14 problems

Let the weights of a stick-breaking prior be given by … including, in particular, the Pitman--Yor choice $a_k=1-\sigma$ and $b_k=\alpha+\sigma k$ with $\sigma\in[0,1)$. Suppose the…

Let $P_{\beta}$ be the exchangeable Dirichlet-driven length-variable process, let $P'$ be the geometric process, and let $D_{\theta}(\beta)$ denote the expectation of the Kullback–…

Let $P_{\beta}$ and $P'$ denote the exchangeable stick-breaking process with parameter $\beta$ and the geometric process, respectively, and let $D_{\theta}(\beta)$ denote the expec…

For Bayesian models such as deep Gaussian processes, the paper distinguishes fractional posteriors with likelihood power $\rho<1$ from the ordinary posterior with $\rho=1$. Ordinar…

The paper studies heavy-tailed priors and proves convergence results for fractional posteriors, including results for density estimation and classification. The standard posterior…

Normalizer-only reformulation conjecture. Our assumptions could be almost equivalently restated in terms of the normalizer $Z$ alone.

The noisy pseudo-marginal algorithm is considered for inference in an 11-dimensional posterior arising from a $\Lambda$-coalescent model. The algorithm's trace plot exhibits residu…

The discussion concerns Dirichlet process mixture (DPM) and normalized random measure (NRM) models for Bayesian kernel mixtures, and the posterior distribution is studied for consi…

Consider the priors … and … where $\{\lambda_i\}_{i\ge1}$ is a sequence of positive nondecreasing real numbers. The question concerns empirical- or full-Bayes estimation of the reg…

A Dirichlet process mixture may place a prior on the concentration parameter $\vartheta$, or allow $\vartheta$ to depend on the sample size $n$. Inconsistency conjecture. Inconsist…

Gibbs-type extension conjecture. The same asymptotic regime, up to certain transformations of the limiting random variable, should hold for the wide class of Gibbs-type priors.

Let $\{M_{m}^{(n)},m\geq0\}$ be the Markov chain indexed by the positive integer $n$, and let $M$ denote its limiting distribution. Convergence-rate conjecture. The convergence of…

Suboptimal contraction-rate conjecture. Bayesian posteriors may suffer from suboptimal contraction rates in density estimation problems under the $L^r$-loss when $r>2$.

Let $H_{M,N}$ be the number of clusters of size $M$ in a partition of $N$ observations, and let ${\rm UP}$ denote the uniform process with parameter $\theta$. Uniform-process clust…