150,966 research outputs found
Testing hypotheses via a mixture estimation model
We consider a novel paradigm for Bayesian testing of hypotheses and Bayesian
model comparison. Our alternative to the traditional construction of posterior
probabilities that a given hypothesis is true or that the data originates from
a specific model is to consider the models under comparison as components of a
mixture model. We therefore replace the original testing problem with an
estimation one that focus on the probability weight of a given model within a
mixture model. We analyze the sensitivity on the resulting posterior
distribution on the weights of various prior modeling on the weights. We stress
that a major appeal in using this novel perspective is that generic improper
priors are acceptable, while not putting convergence in jeopardy. Among other
features, this allows for a resolution of the Lindley-Jeffreys paradox. When
using a reference Beta B(a,a) prior on the mixture weights, we note that the
sensitivity of the posterior estimations of the weights to the choice of a
vanishes with the sample size increasing and avocate the default choice a=0.5,
derived from Rousseau and Mengersen (2011). Another feature of this easily
implemented alternative to the classical Bayesian solution is that the speeds
of convergence of the posterior mean of the weight and of the corresponding
posterior probability are quite similar.Comment: 25 pages, 6 figures, 2 table
Importance sampling schemes for evidence approximation in mixture models
The marginal likelihood is a central tool for drawing Bayesian inference
about the number of components in mixture models. It is often approximated
since the exact form is unavailable. A bias in the approximation may be due to
an incomplete exploration by a simulated Markov chain (e.g., a Gibbs sequence)
of the collection of posterior modes, a phenomenon also known as lack of label
switching, as all possible label permutations must be simulated by a chain in
order to converge and hence overcome the bias. In an importance sampling
approach, imposing label switching to the importance function results in an
exponential increase of the computational cost with the number of components.
In this paper, two importance sampling schemes are proposed through choices for
the importance function; a MLE proposal and a Rao-Blackwellised importance
function. The second scheme is called dual importance sampling. We demonstrate
that this dual importance sampling is a valid estimator of the evidence and
moreover show that the statistical efficiency of estimates increases. To reduce
the induced high demand in computation, the original importance function is
approximated but a suitable approximation can produce an estimate with the same
precision and with reduced computational workload.Comment: 24 pages, 5 figure
The Importance of Being Clustered: Uncluttering the Trends of Statistics from 1970 to 2015
In this paper we retrace the recent history of statistics by analyzing all
the papers published in five prestigious statistical journals since 1970,
namely: Annals of Statistics, Biometrika, Journal of the American Statistical
Association, Journal of the Royal Statistical Society, series B and Statistical
Science. The aim is to construct a kind of "taxonomy" of the statistical papers
by organizing and by clustering them in main themes. In this sense being
identified in a cluster means being important enough to be uncluttered in the
vast and interconnected world of the statistical research. Since the main
statistical research topics naturally born, evolve or die during time, we will
also develop a dynamic clustering strategy, where a group in a time period is
allowed to migrate or to merge into different groups in the following one.
Results show that statistics is a very dynamic and evolving science, stimulated
by the rise of new research questions and types of data
Volatility forecasting
Volatility has been one of the most active and successful areas of research in time series econometrics and economic forecasting in recent decades. This chapter provides a selective survey of the most important theoretical developments and empirical insights to emerge from this burgeoning literature, with a distinct focus on forecasting applications. Volatility is inherently latent, and Section 1 begins with a brief intuitive account of various key volatility concepts. Section 2 then discusses a series of different economic situations in which volatility plays a crucial role, ranging from the use of volatility forecasts in portfolio allocation to density forecasting in risk management. Sections 3, 4 and 5 present a variety of alternative procedures for univariate volatility modeling and forecasting based on the GARCH, stochastic volatility and realized volatility paradigms, respectively. Section 6 extends the discussion to the multivariate problem of forecasting conditional covariances and correlations, and Section 7 discusses volatility forecast evaluation methods in both univariate and multivariate cases. Section 8 concludes briefly. JEL Klassifikation: C10, C53, G1
Bayesian computational methods
In this chapter, we will first present the most standard computational
challenges met in Bayesian Statistics, focussing primarily on mixture
estimation and on model choice issues, and then relate these problems with
computational solutions. Of course, this chapter is only a terse introduction
to the problems and solutions related to Bayesian computations. For more
complete references, see Robert and Casella (2004, 2009), or Marin and Robert
(2007), among others. We also restrain from providing an introduction to
Bayesian Statistics per se and for comprehensive coverage, address the reader
to Robert (2007), (again) among others.Comment: This is a revised version of a chapter written for the Handbook of
Computational Statistics, edited by J. Gentle, W. Hardle and Y. Mori in 2003,
in preparation for the second editio
Bayesian Optimization for Probabilistic Programs
We present the first general purpose framework for marginal maximum a
posteriori estimation of probabilistic program variables. By using a series of
code transformations, the evidence of any probabilistic program, and therefore
of any graphical model, can be optimized with respect to an arbitrary subset of
its sampled variables. To carry out this optimization, we develop the first
Bayesian optimization package to directly exploit the source code of its
target, leading to innovations in problem-independent hyperpriors, unbounded
optimization, and implicit constraint satisfaction; delivering significant
performance improvements over prominent existing packages. We present
applications of our method to a number of tasks including engineering design
and parameter optimization
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