, item and person parameters can be related in both a
linear or non-linear manner. Various distributions for categorical, ordinal,
and continuous responses are supported. Users may even define their own custom
response distribution for use in the presented framework. Common IRT model
classes that can be specified natively in the presented framework include 1PL
and 2PL logistic models optionally also containing guessing parameters, graded
response and partial credit ordinal models, as well as drift diffusion models
of response times coupled with binary decisions. Posterior distributions of
item and person parameters can be conveniently extracted and post-processed.
Model fit can be evaluated and compared using Bayes factors and efficient
cross-validation procedures.Comment: 54 pages, 16 figures, 3 table
Biaxial Dynamic Fatigue Tests of Wind Turbine Blades
Testing rotor blades of wind turbines is essential to mitigate financial risks caused by serial damages. Present day uniaxial
dynamic tests are time consuming and often inaccurate regarding the applied loading. This thesis proposes a faster
fatigue test method by loading the two primary directions at the same time. In addition, a more realistic test, compared
to uniaxial tests, is accomplished by loading larger areas of the blade cross-sections. To achieve this, an elliptical biaxial
dynamic excitation is used. To fulfill the industry requirement for cost effective tests, a relatively simple test setup was
developed, still achieving an elliptical dynamic excitation of the rotor blade. Two methods for an accurate determination
of the applied loadings for dynamic fatigue tests are described. These calibration tests use easily measured values and
simple analysis to achieve accurate test load measurements in a cost-effective way.German Federal Ministry of Nature Conservation and Nuclear Safety (BMU)/Better Blade/FKZ 0325169/E
Rank-normalization, folding, and localization: An improved for assessing convergence of MCMC
Markov chain Monte Carlo is a key computational tool in Bayesian statistics,
but it can be challenging to monitor the convergence of an iterative stochastic
algorithm. In this paper we show that the convergence diagnostic
of Gelman and Rubin (1992) has serious flaws. Traditional will
fail to correctly diagnose convergence failures when the chain has a heavy tail
or when the variance varies across the chains. In this paper we propose an
alternative rank-based diagnostic that fixes these problems. We also introduce
a collection of quantile-based local efficiency measures, along with a
practical approach for computing Monte Carlo error estimates for quantiles. We
suggest that common trace plots should be replaced with rank plots from
multiple chains. Finally, we give recommendations for how these methods should
be used in practice.Comment: Minor revision for improved clarit
Posterior accuracy and calibration under misspecification in Bayesian generalized linear models
Generalized linear models (GLMs) are popular for data-analysis in almost all
quantitative sciences, but the choice of likelihood family and link function is
often difficult. This motivates the search for likelihoods and links that
minimize the impact of potential misspecification. We perform a large-scale
simulation study on double-bounded and lower-bounded response data where we
systematically vary both true and assumed likelihoods and links. In contrast to
previous studies, we also study posterior calibration and uncertainty metrics
in addition to point-estimate accuracy. Our results indicate that certain
likelihoods and links can be remarkably robust to misspecification, performing
almost on par with their respective true counterparts. Additionally, normal
likelihood models with identity link (i.e., linear regression) often achieve
calibration comparable to the more structurally faithful alternatives, at least
in the studied scenarios. On the basis of our findings, we provide practical
suggestions for robust likelihood and link choices in GLMs
Rank-normalization, folding, and localization: An improved for assessing convergence of MCMC
Markov chain Monte Carlo is a key computational tool in Bayesian statistics,
but it can be challenging to monitor the convergence of an iterative stochastic
algorithm. In this paper we show that the convergence diagnostic
of Gelman and Rubin (1992) has serious flaws. Traditional will
fail to correctly diagnose convergence failures when the chain has a heavy tail
or when the variance varies across the chains. In this paper we propose an
alternative rank-based diagnostic that fixes these problems. We also introduce
a collection of quantile-based local efficiency measures, along with a
practical approach for computing Monte Carlo error estimates for quantiles. We
suggest that common trace plots should be replaced with rank plots from
multiple chains. Finally, we give recommendations for how these methods should
be used in practice.Comment: Minor revision for improved clarit
Ambiguous avant-gardes and their geographies: on blank spots of the postgrowth debate
In the following article, the focus is on the transformative potentials created by so-called persistence avant-gardes and prevention innovators. The text extends Blühdorn’s guiding concept of narratives of hope (Blühdorn 2017; Blühdorn and Butzlaff 2019) by considering those groups that are marginalized within debates on socio-ecological transformation. With a closer look at the narratives of prevention and blockade that these actors engage, the ambiguous nature of postgrowth avant-gardes is carved out. Their discursive, argumentative, and effective inhibition of transitory policies is interpreted as a pro-active potential, rather than a mere obstacle to socio-ecological transformation. Adding a geographical perspective, the paper pleads for a more precise theoretical penetration of the ambivalent figure of avant-gardes when analyzing processes of local and regional postgrowth
Testing for Publication Bias in Diagnostic Meta-Analysis: A Simulation Study
The present study investigates the performance of several statistical tests
to detect publication bias in diagnostic meta-analysis by means of simulation.
While bivariate models should be used to pool data from primary studies in
diagnostic meta-analysis, univariate measures of diagnostic accuracy are
preferable for the purpose of detecting publication bias. In contrast to
earlier research, which focused solely on the diagnostic odds ratio or its
logarithm (), the tests are combined with four different univariate
measures of diagnostic accuracy. For each combination of test and univariate
measure, both type I error rate and statistical power are examined under
diverse conditions. The results indicate that tests based on linear regression
or rank correlation cannot be recommended in diagnostic meta-analysis, because
type I error rates are either inflated or power is too low, irrespective of the
applied univariate measure. In contrast, the combination of trim and fill and
has non-inflated or only slightly inflated type I error rates and
medium to high power, even under extreme circumstances (at least when the
number of studies per meta-analysis is large enough). Therefore, we recommend
the application of trim and fill combined with to detect funnel
plot asymmetry in diagnostic meta-analysis. Please cite this paper as published
in Statistics in Medicine (https://doi.org/10.1002/sim.6177).Comment: arXiv admin note: text overlap with arXiv:2002.04775 by other author
Prediction can be safely used as a proxy for explanation in causally consistent Bayesian generalized linear models
Bayesian modeling provides a principled approach to quantifying uncertainty
in model parameters and model structure and has seen a surge of applications in
recent years. Within the context of a Bayesian workflow, we are concerned with
model selection for the purpose of finding models that best explain the data,
that is, help us understand the underlying data generating process. Since we
rarely have access to the true process, all we are left with during real-world
analyses is incomplete causal knowledge from sources outside of the current
data and model predictions of said data. This leads to the important question
of when the use of prediction as a proxy for explanation for the purpose of
model selection is valid. We approach this question by means of large-scale
simulations of Bayesian generalized linear models where we investigate various
causal and statistical misspecifications. Our results indicate that the use of
prediction as proxy for explanation is valid and safe only when the models
under consideration are sufficiently consistent with the underlying causal
structure of the true data generating process
Graphical Test for Discrete Uniformity and its Applications in Goodness of Fit Evaluation and Multiple Sample Comparison
Assessing goodness of fit to a given distribution plays an important role in
computational statistics. The Probability integral transformation (PIT) can be
used to convert the question of whether a given sample originates from a
reference distribution into a problem of testing for uniformity. We present new
simulation and optimization based methods to obtain simultaneous confidence
bands for the whole empirical cumulative distribution function (ECDF) of the
PIT values under the assumption of uniformity. Simultaneous confidence bands
correspond to such confidence intervals at each point that jointly satisfy a
desired coverage. These methods can also be applied in cases where the
reference distribution is represented only by a finite sample. The confidence
bands provide an intuitive ECDF-based graphical test for uniformity, which also
provides useful information on the quality of the discrepancy. We further
extend the simulation and optimization methods to determine simultaneous
confidence bands for testing whether multiple samples come from the same
underlying distribution. This multiple sample comparison test is especially
useful in Markov chain Monte Carlo convergence diagnostics. We provide
numerical experiments to assess the properties of the tests using both
simulated and real world data and give recommendations on their practical
application in computational statistics workflows
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