Inferential models: A framework for prior-free posterior probabilistic inference

Posterior probabilistic statistical inference without priors is an important but so far elusive goal. Fisher's fiducial inference, Dempster-Shafer theory of belief functions, and Bayesian inference with default priors are attempts to achieve this goal but, to date, none has given a completely satisfactory picture. This paper presents a new framework for probabilistic inference, based on inferential models (IMs), which not only provides data-dependent probabilistic measures of uncertainty about the unknown parameter, but does so with an automatic long-run frequency calibration property. The key to this new approach is the identification of an unobservable auxiliary variable associated with observable data and unknown parameter, and the prediction of this auxiliary variable with a random set before conditioning on data. Here we present a three-step IM construction, and prove a frequency-calibration property of the IM's belief function under mild conditions. A corresponding optimality theory is developed, which helps to resolve the non-uniqueness issue. Several examples are presented to illustrate this new approach.Comment: 29 pages with 3 figures. Main text is the same as the published version. Appendix B is an addition, not in the published version, that contains some corrections and extensions of two of the main theorem

Lateral Separation of Macromolecules and Polyelectrolytes in Microlithographic Arrays

A new approach to separation of a variety of microscopic and mesoscopic objects in dilute solution is presented. The approach takes advantage of unique properties of a specially designed separation device (sieve), which can be readily built using already developed microlithographic techniques. Due to the broken reflection symmetry in its design, the direction of motion of an object in the sieve varies as a function of its self-diffusion constant, causing separation transverse to its direction of motion. This gives the device some significant and unique advantages over existing fractionation methods based on centrifugation and electrophoresis.Comment: 4 pages with 3 eps figures, needs RevTeX 3.0 and epsf, also available in postscript form http://cmtw.harvard.edu/~deniz

Towards a transportable aluminium ion quantum logic optical clock

With the advent of optical clocks featuring fractional frequency uncertainties on the order of 10-17 and below, new applications such as chronometric leveling with few-centimeter height resolution emerge. We are developing a transportable optical clock based on a single trapped aluminum ion, which is interrogated via quantum logic spectroscopy. We employ singly charged calcium as the logic ion for sympathetic cooling, state preparation, and readout. Here, we present a simple and compact physics and laser package for manipulation of 40Ca+. Important features are a segmented multilayer trap with separate loading and probing zones, a compact titanium vacuum chamber, a near-diffraction-limited imaging system with high numerical aperture based on a single biaspheric lens, and an all-in-fiber 40Ca+ repump laser system. We present preliminary estimates of the trap-induced frequency shifts on 27Al+, derived from measurements with a single calcium ion. The micromotion-induced second-order Doppler shift for 27Al+ has been determined to be δνEMMν=-0.4-0.3 +0.4×10-18 and the black-body radiation shift is δνBBR/ν = (-4.0 ± 0.4) × 10-18. Moreover, heating rates of 30 (7) quanta per second at trap frequencies of ωrad,Ca+ ≈ 2π × 2.5 MHz (ωax,Ca+ ≈ 2π × 1.5 MHz) in radial (axial) direction have been measured, enabling interrogation times of a few hundreds of milliseconds

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

A prospective cohort study assessing clinical referral management & workforce allocation within a UK regional medical genetics service

Abstract Ensuring patient access to genomic information in the face of increasing demand requires clinicians to develop innovative ways of working. This paper presents the first empirical prospective observational cohort study of UK multi-disciplinary genetic service delivery. It describes and explores collaborative working practices including the utilisation and role of clinical geneticists and non-medical genetic counsellors. Six hundred and fifty new patients referred to a regional genetics service were tracked through 850 clinical contacts until discharge. Referral decisions regarding allocation of lead health professional assigned to the case were monitored, including the use of initial clinical contact guidelines. Significant differences were found in the cases led by genetic counsellors and those led by clinical geneticists. Around a sixth, 16.8% (109/650) of referrals were dealt with by a letter back to the referrer or re-directed to another service provider and 14.8% (80/541) of the remaining patients chose not to schedule an appointment. Of the remaining 461 patients, genetic counsellors were allocated as lead health professional for 46.2% (213/461). A further 61 patients did not attend. Of those who did, 86% (345/400) were discharged after one or two appointments. Genetic counsellors contributed to 95% (784/825) of total patient contacts. They provided 93.7% (395/432) of initial contacts and 26.8% (106/395) of patients were discharged at that point. The information from this study informed a planned service re-design. More research is needed to assess the effectiveness and efficiency of different models of collaborative multi-disciplinary working within genetics services. Keywords (MeSH terms) Genetic Services, Genetic Counseling, Interdisciplinary Communication, Cohort Studies, Delivery of Healthcare, Referral and Consultation