scholarly journals Deriving frequency effects from biases in learning

2021 ◽  
Vol 6 (1) ◽  
pp. 514
Author(s):  
Maggie Baird
Keyword(s):  
Bayesian Inference ◽  
Maximum Entropy ◽  
Frequency Effects ◽  
Reduction Processes ◽  
Frequent Items ◽  
Surface Patterns

This paper presents a phonological learner that derives frequency effects – the propensity of more frequent items undergo deletion and reduction processes at higher rates. The model is a bidirectional Maximum Entropy grammar which has two distinct learning steps, one mapping from UR to SR, and another mapping back from SR to UR using Bayesian inference. The model is tested on the case of t/d deletion in English and correctly derives the frequency-based pattern of deletion without access to surface patterns. 

Wordform-specific frequency effects cause acoustic variation in zero-inflected homophones

2020 ◽  
Vol 56 (4) ◽  
pp. 711-739
Author(s):  
Eva Maria Luef ◽  
Jong-Seung Sun
Keyword(s):  
Lexical Access ◽  
High Frequency ◽  
Relative Frequency ◽  
Frequency Effects ◽  
Reduction Processes ◽  
Specific Frequency ◽  
Phonetic Reduction ◽  
Acoustic Variation

Abstract The frequency with which a word appears in the lexicon has implications for its pronunciation. Numerous studies have shown that high-frequency lemma are characterized by more phonetic reduction than lower-frequency lemma. These findings have proven to be particularly useful in the study of homophones where frequency-related reduction processes can give insights into lexical access theories. The majority of research on homophones and frequency effects has focused on heterographic and semantically unrelated homophones (e.g., English time – thyme) or investigated zero-derived homophones (e.g., English the cut, noun – to cut, verb). Here, zero inflection in German pluralization (e.g., ein Würfel ‘one die’– zwei Würfel ‘two dice’) was investigated to determine if and how frequency effects impact on the acoustic realization of the homophonous singular-plural word pairs. The findings indicate that the number-specified wordforms show acoustic variation related to wordform frequency and the relative frequency of the singular to plural inflected forms. Results differ for durations of wordforms, stem vowels, and final phonemes. Our findings have implications for lexical access theories and can inform about ‘frequency inheritance’ across the singular and plural homophones of the zero-inflected plurals.

BAYESIAN INFERENCE, PRIOR INFORMATION ON VOLATILITY, AND OPTION PRICING: A MAXIMUM ENTROPY APPROACH

2005 ◽  
Vol 08 (01) ◽  
pp. 1-12 ◽  
Author(s):  
FRANCISCO VENEGAS-MARTÍNEZ
Keyword(s):  
Bayesian Inference ◽  
Option Pricing ◽  
Maximum Entropy ◽  
Bayesian Model ◽  
Prior Information ◽  
Bessel Functions ◽  
Derivative Securities ◽  
Expected Values ◽  
Pricing Derivative Securities ◽  
Approximate Formulas

This paper develops a Bayesian model for pricing derivative securities with prior information on volatility. Prior information is given in terms of expected values of levels and rates of precision: the inverse of variance. We provide several approximate formulas, for valuing European call options, on the basis of asymptotic and polynomial approximations of Bessel functions.

Preface: Bayesian Inference and Maximum Entropy Methods in Science and Engineering

2014 ◽  
Author(s):  
Robert K. Niven ◽  
Brendon Brewer ◽  
David Paull ◽  
Kamran Shafi ◽  
Barrie Stokes
Keyword(s):  
Bayesian Inference ◽  
Maximum Entropy ◽  
Science And Engineering ◽  
Entropy Methods

scholarly journals Bayesian Inference in Auditing With Partial Prior Information Using Maximum Entropy Priors

Entropy ◽  
2018 ◽  
Vol 20 (12) ◽  
pp. 919
Author(s):  
María Martel-Escobar ◽  
Francisco-José Vázquez-Polo ◽  
Agustín Hernández-Bastida 
Keyword(s):  
Bayesian Inference ◽  
Bayesian Analysis ◽  
Maximum Entropy ◽  
Prior Information ◽  
Likelihood Function ◽  
Bayes Theorem ◽  
Main Interest ◽  
Book Value ◽  
Numerical Examples ◽  
Modified Likelihood

Problems in statistical auditing are usually one–sided. In fact, the main interest for auditors is to determine the quantiles of the total amount of error, and then to compare these quantiles with a given materiality fixed by the auditor, so that the accounting statement can be accepted or rejected. Dollar unit sampling (DUS) is a useful procedure to collect sample information, whereby items are chosen with a probability proportional to book amounts and in which the relevant error amount distribution is the distribution of the taints weighted by the book value. The likelihood induced by DUS refers to a 201–variate parameter p but the prior information is in a subparameter θ linear function of p , representing the total amount of error. This means that partial prior information must be processed. In this paper, two main proposals are made: (1) to modify the likelihood, to make it compatible with prior information and thus obtain a Bayesian analysis for hypotheses to be tested; (2) to use a maximum entropy prior to incorporate limited auditor information. To achieve these goals, we obtain a modified likelihood function inspired by the induced likelihood described by Zehna (1966) and then adapt the Bayes’ theorem to this likelihood in order to derive a posterior distribution for θ . This approach shows that the DUS methodology can be justified as a natural method of processing partial prior information in auditing and that a Bayesian analysis can be performed even when prior information is only available for a subparameter of the model. Finally, some numerical examples are presented.

scholarly journals A Measure of Uncertainty regarding the Interval Constraint of Normal Mean Elicited by Two Stages of a Prior Hierarchy

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Hea-Jung Kim
Keyword(s):  
Bayesian Inference ◽  
Maximum Entropy ◽  
Gaussian Model ◽  
Objective Measure ◽  
Estimation Procedure ◽  
Uncertainty Measure ◽  
Normal Mean ◽  
Two Stages ◽  
The Relationship ◽  
Interval Constraint

This paper considers ahierarchical screened Gaussian model(HSGM) for Bayesian inference of normal models when an interval constraint in the mean parameter space needs to be incorporated in the modeling but when such a restriction is uncertain. An objective measure of the uncertainty, regarding the interval constraint, accounted for by using the HSGM is proposed for the Bayesian inference. For this purpose, we drive a maximum entropy prior of the normal mean, eliciting the uncertainty regarding the interval constraint, and then obtain the uncertainty measure by considering the relationship between the maximum entropy prior and the marginal prior of the normal mean in HSGM. Bayesian estimation procedure of HSGM is developed and two numerical illustrations pertaining to the properties of the uncertainty measure are provided.

scholarly journals Maximum Entropy and Bayesian Inference for the Monty Hall Problem

2016 ◽  
Vol 04 (07) ◽  
pp. 1222-1230
Author(s):  
Jennifer L. Wang ◽  
Tina Tran ◽  
Fisseha Abebe
Keyword(s):  
Bayesian Inference ◽  
Maximum Entropy ◽  
Monty Hall ◽  
Monty Hall Problem

scholarly journals Bayesian Inference and Maximum Entropy Methods in Science and Engineering—MaxEnt 2019†

Proceedings ◽  
2019 ◽  
Vol 33 (1) ◽  
pp. 8
Author(s):  
Udo von Toussaint ◽  
Roland Preuss
Keyword(s):  
Parameter Estimation ◽  
Bayesian Inference ◽  
Data Processing ◽  
Maximum Entropy ◽  
Density Estimation ◽  
Model Comparison ◽  
Building Blocks ◽  
Research Area ◽  
Science And Engineering ◽  
Entropy Methods

As key building blocks for modern data processing and analysis methods—ranging from AI, ML and UQ to model comparison, density estimation and parameter estimation—Bayesian inference and entropic concepts are in the center of this rapidly growing research area. [...]

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