By expressing prior distributions as general stochastic processes, nonparametric Bayesian methods provide a flexible way to incorporate prior knowledge and constrain the latent structure in statistical inference. The Indian buffet process (IBP) is such an example that can be used to define a prior distribution on infinite binary features, where the exchangeability among subjects is assumed. The...

We study the stochastic system of interacting neurons introduced in [5] and [10] a diffusive scaling. The consists N neurons, each spiking randomly with rate depending on its membrane potential. At time, potential neuron is reset to 0 all other receive an additional amount which centred random variable order 1? N. In between successive spikes, neuron’s follows deterministic flow. prove converge...

Given a sample from a finite population, we provide a nonparametric Bayesian prediction interval for a finite population mean when a standard normal assumption may be tenuous. We will do so using a Dirichlet process (DP), a nonparametric Bayesian procedure which is currently receiving much attention. An asymptotic Bayesian prediction interval is well known but it does not incorporate all the fe...

Abstract Richard Jeffrey’s “Conditioning, Kinematics, and Exchangeability” is one of the foundational documents probability kinematics. However, section entitled “Successive Updating” contains a subtle error regarding applicability updating by so-called relevance quotients in order to ensure commutativity successive kinematical revisions. Upon becoming aware this error, Jeffrey formulated appro...

We present estimators for panel data sample selection and switching models where the regression equations are dynamic and it is allowed for the existence of endogenous regressors and correlated individual unobserved heterogeneity. We consider two types of switching models under the names of observed dynamics switching and latent dynamics switching. The dynamic sample selection model implicitly ...

A sufficient condition is given for a probability function in Inductive Logic (with relations of all arities) satisfying spectrum exchangeability to additionally satisfy Language Invariance. This condition is shown to also be necessary in the case of homogeneous probability functions.

Several Turing-complete probabilistic programming languages such as Church, Venture and Anglican support so-called exchangeable random processes (XRPs) as built-in abstract data types. Instances of these data types denote infinite sequences of random values. Every such object satisfies the so-called exchangeability property, which says that the probability distribution of the object does not ch...

Statistical methods for network data often parameterize the edge-probability by attributing latent traits such as block structure to the vertices and assume exchangeability in the sense of the Aldous-Hoover representation theorem. These assumptions are however incompatible with traits found in real-world networks such as a power-law degree-distribution. Recently, Caron & Fox (2014) proposed the...