اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدBayesian Inference of Local Projections with Roughness Penalty Priors
63
0
0.0
(
0
)
تأليف
Masahiro Tanaka
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
A local projection is a statistical framework that accounts for the relationship between an exogenous variable and an endogenous variable, measured at different time points. Local projections are often applied in impulse response analyses and direct forecasting. While local projections are becoming increasingly popular because of their robustness to misspecification and their flexibility, they are less statistically efficient than standard methods, such as vector autoregression. In this study, we seek to improve the statistical efficiency of local projections by developing a fully Bayesian approach that can be used to estimate local projections using roughness penalty priors. By incorporating such prior-induced smoothness, we can use information contained in successive observations to enhance the statistical efficiency of an inference. We apply the proposed approach to an analysis of monetary policy in the United States, showing that the roughness penalty priors successfully estimate the impulse response functions and improve the predictive accuracy of local projections.
قيم البحث
اقرأ أيضاً
In this paper, we consider Bayesian variable selection problem of linear regression model with global-local shrinkage priors on the regression coefficients. We propose a variable selection procedure that select a variable if the ratio of the posterio
r mean to the ordinary least square estimate of the corresponding coefficient is greater than $1/2$. Under the assumption of orthogonal designs, we show that if the local parameters have polynomial-tailed priors, our proposed method enjoys the oracle property in the sense that it can achieve variable selection consistency and optimal estimation rate at the same time. However, if, instead, an exponential-tailed prior is used for the local parameters, the proposed method does not have the oracle property.
Bayesian approaches are appealing for constrained inference problems in allowing a probabilistic characterization of uncertainty, while providing a computational machinery for incorporating complex constraints in hierarchical models. However, the usu
al Bayesian strategy of placing a prior on the constrained space and conducting posterior computation with Markov chain Monte Carlo algorithms is often intractable. An alternative is to conduct inference for a less constrained posterior and project samples to the constrained space through a minimal distance mapping. We formalize and provide a unifying framework for such posterior projections. For theoretical tractability, we initially focus on constrained parameter spaces corresponding to closed and convex subsets of the original space. We then consider non-convex Stiefel manifolds. We provide a general formulation of the projected posterior and show that it can be viewed as an update of a data-dependent prior with the likelihood for particular classes of priors and likelihood functions. We also show that asymptotic properties of the unconstrained posterior are transferred to the projected posterior. Posterior projections are illustrated through multiple examples, both in simulation studies and real data applications.
This paper presents objective priors for robust Bayesian estimation against outliers based on divergences. The minimum $gamma$-divergence estimator is well-known to work well estimation against heavy contamination. The robust Bayesian methods by usin
g quasi-posterior distributions based on divergences have been also proposed in recent years. In objective Bayesian framework, the selection of default prior distributions under such quasi-posterior distributions is an important problem. In this study, we provide some properties of reference and moment matching priors under the quasi-posterior distribution based on the $gamma$-divergence. In particular, we show that the proposed priors are approximately robust under the condition on the contamination distribution without assuming any conditions on the contamination ratio. Some simulation studies are also presented.
There is a wide range of applications where the local extrema of a function are the key quantity of interest. However, there is surprisingly little work on methods to infer local extrema with uncertainty quantification in the presence of noise. By vi
ewing the function as an infinite-dimensional nuisance parameter, a semiparametric formulation of this problem poses daunting challenges, both methodologically and theoretically, as (i) the number of local extrema may be unknown, and (ii) the induced shape constraints associated with local extrema are highly irregular. In this article, we address these challenges by suggesting an encompassing strategy that eliminates the need to specify the number of local extrema, which leads to a remarkably simple, fast semiparametric Bayesian approach for inference on local extrema. We provide closed-form characterization of the posterior distribution and study its large sample behaviors under this encompassing regime. We show a multi-modal Bernstein-von Mises phenomenon in which the posterior measure converges to a mixture of Gaussians with the number of components matching the underlying truth, leading to posterior exploration that accounts for multi-modality. We illustrate the method through simulations and a real data application to event-related potential analysis.
In this paper, we introduce a new methodology for Bayesian variable selection in linear regression that is independent of the traditional indicator method. A diagonal matrix $mathbf{G}$ is introduced to the prior of the coefficient vector $boldsymbol
{beta}$, with each of the $g_j$s, bounded between $0$ and $1$, on the diagonal serves as a stabilizer of the corresponding $beta_j$. Mathematically, a promising variable has a $g_j$ value that is close to $0$, whereas the value of $g_j$ corresponding to an unpromising variable is close to $1$. This property is proven in this paper under orthogonality together with other asymptotic properties. Computationally, the sample path of each $g_j$ is obtained through Metropolis-within-Gibbs sampling method. Also, in this paper we give two simulations to verify the capability of this methodology in variable selection.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
