scholarly journals A Tutorial on Levels of Granularity: From Histograms to Clusters to Predictive Distributions

2018 ◽  
Vol 17 (2) ◽  
pp. 307
Author(s):  
Stanley L. Sclove
Keyword(s):  
Predictive Distributions

scholarly journals Predictive Constructions Based on Measure-Valued Pólya Urn Processes

Mathematics ◽  
2021 ◽  
Vol 9 (22) ◽  
pp. 2845
Author(s):  
Sandra Fortini ◽  
Sonia Petrone ◽  
Hristo Sariev
Keyword(s):  
Polish Space ◽  
Asymptotic Properties ◽  
Transition Kernel ◽  
Urn Model ◽  
Additive Structure ◽  
Predictive Distributions ◽  
Pólya Urn ◽  
Random Weights ◽  
Random Transition ◽  
Polya Urn

Measure-valued Pólya urn processes (MVPP) are Markov chains with an additive structure that serve as an extension of the generalized k-color Pólya urn model towards a continuum of possible colors. We prove that, for any MVPP (μn)n≥0 on a Polish space X, the normalized sequence (μn/μn(X))n≥0 agrees with the marginal predictive distributions of some random process (Xn)n≥1. Moreover, μn=μn−1+RXn, n≥1, where x↦Rx is a random transition kernel on X; thus, if μn−1 represents the contents of an urn, then Xn denotes the color of the ball drawn with distribution μn−1/μn−1(X) and RXn—the subsequent reinforcement. In the case RXn=WnδXn, for some non-negative random weights W1,W2,…, the process (Xn)n≥1 is better understood as a randomly reinforced extension of Blackwell and MacQueen’s Pólya sequence. We study the asymptotic properties of the predictive distributions and the empirical frequencies of (Xn)n≥1 under different assumptions on the weights. We also investigate a generalization of the above models via a randomization of the law of the reinforcement.

Extending Extended Logistic Regression: Extended versus Separate versus Ordered versus Censored

2014 ◽  
Vol 142 (8) ◽  
pp. 3003-3014 ◽  
Author(s):  
Jakob W. Messner ◽  
Georg J. Mayr ◽  
Daniel S. Wilks ◽  
Achim Zeileis
Keyword(s):  
Logistic Regression ◽  
Probability Distribution ◽  
Calibration Method ◽  
Logistic Distribution ◽  
Censored Regression ◽  
Ensemble Forecasts ◽  
Predictive Distributions ◽  
Logistic Regression Models ◽  
Weather Forecasts ◽  
Ordered Logistic Regression

Abstract Extended logistic regression is a recent ensemble calibration method that extends logistic regression to provide full continuous probability distribution forecasts. It assumes conditional logistic distributions for the (transformed) predictand and fits these using selected predictand category probabilities. In this study extended logistic regression is compared to the closely related ordered and censored logistic regression models. Ordered logistic regression avoids the logistic distribution assumption but does not yield full probability distribution forecasts, whereas censored regression directly fits the full conditional predictive distributions. The performance of these and other ensemble postprocessing methods is tested on wind speed and precipitation data from several European locations and ensemble forecasts from the European Centre for Medium-Range Weather Forecasts (ECMWF). Ordered logistic regression performed similarly to extended logistic regression for probability forecasts of discrete categories whereas full predictive distributions were better predicted by censored regression.

Infinite Markov pooling of predictive distributions

2021 ◽  
Author(s):  
Xin Jin ◽  
John M. Maheu ◽  
Qiao Yang
Keyword(s):  
Predictive Distributions

Predictive distributions that mimic frequencies over a restricted subdomain

2020 ◽  
Vol 43 (1) ◽  
pp. 17-41 ◽  
Author(s):  
Frank Lad ◽  
Giuseppe Sanfilippo
Keyword(s):  
Predictive Distributions

scholarly journals Computationally efficient versions of conformal predictive distributions

2020 ◽  
Vol 397 ◽  
pp. 292-308 ◽  
Author(s):  
Vladimir Vovk ◽  
Ivan Petej ◽  
Ilia Nouretdinov ◽  
Valery Manokhin ◽  
Alexander Gammerman
Keyword(s):  
Computationally Efficient ◽  
Predictive Distributions

APPLICATIONS OF LIKELIHOOD RATIO ORDER IN BAYESIAN INFERENCES

2018 ◽  
Vol 34 (1) ◽  
pp. 1-13 ◽  
Author(s):  
Kai Huang ◽  
Jie Mi
Keyword(s):  
Likelihood Ratio ◽  
Bayes Factor ◽  
Loss Functions ◽  
Posterior Distributions ◽  
Likelihood Ratio Order ◽  
Predictive Distributions ◽  
Sufficient Statistic ◽  
Bayesian Inferences ◽  
Bayesian Estimators ◽  
General Error

The present paper studies the likelihood ratio order of posterior distributions of parameter when the same order exists between the corresponding prior of the parameter, or when the observed values of the sufficient statistic for the parameter differ. The established likelihood order allows one to compare the Bayesian estimators associated with many common and general error loss functions analytically. It can also enable one to compare the Bayes factor in hypothesis testing without using numerical computation. Moreover, using the likelihood ratio (LR) order of the posterior distributions can yield the LR order between marginal predictive distributions, and posterior predictive distributions.

Using predictive distributions to estimate uncertainty in classifying landmine targets

2011 ◽  
Author(s):  
Ryan Close ◽  
Ken Watford ◽  
Taylor Glenn ◽  
Paul Gader ◽  
Joseph Wilson
Keyword(s):  
Predictive Distributions ◽  
Estimate Uncertainty
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