1,546 research outputs found
Inference about Non-Identified SVARs
We propose a method for conducting inference on impulse responses in structural vector autoregressions (SVARs) when the impulse response is not point identiļ¬ed because the number of equality restrictions one can credibly impose is not suļ¬cient for point identiļ¬cation and/or one imposes sign restrictions. We proceed in three steps. We ļ¬rst deļ¬ne the object of interest as the identiļ¬ed set for a given impulse response at a given horizon and discuss how inference is simple when the identiļ¬ed set is convex, as one can limit attention to the setās upper and lower bounds. We then provide easily veriļ¬able conditions on the type of equality and sign restrictions that guarantee convexity. These cover most cases of practical interest, with exceptions including sign restrictions on multiple shocks and equality restrictions that make the impulse response locally, but not globally, identiļ¬ed. Second, we show how to conduct inference on the identiļ¬ed set. We adopt a robust Bayes approach that considers the class of all possible priors for the non-identiļ¬ed aspects of the model and delivers a class of associated posteriors. We summarize the posterior class by reporting the āposterior mean boundsā, which can be interpreted as an estimator of the identiļ¬ed set. We also consider a ārobustiļ¬ed credible regionā which is a measure of the posterior uncertainty about the identiļ¬ed set. The two intervals can be obtained using a computationally convenient numerical procedure. Third, we show that the posterior bounds converge asymptotically to the identiļ¬ed set if the set is convex. If the identiļ¬ed set is not convex, our posterior bounds can be interpreted as an estimator of the convex hull of the identiļ¬ed set. Finally, a useful diagnostic tool delivered by our procedure is the posterior belief about the plausibility of the imposed identifying restrictions
Robust Bayesian Inference for Set-Identified Models
This paper reconciles the asymptotic disagreement between Bayesian and frequentist inference in setāidentified models by adopting a multipleāprior (robust) Bayesian approach. We propose new tools for Bayesian inference in setāidentified models and show that they have a wellādefined posterior interpretation in finite samples and are asymptotically valid from the frequentist perspective. The main idea is to construct a prior class that removes the source of the disagreement: the need to specify an unrevisable prior for the structural parameter given the reducedāform parameter. The corresponding class of posteriors can be summarized by reporting the āposterior lower and upper probabilitiesā of a given event and/or the āset of posterior meansā and the associated ārobust credible regionā. We show that the set of posterior means is a consistent estimator of the true identified set and the robust credible region has the correct frequentist asymptotic coverage for the true identified set if it is convex. Otherwise, the method provides posterior inference about the convex hull of the identified set. For impulseāresponse analysis in setāidentified Structural Vector Autoregressions, the new tools can be used to overcome or quantify the sensitivity of standard Bayesian inference to the choice of an unrevisable prior
Experimental achievement of the entanglement assisted capacity for the depolarizing channel
We experimentally demonstrate the achievement of the entanglement assisted
capacity for classical information transmission over a depolarizing channel.
The implementation is based on the generation and local manipulation of 2-qubit
Bell states, which are finally measured at the receiver by a complete Bell
state analysis. The depolarizing channel is realized by introducing quantum
noise in a controlled way on one of the two qubits. This work demonstrates the
achievement of the maximum allowed amount of information that can be shared in
the presence of noise and the highest reported value in the noiseless case.Comment: 4 pages, 3 figure
Effectiveness of delayed-release dimethyl fumarate on patient-reported outcomes and clinical measures in patients with relapsing-remitting multiple sclerosis in a real-world clinical setting: PROTEC.
Ensaio clĆnico PROTEC, Protocolo nĀŗ 109MS408Abstract
BACKGROUND:
Patient-reported outcomes (PRO) and clinical outcomes give a broad assessment of relapsing-remitting multiple sclerosis (RRMS) disease.
OBJECTIVE:
The aim is to evaluate the effectiveness of delayed-release dimethyl fumarate (DMF) on disease activity and PROs in patients with RRMS in the clinic.
METHODS:
PROTEC, a phase 4, open-label, 12-month observational study, assessed annualized relapse rate (ARR), proportion of patients relapsed, and changes in PROs. Newly diagnosed and early MS (ā¤3.5 EDSS and ā¤1 relapse in the prior year) patient subgroups were evaluated.
RESULTS:
Unadjusted ARR at 12 months post-DMF versus 12 months before DMF initiation was 75% lower (0.161 vs. 0.643, pā<ā0.0001) overall (nā=ā1105) and 84%, 77%, and 71% lower in newly diagnosed, ā¤3.5 EDSS, and ā¤1 relapse subgroups, respectively. Overall, 88% of patients were relapse-free 12 months after DMF initiation (84%, newly diagnosed; 88%, ā¤3.5 EDSS; 88%, ā¤1 relapse). PRO measures for fatigue, treatment satisfaction, daily living, and work improved significantly over 12 months of DMF versus baseline.
CONCLUSION:
At 12 months after versus 12 months before DMF initiation, ARR was significantly lower, the majority of patients were relapse-free, and multiple PRO measures showed improvement (overall and for subgroups), suggesting that DMF is effective based on clinical outcomes and from a patient perspective.Clinical trial: A Study Evaluating the Effectiveness of Tecfidera (Dimethyl Fumarate) on Multiple Sclerosis (MS) Disease Activity and Patient-Reported Outcomes (PROTEC), NCT01930708,info:eu-repo/semantics/publishedVersio
Uncertain identification
Uncertainty about the choice of identifying assumptions is common in causal studies, but is often ignored in empirical practice. This paper considers uncertainty over models that impose different identifying assumptions, which can lead to a mix of point- and set- identified models. We propose performing inference in the presence of such uncertainty by generalizing Bayesian model averaging. The method considers multiple posteriors for the set-identified models and combines them with a single posterior for models that are either point-identified or that impose non-dogmatic assumptions. The output is a set of posteriors (post-averaging ambiguous belief ), which can be summarized by reporting the set of posterior means and the associated credible region. We clarify when the prior model probabilities are updated and characterize the asymptotic behavior of the posterior model probabilities. The method provides a formal framework for conducting sensitivity analysis of empirical findings to the choice of identifying assumptions. For example, we find that in a standard monetary model one would need to attach a prior probability greater than 0.28 to the validity of the assumption that prices do not react contemporaneously to a monetary policy shock, in order to obtain a negative response of output to the shock
Uncertain identification
Uncertainty about the choice of identifying assumptions is common in causal studies, but is often ignored in empirical practice. This paper considers uncertainty over models that impose different identifying assumptions, which, in general, leads to a mix of point- and set-identified models. We propose performing inference in the presence of such uncertainty by generalizing Bayesian model averaging. The method considers multiple posteriors for the set-identified models and combines them with a single posterior for models that are either point-identified or that impose non-dogmatic assumptions. The output is a set of posteriors (post-averaging ambiguous belief) that are mixtures of the single posterior and any element of the class of multiple posteriors, with weights equal to the posterior model probabilities. We suggest reporting the range of posterior means and the associated credible region in practice, and provide a simple algorithm to compute them. We establish that the prior model probabilities are updated when the models are "distinguishable" and/or they specify different priors for reduced-form parameters, and characterize the asymptotic behavior of the posterior model probabilities. The method provides a formal framework for conducting sensitivity analysis of empirical findings to the choice of identifying assumptions. In a standard monetary model, for example, we show that, in order to support a negative response of output to a contractionary monetary policy shock, one would need to attach a prior probability greater than 0.32 to the validity of the assumption that prices do not react contemporaneously to such a shock. The method is general and allows for dogmatic and non-dogmatic identifying assumptions, multiple point-identified models, multiple set-identified models, and nested or non-nested models
On the number of limit cycles of the Lienard equation
In this paper, we study a Lienard system of the form dot{x}=y-F(x),
dot{y}=-x, where F(x) is an odd polynomial. We introduce a method that gives a
sequence of algebraic approximations to the equation of each limit cycle of the
system. This sequence seems to converge to the exact equation of each limit
cycle. We obtain also a sequence of polynomials R_n(x) whose roots of odd
multiplicity are related to the number and location of the limit cycles of the
system.Comment: 10 pages, 5 figures. Submitted to Physical Review
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