The coincidence of measure algebras under an exchangeable probability

Richard A. Olshen

doi:10.1007/bf00569185

The coincidence of measure algebras under an exchangeable probability

Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete ◽

10.1007/bf00569185 ◽

1971 ◽

Vol 18 (2) ◽

pp. 153-158 ◽

Cited By ~ 4

Author(s):

Richard A. Olshen

Keyword(s):

Exchangeable Probability

Mean deep coalescence cost under exchangeable probability distributions

Discrete Applied Mathematics ◽

10.1016/j.dam.2014.02.010 ◽

2014 ◽

Vol 174 ◽

pp. 11-26 ◽

Cited By ~ 6

Author(s):

C.V. Than ◽

N.A. Rosenberg

Keyword(s):

Probability Distributions ◽

Deep Coalescence ◽

Exchangeable Probability

On the extendibility of finitely exchangeable probability measures

Transactions of the American Mathematical Society ◽

10.1090/tran/7701 ◽

2018 ◽

Vol 371 (10) ◽

pp. 7067-7092 ◽

Cited By ~ 1

Author(s):

Takis Konstantopoulos ◽

Linglong Yuan

Keyword(s):

Probability Measures ◽

Exchangeable Probability

On Contamination of Symbolic Datasets

10.1101/2020.02.13.947754 ◽

2020 ◽

Author(s):

Antony Pearson ◽

Manuel E. Lladser

Keyword(s):

Dna Sequences ◽

Probability Distributions ◽

Biological Research ◽

Methylation Data ◽

Proof Of Concept ◽

Discrete Sample ◽

Genomic Locations ◽

Methylation Patterns ◽

Exchangeable Probability ◽

Sources Of Contamination

AbstractData taking values on discrete sample spaces are the embodiment of modern biological research. “Omics” experiments produce millions of symbolic outcomes in the form of reads (i.e., DNA sequences of a few dozens to a few hundred nucleotides). Unfortunately, these intrinsically non-numerical datasets are often highly contaminated, and the possible sources of contamination are usually poorly characterized. This contrasts with numerical datasets where Gaussian-type noise is often well-justified. To overcome this hurdle, we introduce the notion of latent weight, which measures the largest expected fraction of samples from a contaminated probabilistic source that conform to a model in a well-structured class of desired models. We examine various properties of latent weights, which we specialize to the class of exchangeable probability distributions. As proof of concept, we analyze DNA methylation data from the 22 human autosome pairs. Contrary to what it is usually assumed, we provide strong evidence that highly specific methylation patterns are overrepresented at some genomic locations when contamination is taken into account.