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统计稀疏性AI 解读

The main contribution of this paper is a mathematical definition of statistical sparsity, which is expressed as a limiting property of a sequence of probability distributions. The limit is characterized by an exceedance measure |$H$| and a rate parameter |$\rho > 0$|⁠, both of which are unrelated to sample size. The definition encompasses all sparsity models that have been suggested in the signal-detection literature. Sparsity implies that |$\rho$| is small, and a sparse…

具有状态依赖方差的非线性状态空间模型AI 解读

Nonlinear state-space models with state-dependent variances (SDVs) are commonly used in financial time series. Important examples include stochastic volatility (SV) and affine term structure models. We propose a methodology for state smoothing in this class of models. Our smoothing technique is simulation based and uses an auxiliary mixture model. Key features of the auxiliary mixture model are the use of state-dependent weights and efficient block sampling algorithms to…

随机波动率模型的贝叶斯分析AI 解读

New techniques for the analysis of stochastic volatility models in which the logarithm of conditional variance follows an autoregressive model are developed. A cyclic Metropolis algorithm is used to construct a Markov-chain simulation tool. Simulations from this Markov chain coverage in distribution to draws from the posterior distribution enabling exact finite-sample inference. The exact solution to the filtering/smoothing problem of inferring about the unobserved variance…