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Conjugate Exponential Family Priors For Exponential Family Likelihoods
Statistics, 1993General classes of conjugate exponential family priors are identified for exponential family likelihoods. Both joint and conditional specification of the priors are discussed. The normal and inverse Gaussian cases provide illustrations.
Barry C. Arnold +2 more
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‘Exponential mixtures and quadratic exponential families’
Biometrika, 1994Correlated responses are common in many fields of application such as time series, spatial statistics and longitudinal studies. In medical statistics and in epidemiological studies, correlation can arise because of cluster sampling. Individuals in a cluster have in common unobserved traits, either genetic or environmental, as a result of which their ...
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Family of Exponentiated Exponential Distribution
2015As was mentioned, in Chap. 1, that Gompertz (1825) raised the extreme value distribution to a positive parameter. Verhulst (1847) introduced the following CDF of a random variable X.
Essam K. AL-Hussaini +1 more
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Stability for Multivariate Exponential Families
Journal of Mathematical Sciences, 2001Let \(E\) be a Euclidean space, let \(Z :\Omega\to E\) be a nondegenerate random vector, and suppose there is an open convex set \(D\subset E\) such that \(P(Z\in \overline{D}) = 1\). If \(\mu\) is the distribution of \(Z\), define measures \(\mu_\lambda\) by \(d\mu_\lambda(x) = e^{\lambda x}d\mu(x)\), \(x\in E\), for any \(\lambda\) in the dual space \
Balkema, A. A. +2 more
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Registration for Exponential Family Functional Data
Biometrics, 2018Summary We introduce a novel method for separating amplitude and phase variability in exponential family functional data. Our method alternates between two steps: the first uses generalized functional principal components analysis to calculate template functions, and the second estimates smooth warping functions that map observed curves ...
Julia Wrobel +3 more
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2009
Curved exponential families may arise when the parameters of an exponential family satisfy constraints. For these families the minimal sufficient statistic may not be complete, and UMVU estimation may not be possible. Curved exponential families arise naturally with data from sequential experiments, considered in Section 5.2, and Section 5.3 considers ...
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Curved exponential families may arise when the parameters of an exponential family satisfy constraints. For these families the minimal sufficient statistic may not be complete, and UMVU estimation may not be possible. Curved exponential families arise naturally with data from sequential experiments, considered in Section 5.2, and Section 5.3 considers ...
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Nonlinear exponential families
1993The nonlinear regression model $$\begin{array}{*{20}{c}} {y = \eta \left( \vartheta \right) + \varepsilon ;\quad \left( {\vartheta \in \Theta } \right),} \\ {\varepsilon \sim N\left( {0,{{\sigma }^{2}}W} \right)} \\ \end{array}$$ considered in previous chapters, can be presented equivalently as a family of densities $$\left\{ {f(y\left ...
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Information Property of Exponential Families
Theory of Probability & Its Applications, 1986See the review in Zbl 0582.60022.
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Exponential Families and Game Dynamics
Canadian Journal of Mathematics, 1982A symmetric game consists of a set of pure strategies indexed by {0, …, n} and a real payoff matrix (aij). When two players choose strategies i and j the payoffs are aij and aji to the i-player and j-player respectively. In classical game theory of Von Neumann and Morgenstern [16] the payoffs are measured in units of utility, i.e., desirability, or in
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2012
Exponential families of distributions are parametric dominated families in which the logarithm of probability densities take a simple bilinear form (bilinear in the parameter and a statistic). As a consequence of that special form, sampling models in those families admit a finite-dimensional sufficient statistic irrespective of the sample size, and ...
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Exponential families of distributions are parametric dominated families in which the logarithm of probability densities take a simple bilinear form (bilinear in the parameter and a statistic). As a consequence of that special form, sampling models in those families admit a finite-dimensional sufficient statistic irrespective of the sample size, and ...
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