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发现新类别的条件概率预测AI 解读

Consider a population comprising disjoint classes. An important problem arising from various fields is prediction of the random conditional probability of discovering a new class. The asymptotic normality of the discovery probability is established in a Poisson model, where the number of individuals from each class is a Poisson process with a class-specific rate. A new derivation is presented for the well-known Good–Toulmin predictor as a moment-based estimator for the…

使用渐近众数的全指数拉普拉斯近似AI 解读

Posterior means of positive functions can be expressed as the ratio of integrals which is called fully exponential form. When approximating the posterior means analytically, we usually use Laplace's method. Tierney and Kadane presented a second-order approximation by using the Laplace approximations in each of the numerator and denominator of the fully exponential form. However, Laplace's method requires the exact mode of the integrand. In this article we introduce the…

平滑样条非线性非参数回归模型AI 解读

Almost all of the current nonparametric regression methods, such as smoothing splines, generalized additive models, and varyingcoefficients models, assume a linear relationship when nonparametric functions are regarded as parameters. In this article we propose a general class of smoothing spline nonlinear nonparametric models that allow nonparametric functions to act nonlinearly. They arise in many fields as either theoretical or empirical models. Our new estimation methods…

时间序列谱密度的贝叶斯估计AI 解读

This article describes a Bayesian approach to estimating the spectral density of a stationary time series. A nonparametric prior on the spectral density is described through Bernstein polynomials. Because the actual likelihood is very complicated, a pseudoposterior distribution is obtained by updating the prior using the Whittle likelihood. A Markov chain Monte Carlo algorithm for sampling from this posterior distribution is described that is used for computing the posterior…

使用复数小波的实值非参数回归AI 解读

Summary Wavelet shrinkage is an effective nonparametric regression technique, especially when the underlying curve has irregular features such as spikes or discontinuities. The basic idea is simple: take the discrete wavelet transform of data consisting of a signal corrupted by noise; shrink or remove the wavelet coefficients to remove the noise; then invert the discrete wavelet transform to form an estimate of the true underlying curve. Various researchers have proposed…

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随机前沿模型的半参数贝叶斯推断AI 解读

In this paper we propose a semiparametric Bayesian framework for the analysis of stochastic frontiers and efficiency measurement. The distribution of inefficiencies is modelled nonparametrically through a Dirichlet process prior. We suggest prior distributions and implement a Bayesian analysis through an efficient Markov chain Monte Carlo sampler, which allows us to deal with practically relevant sample sizes. We also allow for the efficiency distribution to vary with firm…

认识教育回报的异质性AI 解读

Abstract Using data from the National Longitudinal Survey of Youth (NLSY) we introduce and estimate various Bayesian hierarchical models that investigate the nature of unobserved heterogeneity in returns to schooling. We consider a variety of possible forms for the heterogeneity, some motivated by previous theoretical and empirical work and some new ones, and let the data decide among the competing specifications. Empirical results indicate that heterogeneity is present in…

隐马尔可夫模型中最优变点检测的渐近运行特性AI 解读

Let ξ0,ξ1,…,ξω−1 be observations from the hidden Markov model with probability distribution Pθ0, and let ξω,ξω+1,… be observations from the hidden Markov model with probability distribution Pθ1. The parameters θ0 and θ1 are given, while the change point ω is unknown. The problem is to raise an alarm as soon as possible after the distribution changes from Pθ0 to Pθ1, but to avoid false alarms. Specifically, we seek a stopping rule N which allows us to observe the ξ's…

有限混合模型成分数的后验分布AI 解读

The posterior distribution of the number of components k in a finite mixture satisfies a set of inequality constraints. The result holds irrespective of the parametric form of the mixture components and under assumptions on the prior distribution weaker than those routinely made in the literature on Bayesian analysis of finite mixtures. The inequality constraints can be used to perform an “internal” consistency check of MCMC estimates of the posterior distribution of k and…

贝叶斯一致性的新方法AI 解读

We use martingales to study Bayesian consistency. We derive sufficient conditions for both Hellinger and Kullback–Leibler consistency, which do not rely on the use of a sieve. Alternative sufficient conditions for Hellinger consistency are also found and demonstrated on examples.

区间数据条件估值模型与定价政策的贝叶斯分析AI 解读

The general aim of a contingent valuation survey is to elicit the willingness to pay (WTP) of respondents for some (public) commodity without a clear market price. This could be a program to protect some environmental resource or, as in our application, the access to a recreational area of particular interest. In this context, we want to accommodate the possibility of zero WTP and we need to deal with the fact that observations arise as intervals for WTP, rather than point…

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后验模拟器的正确性检验AI 解读

Analytical or coding errors in posterior simulators can produce reasonable but incorrect approximations of posterior moments. This article develops simple tests of posterior simulators that detect both kinds of errors, and uses them to detect and correct errors in two previously published articles. The tests exploit the fact that a Bayesian model specifies the joint distribution of observables (data) and unobservables (parameters). There are two joint distribution…

We consider regression when the predictor is measured with error and an instrumental variable (IV) is available. The regression function can be modeled linearly, nonlinearly, or nonparametrically. Our major new result shows that the regression function and all parameters in the measurement error model are identified under relatively weak conditions, much weaker than previously known to imply identifiability. In addition, we exploit a characterization of the IV estimator as a…

通过非齐次马尔可夫链模拟实现最优贝叶斯设计AI 解读

We consider decision problems defined by a utility function and an underlying probability model for all unknowns. The utility function quantifies the decision maker's preferences over consequences. The optimal decision maximizes the expected utility function where the expectation is taken with respect to all unknowns, that is, future data and parameters. In many problems, the solution is not analytically tractable. For example, the utility function might involve moments that…

潜在广义 ARCH 结构的似然估计AI 解读

GARCH models are commonly used as latent processes in econometrics, financial economics, and macroeconomics. Yet no exact likelihood analysis of these models has been provided so far. In this paper we outline the issues and suggest a Markov chain Monte Carlo algorithm which allows the calculation of a classical estimator via the simulated EM algorithm or a Bayesian solution in O(T) computational operations, where T denotes the sample size. We assess the performance of our…