
The combinatorial structure of beta negative binomial processes
We characterize the combinatorial structure of conditionallyi.i.d. sequ...
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On Some Resampling Procedures with the Empirical Beta Copula
The empirical beta copula is a simple but effective smoother of the empi...
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The StickBreaking Construction of the Beta Process as a Poisson Process
We show that the stickbreaking construction of the beta process due to ...
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Combinatorial clustering and the beta negative binomial process
We develop a Bayesian nonparametric approach to a general family of late...
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Blackbox constructions for exchangeable sequences of random multisets
We develop constructions for exchangeable sequences of point processes t...
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BetaBinomial stickbreaking nonparametric prior
A new class of nonparametric prior distributions, termed BetaBinomial s...
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On the relationship between betaBartlett and Uhlig extended processes
Stochastic volatility processes are used in multivariate timeseries ana...
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The continuumofurns scheme, generalized beta and Indian buffet processes, and hierarchies thereof
We describe the combinatorial stochastic process underlying a sequence of conditionally independent Bernoulli processes with a shared beta process hazard measure. As shown by Thibaux and Jordan [TJ07], in the special case when the underlying beta process has a constant concentration function and a finite and nonatomic mean, the combinatorial structure is that of the Indian buffet process (IBP) introduced by Griffiths and Ghahramani [GG05]. By reinterpreting the beta process introduced by Hjort [Hjo90] as a measurable family of Dirichlet processes, we obtain a simple predictive rule for the general case, which can be thought of as a continuum of BlackwellMacQueen urn schemes (or equivalently, oneparameter Hoppe urn schemes). The corresponding measurable family of PermanPitmanYor processes leads to a continuum of twoparameter Hoppe urn schemes, whose ordinary component is the threeparameter IBP introduced by Teh and Görür [TG09], which exhibits powerlaw behavior, as further studied by Broderick, Jordan, and Pitman [BJP12]. The idea extends to arbitrary measurable families of exchangeable partition probability functions and gives rise to generalizations of the beta process with matching buffet processes. Finally, in the same way that hierarchies of Dirichlet processes were given Chinese restaurant franchise representations by Teh, Jordan, Beal, and Blei [Teh+06], one can construct representations of sequences of Bernoulli processes directed by hierarchies of beta processes (and their generalizations) using the stochastic process we uncover.
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