Bayesian nonparametric inference for unimodal and multimodal random probability measures on a finite dimensional Euclidean space is examined. After a short discussion on several concepts of multivatiate unimodality, we introduce and study a new class of nonparametric prior distributions on the subspace of random multivariate multimodal distributions. This class in a way generalizes the very res...

•All have the property that E[θn+1 | θn] = θn. •Called the martingale property •Philosophically desirable because it means that information is preserved as we move down the hierarchy •Theorem (Doob): All non-negative martingale sequences have a limit with probability 1. θn+1 | θn ∼ DP(cθn), θn+1 | θn ∼ BP(cθn), θn+1 | θn ∼ GammaP(cθn), θn+1 | θn ∼ PYP(cθn) Pathological Properties of Deep Bayesi...

A general theorem on asymptotically optimal sequential selection of experiments is presented and applied to a Bayesian classification problem when the parameter space is a finite partially ordered set. The main results include establishing conditions under which the posterior probability of the true state converges to one almost surely, and determining optimal rates of convergence. Properties o...

The problem of incomplete and noisy information in profile reconstruction from neutron reflectometry data is considered. In particular methods of Bayesian statistics in combination with modelling or inverse scattering techniques are considered in order to properly include the required a priori knowledge to obtain quantitatively reliable estimates of the reconstructed profiles. Applying Bayes th...

Improper priors are used frequently, but often formally and without reference to a sound theoretical basis. The present paper demonstrates that Kolmogorov’s (1933) formulation of probability theory admits a minimal generalization which includes improper priors and a general Bayes theorem. The resulting theory is closely related to the theory of conditional probability spaces formulated by Renyi...

The Geometric Theory of Ignorance produces posterior distributions from priors and likelihoods without invoking Bayes Theorem at all. The standard bayesian posteriors minimize the ignorance action with parameters δ = ν = 0 when the truth t is replaced by the empirical distribution of n independent observations. Different values for the parameters produce new ways for processing the data obtaini...

I. Basic Statistical Machinery 1.1 Probabilities, Distributions, and Expectations 1.1 Discrete and Continuous Random Variables 1.1 Joint and Conditional Probabilities 1.2 Bayes’ Theorem 1.2 Expectations of Random Variables 1.3 The Normal Distribution 1.4 Covariances 1.4 The Normal Distribution 1.5 Regressions 1.6 Properties of Least-squares Regressions 1.6 Regressions and Correlations 1.7 Maxim...

Bayesian information geometry provides a general error decomposition theorem for arbitrary statistical models and a family of information deviations that include Kullback-Leibler information as a special case. When applied to Gaussian measures it takes the classical Hilbert space (Sobolev space) theories for estimation (regression, filtering, approximation, smoothing) as a special case. When th...

In this paper, we discuss different predictors of times to failure of units censored in a hybrid censored sample from exponential distribution. Bayesian and non-Bayesian point predictors for the times to failure of units are obtained. Non-Bayesian prediction Intervals are obtained based on pivotal and highest conditional density methods. Bayesian prediction intervals are also proposed. One real...

The conditional commitment abilities of mutually transparent computer agents have been studied in previous work on games and program equilibrium. This literature has shown how these can help resolve Prisoner’s Dilemmas other failures cooperation complete information settings. But inefficiencies due to private neglected thus far this literature, despite the fact that problems are pervasive might...