Search results for "Frequentist inference"
showing 10 items of 26 documents
Improvement of Statistical Decisions under Parametric Uncertainty
2011
A large number of problems in production planning and scheduling, location, transportation, finance, and engineering design require that decisions be made in the presence of uncertainty. Decision‐making under uncertainty is a central problem in statistical inference, and has been formally studied in virtually all approaches to inference. The aim of the present paper is to show how the invariant embedding technique, the idea of which belongs to the authors, may be employed in the particular case of finding the improved statistical decisions under parametric uncertainty. This technique represents a simple and computationally attractive statistical method based on the constructive use of the i…
Was there an early reionization component in our universe?
2017
A deep understanding of the Epoch of Reionization is still missing in our knowledge of the universe. While future probes will allow us to test the precise evolution of the free electron fraction from redshifts between $z\simeq 6$ and $z\simeq 20$, at present one could ask what kind of reionization processes are allowed by present Cosmic Microwave Background temperature and polarization measurements. An early contribution to reionization could imply a departure from the standard picture where star formation determines the reionization onset. BBy considering a broad class of possible reionization parameterizations, we find that current data do not require an early reionization component in ou…
Likelihood approach to the first dark matter results from XENON100
2011
Many experiments that aim at the direct detection of Dark Matter are able to distinguish a dominant background from the expected feeble signals, based on some measured discrimination parameter. We develop a statistical model for such experiments using the Profile Likelihood ratio as a test statistic in a frequentist approach. We take data from calibrations as control measurements for signal and background, and the method allows the inclusion of data from Monte Carlo simulations. Systematic detector uncertainties, such as uncertainties in the energy scale, as well as astrophysical uncertainties, are included in the model. The statistical model can be used to either set an exclusion limit or …
Probabilistic inference of approximations
2006
We consider probabilistic inductive inference of Godel numbers of total recursive functions when the set of possible errors is allowed to be infinite, but with bounded density. We have obtained hierarchies of classes of functions identifiable with different probabilities up to sets with fixed density. The obtained hierarchies turn out to be different from those which we have in the case of exact identification.
Weighted-Average Least Squares (WALS): Confidence and Prediction Intervals
2022
We extend the results of De Luca et al. (2021) to inference for linear regression models based on weighted-average least squares (WALS), a frequentist model averaging approach with a Bayesian flavor. We concentrate on inference about a single focus parameter, interpreted as the causal effect of a policy or intervention, in the presence of a potentially large number of auxiliary parameters representing the nuisance component of the model. In our Monte Carlo simulations we compare the performance of WALS with that of several competing estimators, including the unrestricted least-squares estimator (with all auxiliary regressors) and the restricted least-squares estimator (with no auxiliary reg…
A Bayesian Sequential Look at u-Control Charts
2005
We extend the usual implementation of u-control charts (uCCs) in two ways. First, we overcome the restrictive (and often inadequate) assumptions of the Poisson model; next, we eliminate the need for the questionable base period by using a sequential procedure. We use empirical Bayes(EB) and Bayes methods and compare them with the traditional frequentist implementation. EB methods are somewhat easy to implement, and they deal nicely with extra-Poisson variability (and, at the same time, informally check the adequacy of the Poisson assumption). However, they still need the base period. The sequential, full Bayes approach, on the other hand, also avoids this drawback of traditional u-charts. T…
Olley–Pakes productivity decomposition: computation and inference
2016
Summary We show how a moment-based estimation procedure can be used to compute point estimates and standard errors for the two components of the widely used Olley–Pakes decomposition of aggregate (weighted average) productivity. When applied to business level microdata, the procedure allows for autocovariance and heteroscedasticity robust inference and hypothesis testing about, for example, the coevolution of the productivity components in different groups of firms. We provide an application to Finnish firm level data and find that formal statistical inference casts doubt on the conclusions that one might draw on the basis of a visual inspection of the components of the decomposition.
Bayesian survival analysis with BUGS
2020
Survival analysis is one of the most important fields of statistics in medicine and biological sciences. In addition, the computational advances in the last decades have favored the use of Bayesian methods in this context, providing a flexible and powerful alternative to the traditional frequentist approach. The objective of this article is to summarize some of the most popular Bayesian survival models, such as accelerated failure time, proportional hazards, mixture cure, competing risks, multi-state, frailty, and joint models of longitudinal and survival data. Moreover, an implementation of each presented model is provided using a BUGS syntax that can be run with JAGS from the R programmin…
Intrinsic credible regions: An objective Bayesian approach to interval estimation
2005
This paper definesintrinsic credible regions, a method to produce objective Bayesian credible regions which only depends on the assumed model and the available data.Lowest posterior loss (LPL) regions are defined as Bayesian credible regions which contain values of minimum posterior expected loss: they depend both on the loss function and on the prior specification. An invariant, information-theory based loss function, theintrinsic discrepancy is argued to be appropriate for scientific communication. Intrinsic credible regions are the lowest posterior loss regions with respect to the intrinsic discrepancy loss and the appropriate reference prior. The proposed procedure is completely general…
MCMC methods to approximate conditional predictive distributions
2006
Sampling from conditional distributions is a problem often encountered in statistics when inferences are based on conditional distributions which are not of closed-form. Several Markov chain Monte Carlo (MCMC) algorithms to simulate from them are proposed. Potential problems are pointed out and some suitable modifications are suggested. Approximations based on conditioning sets are also explored. The issues are illustrated within a specific statistical tool for Bayesian model checking, and compared in an example. An example in frequentist conditional testing is also given.