Logistic Normal Distribution

The usual candidate distributions for modeling compositions, the Dirichlet and the logistic normal distribution, do not include zero components in their support. Methods have been developed and refined for dealing with zeros that are rounded, or due to a value being below a detection level. Methods have also been developed for zeros in compositions arising from count data. However, essential zeros, cases where a component is truly absent, in continuous compositions are still a problem.The most promising approach is based on extending the logistic normal distribution to model essential zeros using a mixture of additive logistic normal distributions of different dimension, related by common parameters. We continue this approach, and by imposing an additional constraint, develop a likelihood, and show ways of estimating parameters for location and dispersion. The proposed likelihood, conditional on parameters for the probability of zeros, is a mixture of additive logistic normal distributions of different dimensions whose location and dispersion parameters are projections of a common location or dispersion parameter. For some simple special cases, we contrast the relative efficiency of different location estimators.

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A probabilistic assessment of the Indo-Aryan Inner–Outer Hypothesis

Journal of Historical Linguistics ◽

10.1075/jhl.18038.cat ◽

2020 ◽

Vol 10 (1) ◽

pp. 42-86

Author(s):

Chundra A. Cathcart

Keyword(s):

Natural Language Processing ◽

Normal Distribution ◽

Language Processing ◽

Probabilistic Approach ◽

Large Data ◽

Data Driven ◽

Probabilistic Assessment ◽

Data Set ◽

Bayesian Hierarchical ◽

Logistic Normal Distribution

Abstract This paper uses a novel data-driven probabilistic approach to address the century-old Inner-Outer hypothesis of Indo-Aryan. I develop a Bayesian hierarchical mixed-membership model to assess the validity of this hypothesis using a large data set of automatically extracted sound changes operating between Old Indo-Aryan and Modern Indo-Aryan speech varieties. I employ different prior distributions in order to model sound change, one of which, the Logistic Normal distribution, has not received much attention in linguistics outside of Natural Language Processing, despite its many attractive features. I find evidence for cohesive dialect groups that have made their imprint on contemporary Indo-Aryan languages, and find that when a Logistic Normal prior is used, the distribution of dialect components across languages is largely compatible with a core-periphery pattern similar to that proposed under the Inner-Outer hypothesis.

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