The Role of Beliefs in Inference for Rational Expectations Models

This paper discusses inference for rational expectations models estimated via minimum distance methods by characterizing the probability beliefs regarding the data generating process (DGP) that are compatible with given moment conditions. The null hypothesis is taken to be rational expectations and the alternative hypothesis to be distorted beliefs. This distorted beliefs alternative is analyzed from the perspective of a hypothetical semiparametric Bayesian who believes the model and uses it to learn about the DGP. This interpretation provides a different perspective on estimates, test statistics, and confidence regions in large samples, particularly regarding the economic significance of rejections in rational expectations models.

A Global Analysis of Dark Matter Signals from 27 Dwarf Spheroidal Galaxies using 11 Years of Fermi-LAT Observations

We search for a dark matter signal in 11 years of Fermi-LAT gamma-ray data from 27 Milky Way dwarf spheroidal galaxies with spectroscopically measured $J$-factors. Our analysis includes uncertainties in $J$-factors and background normalisations and compares results from a Bayesian and a frequentist perspective. We revisit the dwarf spheroidal galaxy Reticulum II, confirming that the purported gamma-ray excess seen in Pass 7 data is much weaker in Pass 8, independently of the statistical approach adopted. We introduce for the first time posterior predictive distributions to quantify the probability of a dark matter detection from another dwarf galaxy given a tentative excess. A global analysis including all 27 dwarfs shows no indication for a signal in nine annihilation channels. We present stringent new Bayesian and frequentist upper limits on the dark matter cross section as a function of dark matter mass. The best-fit dark matter parameters associated with the Galactic Centre excess are excluded by at least 95% confidence level/posterior probability in the frequentist/Bayesian framework in all cases. However, from a Bayesian model comparison perspective, dark matter annihilation within the dwarfs is not strongly disfavoured compared to a background-only model. These results constitute the highest exposure analysis on the most complete sample of dwarfs to date. Posterior samples and likelihood maps from this study are publicly available.Comment: 27+5 pages, 10 figures. Version 2 corresponds to the Accepted Manuscript version of the JCAP article; the analysis has been updated to Pass 8 R3 data plus 4FGL catalogue, with one more year of data and more annihilation channels. Supplementary Material (tabulated limits, likelihoods, and posteriors) is available on Zenodo at https://doi.org/10.5281/zenodo.261226

A default prior for regression coefficients

When the sample size is not too small, M-estimators of regression coefficients are approximately normal and unbiased. This leads to the familiar frequentist inference in terms of normality-based confidence intervals and p-values. From a Bayesian perspective, use of the (improper) uniform prior yields matching results in the sense that posterior quantiles agree with one-sided confidence bounds. For this, and various other reasons, the uniform prior is often considered objective or non-informative. In spite of this, we argue that the uniform prior is not suitable as a default prior for inference about a regression coefficient in the context of the bio-medical and social sciences. We propose that a more suitable default choice is the normal distribution with mean zero and standard deviation equal to the standard error of the M-estimator. We base this recommendation on two arguments. First, we show that this prior is non-informative for inference about the sign of the regression coefficient. Secondly, we show that this prior agrees well with a meta-analysis of 50 articles from the MEDLINE database

Chronological Profiling for Paleography

This paper approaches manuscript dating from a Bayesian perspective. Prior work on paleographic date recovery has generally sought to predict a single date for a manuscript. Bayesian analysis makes it possible to estimate a probability distribution that varies with respect to time. This in turn enables a number of alternative analyses that may be of more use to practitioners. For example, it may be useful to identify a range of years that will include a document’s creation date with a particular confidence level. The methods are demonstrated on a selection of Syriac documents created prior to 1300 CE

Frequentist validity of Bayesian limits

To the frequentist who computes posteriors, not all priors are useful asymptotically: in this paper, a Bayesian perspective on test sequences is proposed and Schwartz's Kullback-Leibler condition is generalised to widen the range of frequentist applications of posterior convergence. With Bayesian tests and a weakened form of contiguity termed remote contiguity, we prove simple and fully general frequentist theorems, for posterior consistency and rates of convergence, for consistency of posterior odds in model selection, and for conversion of sequences of credible sets into sequences of confidence sets with asymptotic coverage one. For frequentist uncertainty quantification, this means that a prior inducing remote contiguity allows one to enlarge credible sets of calculated, simulated or approximated posteriors to obtain asymptotically consistent confidence sets

A Mathematical Framework for Statistical Decision Confidence

Decision confidence is a forecast about the probability that a decision will be correct. From a statistical perspective, decision confidence can be defined as the Bayesian posterior probability that the chosen option is correct based on the evidence contributing to it. Here, we used this formal definition as a starting point to develop a normative statistical framework for decision confidence. Our goal was to make general predictions that do not depend on the structure of the noise or a specific algorithm for estimating confidence. We analytically proved several interrelations between statistical decision confidence and observable decision measures, such as evidence discriminability, choice, and accuracy. These interrelationships specify necessary signatures of decision confidence in terms of externally quantifiable variables that can be empirically tested. Our results lay the foundations for a mathematically rigorous treatment of decision confidence that can lead to a common framework for understanding confidence across different research domains, from human and animal behavior to neural representations

A global analysis of dark matter signals from 27 dwarf spheroidal galaxies using 11 years of Fermi-LAT observations

We search for a dark matter signal in 11 years of Fermi-LAT gamma-ray data from 27 Milky Way dwarf spheroidal galaxies with spectroscopically measured J-factors. Our analysis includes uncertainties in J-factors and background normalisations and compares results from a Bayesian and a frequentist perspective. We revisit the dwarf spheroidal galaxy Reticulum II, confirming that the purported gamma-ray excess seen in Pass 7 data is much weaker in Pass 8, independently of the statistical approach adopted. We introduce for the first time posterior predictive distributions to quantify the probability of a dark matter detection from another dwarf galaxy given a tentative excess. A global analysis including all 27 dwarfs shows no indication for a signal in nine annihilation channels. We present stringent new Bayesian and frequentist upper limits on the dark matter cross section as a function of dark matter mass. The best-fit dark matter parameters associated with the Galactic Centre excess are excluded by at least 95% confidence level/posterior probability in the frequentist/Bayesian framework in all cases. However, from a Bayesian model comparison perspective, dark matter annihilation within the dwarfs is not strongly disfavoured compared to a background-only model. These results constitute the highest exposure analysis on the most complete sample of dwarfs to date. Posterior samples and likelihood maps from this study are publicly available