Likelihood-Based Confidence Sets for the Timing of Structural Breaks

In this paper, we propose a new approach to constructing confidence sets for the timing of structural breaks. This approach involves using Markov-chain Monte Carlo methods to simulate marginal “fiducial” distributions of break dates from the likelihood function. We compare our proposed approach to asymptotic and bootstrap confidence sets and find that it performs best in terms of producing short confidence sets with accurate coverage rates. Our approach also has the advantages of i) being broadly applicable to different patterns of structural breaks, ii) being computationally efficient, and iii) requiring only the ability to evaluate the likelihood function over parameter values, thus allowing for many possible distributional assumptions for the data. In our application, we investigate the nature and timing of structural breaks in postwar U.S. Real GDP. Based on marginal fiducial distributions, we find much tighter 95% confidence sets for the timing of the so-called “Great Moderation” than has been reported in previous studies.Fiducial Inference; Bootstrap Methods; Structural Breaks; Confidence Intervals and Sets; Coverage Accuracy and Expected Length; Markov-chain Monte Carlo;

The association between sleep patterns and obesity in older adults.

BackgroundReduced sleep duration has been increasingly reported to predict obesity. However, timing and regularity of sleep may also be important. In this study, the cross-sectional association between objectively measured sleep patterns and obesity was assessed in two large cohorts of older individuals.MethodsWrist actigraphy was performed in 3053 men (mean age: 76.4 years) participating in the Osteoporotic Fractures in Men Study and 2985 women (mean age: 83.5 years) participating in the Study of Osteoporotic Fractures. Timing and regularity of sleep patterns were assessed across nights, as well as daytime napping.ResultsGreater night-to-night variability in sleep duration and daytime napping were associated with obesity independent of mean nocturnal sleep duration in both men and women. Each 1 h increase in the standard deviation of nocturnal sleep duration increased the odds of obesity 1.63-fold (95% confidence interval: 1.31-2.02) among men and 1.22-fold (95% confidence interval: 1.01-1.47) among women. Each 1 h increase in napping increased the odds of obesity 1.23-fold (95% confidence interval: 1.12-1.37) in men and 1.29-fold (95% confidence interval: 1.17-1.41) in women. In contrast, associations between later sleep timing and night-to-night variability in sleep timing with obesity were less consistent.ConclusionsIn both older men and women, variability in nightly sleep duration and daytime napping were associated with obesity, independent of mean sleep duration. These findings suggest that characteristics of sleep beyond mean sleep duration may have a role in weight homeostasis, highlighting the complex relationship between sleep and metabolism

Self-Confidence and Timing of Entry

This paper analyzes the impact of overconfidence on the timing of entry in markets, profits, and welfare. To do that the paper uses an endogenous timing model where (i) players have private information about costs and (ii) one player is overconfident and the other is rational. The paper shows that for moderate levels of self-confidence there is a unique cost-dependent equilibrium where the overconfident player has a higher ex-ante probability of entering the market before the rational player. In this equilibrium self-confidence reduces the profits of the rational player but can increase the profits of the overconfident player provided that cost asymmetries are small. Finally, we show that overconfidence reduces welfare, except when cost asymmetries are very small.endogenous timing; entry; overconfidence

Perceptual confidence demonstrates trial-by-trial insight into the precision of audio-visual timing encoding

Peoples’ subjective feelings of confidence typically correlate positively with objective measures of task performance, even when no performance feedback is provided. This relationship has seldom been investigated in the field of human time perception. Here we find a positive relationship between the precision of human timing perception and decisional confidence. We first demonstrate that subjective audio–visual timing judgements are more precise when people report a high, as opposed to a low, level of confidence. We then find that this relationship is more likely to result from variance in sensory timing estimates than the application of variable decision criteria, as the relationship held when we adopted a measure of timing sensitivity designed to limit the influence of subjective criteria. Our results suggest analyses of timing perception and associated decisional confidence reflect the trial-by-trial variability with which timing has been encoded

Taming outliers in pulsar-timing datasets with hierarchical likelihoods and Hamiltonian sampling

Pulsar-timing datasets have been analyzed with great success using probabilistic treatments based on Gaussian distributions, with applications ranging from studies of neutron-star structure to tests of general relativity and searches for nanosecond gravitational waves. As for other applications of Gaussian distributions, outliers in timing measurements pose a significant challenge to statistical inference, since they can bias the estimation of timing and noise parameters, and affect reported parameter uncertainties. We describe and demonstrate a practical end-to-end approach to perform Bayesian inference of timing and noise parameters robustly in the presence of outliers, and to identify these probabilistically. The method is fully consistent (i.e., outlier-ness probabilities vary in tune with the posterior distributions of the timing and noise parameters), and it relies on the efficient sampling of the hierarchical form of the pulsar-timing likelihood. Such sampling has recently become possible with a "no-U-turn" Hamiltonian sampler coupled to a highly customized reparametrization of the likelihood; this code is described elsewhere, but it is already available online. We recommend our method as a standard step in the preparation of pulsar-timing-array datasets: even if statistical inference is not affected, follow-up studies of outlier candidates can reveal unseen problems in radio observations and timing measurements; furthermore, confidence in the results of gravitational-wave searches will only benefit from stringent statistical evidence that datasets are clean and outlier-free.Comment: 6 pages, 2 figures, RevTeX 4.

The noise properties of 42 millisecond pulsars from the European Pulsar Timing Array and their impact on gravitational wave searches

The sensitivity of Pulsar Timing Arrays to gravitational waves depends on the noise present in the individual pulsar timing data. Noise may be either intrinsic or extrinsic to the pulsar. Intrinsic sources of noise will include rotational instabilities, for example. Extrinsic sources of noise include contributions from physical processes which are not sufficiently well modelled, for example, dispersion and scattering effects, analysis errors and instrumental instabilities. We present the results from a noise analysis for 42 millisecond pulsars (MSPs) observed with the European Pulsar Timing Array. For characterising the low-frequency, stochastic and achromatic noise component, or "timing noise", we employ two methods, based on Bayesian and frequentist statistics. For 25 MSPs, we achieve statistically significant measurements of their timing noise parameters and find that the two methods give consistent results. For the remaining 17 MSPs, we place upper limits on the timing noise amplitude at the 95% confidence level. We additionally place an upper limit on the contribution to the pulsar noise budget from errors in the reference terrestrial time standards (below 1%), and we find evidence for a noise component which is present only in the data of one of the four used telescopes. Finally, we estimate that the timing noise of individual pulsars reduces the sensitivity of this data set to an isotropic, stochastic GW background by a factor of >9.1 and by a factor of >2.3 for continuous GWs from resolvable, inspiralling supermassive black-hole binaries with circular orbits.Comment: Accepted for publication by the Monthly Notices of the Royal Astronomical Societ

Contraceptive confidence and timing of first birth in Moldova: an event history analysis of retrospective data

Objectives: To test the contraceptive confidence hypothesis in a modern context. The hypothesis is that women using effective or modern contraceptive methods have increased contraceptive confidence and hence a shorter interval between marriage and first birth than users of ineffective or traditional methods. We extend the hypothesis to incorporate the role of abortion, arguing that it acts as a substitute for contraception in the study context.Setting: Moldova, a country in South-East Europe. Moldova exhibits high use of traditional contraceptive methods and abortion compared with other European countries.Participants: Data are from a secondary analysis of the 2005 Moldovan Demographic and Health Survey, a nationally representative sample survey. 5377 unmarried women were selected.Primary and secondary outcome measures: The outcome measure was the interval between marriage and first birth. This was modelled using a piecewise-constant hazard regression, with abortion and contraceptive method types as primary variables along with relevant sociodemographic controls.Results: Women with high contraceptive confidence (modern method users) have a higher cumulative hazard of first birth 36?months following marriage (0.88 (0.87 to 0.89)) compared with women with low contraceptive confidence (traditional method users, cumulative hazard: 0.85 (0.84 to 0.85)). This is consistent with the contraceptive confidence hypothesis. There is a higher cumulative hazard of first birth among women with low (0.80 (0.79 to 0.80)) and moderate abortion propensities (0.76 (0.75 to 0.77)) than women with no abortion propensity (0.73 (0.72 to 0.74)) 24?months after marriage.Conclusions: Effective contraceptive use tends to increase contraceptive confidence and is associated with a shorter interval between marriage and first birth. Increased use of abortion also tends to increase contraceptive confidence and shorten birth duration, although this effect is non-linear—women with a very high use of abortion tend to have lengthy intervals between marriage and first birth

Search for gravitational waves associated with the August 2006 timing glitch of the Vela pulsar

The physical mechanisms responsible for pulsar timing glitches are thought to excite quasinormal mode oscillations in their parent neutron star that couple to gravitational-wave emission. In August 2006, a timing glitch was observed in the radio emission of PSR B0833-45, the Vela pulsar. At the time of the glitch, the two colocated Hanford gravitational-wave detectors of the Laser Interferometer Gravitational wave observatory (LIGO) were operational and taking data as part of the fifth LIGO science run (S5). We present the first direct search for the gravitational-wave emission associated with oscillations of the fundamental quadrupole mode excited by a pulsar timing glitch. No gravitational-wave detection candidate was found. We place Bayesian 90% confidence upper limits of 6.3 x 10^(-21) to 1.4 x 10^(-20) on the peak intrinsic strain amplitude of gravitational-wave ring-down signals, depending on which spherical harmonic mode is excited. The corresponding range of energy upper limits is 5.0 x 10^(-44) to 1.3 x 10^(-45) erg