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Wright–Fisher 隐马尔可夫模型中预测与平滑的渐近性质及有限样本界AI 解读

We study prediction and smoothing in hidden Markov models with a latent signal given by a multi-type Wright-Fisher diffusion and discrete-time categorical observations, motivated by repeated-sampling time-series settings, including temporally binned ancient-DNA data, in which noisy frequency counts are recorded at finitely many times. Our focus is on the exact Bayesian predictive and smoothing distributions available under parent-independent mutation, in relation to their…

高维概率单位回归中数据增强 Gibbs 抽样的混合时间AI 解读

We investigate the convergence properties of popular data-augmentation samplers for Baye\-sian probit regression. Leveraging recent results on Gibbs samplers for log-concave targets, we provide simple and explicit non-asymptotic bounds on the associated mixing times (in Kullback-Leibler divergence). The bounds depend explicitly on the design matrix and the prior precision, while they hold uniformly over the vector of responses. We specialize the results for different regimes…

We study general coordinate-wise MCMC schemes (such as Metropolis-within-Gibbs samplers), which are commonly used to fit Bayesian non-conjugate hierarchical models. We relate their convergence properties to the ones of the corresponding (potentially not implementable) Gibbs sampler through the notion of conditional conductance. This allows us to study the performances of popular Metropolis-within-Gibbs schemes for non-conjugate hierarchical models, in high-dimensional…