Coherent frequentism

By representing the range of fair betting odds according to a pair of confidence set estimators, dual probability measures on parameter space called frequentist posteriors secure the coherence of subjective inference without any prior distribution. The closure of the set of expected losses corresponding to the dual frequentist posteriors constrains decisions without arbitrarily forcing optimization under all circumstances. This decision theory reduces to those that maximize expected utility when the pair of frequentist posteriors is induced by an exact or approximate confidence set estimator or when an automatic reduction rule is applied to the pair. In such cases, the resulting frequentist posterior is coherent in the sense that, as a probability distribution of the parameter of interest, it satisfies the axioms of the decision-theoretic and logic-theoretic systems typically cited in support of the Bayesian posterior. Unlike the p-value, the confidence level of an interval hypothesis derived from such a measure is suitable as an estimator of the indicator of hypothesis truth since it converges in sample-space probability to 1 if the hypothesis is true or to 0 otherwise under general conditions.Comment: The confidence-measure theory of inference and decision is explicitly extended to vector parameters of interest. The derivation of upper and lower confidence levels from valid and nonconservative set estimators is formalize

Inference for bounded parameters

The estimation of signal frequency count in the presence of background noise has had much discussion in the recent physics literature, and Mandelkern [1] brings the central issues to the statistical community, leading in turn to extensive discussion by statisticians. The primary focus however in [1] and the accompanying discussion is on the construction of a confidence interval. We argue that the likelihood function and $p$-value function provide a comprehensive presentation of the information available from the model and the data. This is illustrated for Gaussian and Poisson models with lower bounds for the mean parameter

Detection and extraction of signals from the epoch of reionization using higher-order one-point statistics

Detecting redshifted 21-cm emission from neutral hydrogen in the early Universe promises to give direct constraints on the epoch of reionization (EoR). It will, though, be very challenging to extract the cosmological signal (CS) from foregrounds and noise which are orders of magnitude larger. Fortunately, the signal has some characteristics which differentiate it from the foregrounds and noise, and we suggest that using the correct statistics may tease out signatures of reionization. We generate mock data cubes simulating the output of the Low Frequency Array (LOFAR) EoR experiment. These cubes combine realistic models for Galactic and extragalactic foregrounds and the noise with three different simulations of the CS. We fit out the foregrounds, which are smooth in the frequency direction, to produce residual images in each frequency band. We denoise these images and study the skewness of the one-point distribution in the images as a function of frequency. We find that, under sufficiently optimistic assumptions, we can recover the main features of the redshift evolution of the skewness in the 21-cm signal. We argue that some of these features ¿ such as a dip at the onset of reionization, followed by a rise towards its later stages ¿ may be generic, and give us a promising route to a statistical detection of reionization

Detection of Extended He II Reionization in the Temperature Evolution of the Intergalactic Medium

We present new measurements of the temperature of the intergalactic medium (IGM) derived from the Lyman-alpha forest over 2.0 < z < 4.8. The small-scale structure in the forest of 61 high-resolution QSO spectra is quantified using a new statistic, the curvature, and the conversion to temperature calibrated using a suite of hydrodynamic simulations. At each redshift we focus on obtaining the temperature at an optimal overdensity probed by the Lyman-alpha forest, T(Delta), where the temperature is nearly a one-to-one function of the curvature regardless of the slope of the temperature-density relation. The median 2-sigma statistical uncertainty in these measurements is 8 per cent, though there may be comparable systematic errors due to the unknown amount of Jeans smoothing in the IGM. We use our T(Delta) results to infer the temperature at the mean density, T0. Even for a maximally steep temperature-density relation, T0 must increase from ~8000 K at z ~ 4.4 to >~12000 K at z ~ 2.8. This increase is not consistent with the monotonic decline in T0 expected in the absence of He II reionization. We therefore interpret the observed rise in temperature as evidence of He II reionization beginning at z >~ 4.4. The evolution of T0 is consistent with an end to He II reionization at z ~ 3, as suggested by opacity measurements of the He II Lyman-alpha forest, although the redshift at which T0 peaks will depend somewhat on the evolution of the temperature-density relation. These new temperature measurements suggest that the heat input due to the reionization of He II dominates the thermal balance of the IGM over an extended period with Delta_z >~ 1.Comment: 19 pages, 15 figures, accepted to MNRA

Realistic Simulations of the Galactic Polarized Foreground: Consequences for 21-cm Reionization Detection Experiments

Experiments designed to measure the redshifted 21~cm line from the Epoch of Reionization (EoR) are challenged by strong astrophysical foreground contamination, ionospheric distortions, complex instrumental response and other different types of noise (e.g. radio frequency interference). The astrophysical foregrounds are dominated by diffuse synchrotron emission from our Galaxy. Here we present a simulation of the Galactic emission used as a foreground module for the LOFAR- EoR key science project end-to-end simulations. The simulation produces total and polarized intensity over $10^\circ \times 10^\circ$ maps of the Galactic synchrotron and free-free emission, including all observed characteristics of the emission: spatial fluctuations of amplitude and spectral index of the synchrotron emission, together with Faraday rotation effects. The importance of these simulations arise from the fact that the Galactic polarized emission could behave in a manner similar to the EoR signal along the frequency direction. As a consequence, an improper instrumental calibration will give rise to leakages of the polarized to the total signal and mask the desired EoR signal. In this paper we address this for the first time through realistic simulations.Comment: 14 pages, 8 figures, published in MNRA

Effectiveness of physiotherapy exercise following hip arthroplasty for osteoarthritis: a systematic review of clinical trials

Background: Physiotherapy has long been a routine component of patient rehabilitation following hip joint replacement. The purpose of this systematic review was to evaluate the effectiveness of physiotherapy exercise after discharge from hospital on function, walking, range of motion, quality of life and muscle strength, for osteoarthritic patients following elective primary total hip arthroplasty. Methods: Design: Systematic review, using the Cochrane Collaboration Handbook for Systematic Reviews of Interventions and the Quorom Statement. Database searches: AMED, CINAHL, EMBASE, KingsFund, MEDLINE, Cochrane library (Cochrane reviews, Cochrane Central Register of Controlled Trials, DARE), PEDro, The Department of Health National Research Register. Handsearches: Physiotherapy, Physical Therapy, Journal of Bone and Joint Surgery (Britain) Conference Proceedings. No language restrictions were applied. Selection: Trials comparing physiotherapy exercise versus usual/standard care, or comparing two types of relevant exercise physiotherapy, following discharge from hospital after elective primary total hip replacement for osteoarthritis were reviewed. Outcomes: Functional activities of daily living, walking, quality of life, muscle strength and range of hip joint motion. Trial quality was extensively evaluated. Narrative synthesis plus meta-analytic summaries were performed to summarise the data. Results: 8 trials were identified. Trial quality was mixed. Generally poor trial quality, quantity and diversity prevented explanatory meta-analyses. The results were synthesised and meta-analytic summaries were used where possible to provide a formal summary of results. Results indicate that physiotherapy exercise after discharge following total hip replacement has the potential to benefit patients. Conclusion: Insufficient evidence exists to establish the effectiveness of physiotherapy exercise following primary hip replacement for osteoarthritis. Further well designed trials are required to determine the value of post discharge exercise following this increasingly common surgical procedure

A frequentist framework of inductive reasoning

Reacting against the limitation of statistics to decision procedures, R. A. Fisher proposed for inductive reasoning the use of the fiducial distribution, a parameter-space distribution of epistemological probability transferred directly from limiting relative frequencies rather than computed according to the Bayes update rule. The proposal is developed as follows using the confidence measure of a scalar parameter of interest. (With the restriction to one-dimensional parameter space, a confidence measure is essentially a fiducial probability distribution free of complications involving ancillary statistics.) A betting game establishes a sense in which confidence measures are the only reliable inferential probability distributions. The equality between the probabilities encoded in a confidence measure and the coverage rates of the corresponding confidence intervals ensures that the measure's rule for assigning confidence levels to hypotheses is uniquely minimax in the game. Although a confidence measure can be computed without any prior distribution, previous knowledge can be incorporated into confidence-based reasoning. To adjust a p-value or confidence interval for prior information, the confidence measure from the observed data can be combined with one or more independent confidence measures representing previous agent opinion. (The former confidence measure may correspond to a posterior distribution with frequentist matching of coverage probabilities.) The representation of subjective knowledge in terms of confidence measures rather than prior probability distributions preserves approximate frequentist validity.Comment: major revisio

Cardiorespiratory and perceptual responses to self-regulated and imposed submaximal arm-leg ergometry

Purpose: This study compared cardiorespiratory and perceptual responses to exercise using self-regulated and imposed power outputs distributed between the arms and legs. Methods Ten males (age 21.7 ± 3.4 years) initially undertook incremental arm-crank ergometry (ACE) and cycle ergometry (CYC) tests to volitional exhaustion to determine peak power output (Wpeak). Two subsequent tests involved 20-min combined arm–leg ergometry (ALE) trials, using imposed and self-regulated protocols, both of which aimed to elicit an exercising heart rate of 160 beats min−1. During the imposed trial, arm and leg intensity were set at 40% of each ergometer-specific Wpeak. During the self-regulated trial, participants were asked to self-regulate cadence and resistance to achieve the target heart rate. Heart rate (HR), oxygen uptake (V˙O2 ), pulmonary ventilation (V˙E ), and ratings of perceived exertion (RPE) were recorded continuously. Results As expected, there were no differences between imposed and self-regulated trials for HR, V˙O2 , and V˙E (all P ≥ 0.05). However, central RPE and local RPE for the arms were lower during self-regulated compared imposed trials (P ≤ 0.05). Lower RPE during the self-regulated trial was related to preferential adjustments in how the arms (33 ± 5% Wpeak) and legs (46 ± 5% Wpeak) contributed to the exercise intensity. Conclusions: This study demonstrates that despite similar metabolic and cardiovascular strain elicited by imposed and self-regulated ALE, the latter was perceived to be less strenuous, which is related to participants doing more work with the legs and less work with the arms to achieve the target intensity