Combining the arts with science and technology has had many beneficial results. Computers and music have been connected for many years. Computers have been used in music composition, electronic keyboards, music publishing and digital sound processing. Artificial intelligence has been used in creating expert systems for training people in various fields. An attempt will be made to tie together expert systems for training with current computerized music technology.
This research report proposes that an expert system be developed to teach piano lessons. The fields of music and artificial intelligence will be drawn upon in developing this expert system structure. While existing technology makes the choice of an electronic keyboard the logical one, using an acoustic piano will also be addressed

Chew, Carol

English

In this dissertation we advocate the use of Bayes factors in empirical research to replace or complement standard null hypothesis tests based on p-values. These Bayes factors were specifically designed to quantify the evidence for or against the existence of an effect. This was done by comparing two models with the same distributional assumptions, where the alternative model is an extension of the null model by incorporating one extra parameter. Instead of returning a decision to “reject” or “not reject”, a Bayes factor BF10(d) returns a non-negative number that represents the evidence provided by the observed data d for the model that includes the effect. The returned number can be seen as a refinement of the binary decision with BF10(d) = ∞ and BF10(d) = 0 corresponding to definite rejection and acceptance of the null, respectively. Moreover, the Bayes factor allows its users to forgo the binary decision and acknowledge uncertainty, so that the evidence can be updated continually in light of new data, directly and easily. For empirical scientists to be able to use these Bayes factors, we implemented them in Jeffreys’s Amazing Statistics Program, JASP, which is freely available and open-source (url: https://jasp-stats.org)

Ly, A.

NARCIS 

Bayes factors for research workers

Ly, A. (Alexander)

CWI's Institutional Repository

Ly, Alexander

University of Central Florida (UCF): STARS (Showcase of Text, Archives, Research & Scholarship)

The Creation of an Expert System for Teaching Piano Lessons

International Migration, Integration and Social Cohesion online publications

UvA-DARE is a service provided by the library of the University of Amsterdam (https://dare.uva.nl)UvA-DARE (Digital Academic Repository)Bayes factors for research workersLy, A.Publication date2018Document VersionOther versionLicenseOtherLink to publicationCitation for published version (APA):Ly, A. (2018). Bayes factors for research workers.General rightsIt is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s)and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an opencontent license (like Creative Commons).Disclaimer/Complaints regulationsIf you believe that digital publication of certain material infringes any of your rights or (privacy) interests, pleaselet the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the materialinaccessible and/or remove it from the website. Please Ask the Library: https://uba.uva.nl/en/contact, or a letterto: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. Youwill be contacted as soon as possible.Download date:11 Nov 2022Chapter 14Discussion and Future DirectionsIn this dissertation we advocate the use of Bayes factors in empirical research toreplace or complement standard null hypothesis tests based on p-values. TheseBayes factors were specifically designed to quantify the evidence for or against theexistence of an e↵ect. This was done by comparing two models with the samedistributional assumptions, where the alternative model is an extension of the nullmodel by incorporating one extra parameter. Furthermore, instead of returning adecision to “reject” or “not reject”, a Bayes factor BF10(d) returns a non-negativenumber that represents the evidence within the observed data for the model thatincludes the e↵ect. The returned number can be seen as a refinement of the binarydecision with BF10(d) = 1 and BF10(d) = 0 corresponding to definite rejectionand acceptance of the null, respectively. Moreover, the Bayes factor allows its usersto forgo the binary decision and acknowledge uncertainty, so that the evidencecan be updated continually in light of new data, directly and easily. For empiricalscientists to be able to use these Bayes factors we implemented them in Je↵reys’sAmazing Statistics Program, JASP, which is freely available and open-source (url:https://jasp-stats.org).In Chapter 8 we showed how easy it is do a Bayesian reanalysis of publishedresults in JASP. Most of the discussion centred on how Bayes factors quantifyevidence from data already observed, but future research should also focus onhow the already observed data can be used for follow-up experiments. This ideaof generalising past observations to future data underlies the replication Bayesfactor discussed in Chapter 9. Comprehensive knowledge updating requires thatthe data come from the same population, which is why we emphasised the roleof openness and transparency in Chapter 7. By making research materials anddata available, future researchers can then conduct a direct replication and buildupon previous work. In some cases, however, a replication on the same populationis not possible. For correlation and t-test Bayes factors we can nonetheless domeaningful inference by relocating the data, while for more complicated settingssuch as ANOVAs and contingency tables this is still work in progress.When no previous data are available we recommend the use of default Je↵reys’sBayes factors that are constructed from priors that adhere to the general criteria26714. Discussion and Future Directionsfor Bayesian model choice (Bayarri et al., 2012). One goal of this dissertationwas to explain, apply, and extend these general criteria to scenarios common toempirical scientists. The first extension was to Pearson’s correlation, Chapter 2,resulting in an analytic Bayes factor, which was further extended to Kendall’s ⌧in Chapter 4. By modelling the test statistic, more specifically, approximatingthe sampling distribution of the test statistic with its asymptotic normal equiv-alent, a Bayes factor was derived that leads to interpretable results and is fastto compute. In future research we plan to apply the general procedure based onthe asymptotic normal approximation and parametric yoking to other scenarios.The use of the normal approximation to the true sampling distribution, however,is not as principled as we wanted it to be and led to Bayes factors that provideless evidence for the alternative, whenever ⌧ is far from zero. This motivated usto consider di↵erent approaches and the latent normal approach in van Doornet al. (2017) in particular. Future research should further explore the relationshipbetween Kendall’s ⌧ and certain copula families as this will provide insights instatistical research on dependency.The calculations used for the analytic posteriors for Pearson’s ⇢ also led to theinformed t-test in Chapter 5. This work can easily be adapted to linear regressionand is worth exploring further.The first analytic result of Chapter 11 was used to construct a limit-consistentBayes factor for the two-sample Poisson problem in Chapter 6. In future researchwe will use the posterior for the odds ratio to formulate a Bayesian test for twoproportions, the homogeneity of the odds ratio and the test for independence inmultiple 2-by-2 tables. Chapter 6 also described our attempt to extend Je↵reys’sprinciples of testing to problems that deal with discrete random variables basedon the desideratum of limit-consistency. Further research should also focus onthe relationship between predictive matching and limit-consistency, as the lattercriterion might provide a fruitful technique to generalise Je↵reys’s ideas on testingto other settings.Je↵reys’s principles to construct Bayes factors, however, requires one of the pa-rameters to be perceived as the test-relevant one and the others as nuisance. Thismight be di cult for high-dimensional problems, but can be done for location-scaleproblems and the variable selection problem in particular. The multiplicity intro-duced can then be tackled by the method discussed by Scott and Berger (2006,2010), which have yet to be incorporated in JASP. Furthermore, Je↵reys’s con-struction also requires that we choose the distribution form of the models, whichincreases the hazard of model misspecification. Model misspecification can havedramatic e↵ects on Bayesian methods as was shown by Grünwald and van Ommen(2014). Fortunately, Grünwald (2017) and colleagues also developed a frameworkfor safe Bayesian inference and methods to detect model misspecification. Furtherresearch in this area is necessary and on the way. One goal, therefore, is to extendJe↵reys’s principled Bayes factors to nonparametric models, which in itself comeswith additional challenges of tractability and once again multiplicity.To control for multiplicity with the Bayes factors described here, we recom-mended that researchers preregister their hypotheses and the tests they perform.The reason for this is that testing is a confirmatory tool of inference concernedwith model uncertainty and that this di↵ers from an estimation problem. Esti-268mation and exploration, however, should not be undervalued as they allow for theconstruction of theories and models, which can subsequently be tested. Modelsare always simplified description of reality and can always be improved upon.Bayesian methods can help discover and improve models. For instance, byBayesian model averaging, or by exploring the posterior of fitted models usingso-called plausible values to give insights to how a hierarchical model should beformulated (e.g., Ly et al., 2017a; Marsman, 2014; Marsman et al., 2016b). Forinstance, in Ly et al. (2017a) we used plausible values to generalise the findingof Forstmann et al. (2008) based on n = 19 participants to the general popula-tion. Key to this generalisation was the acknowledgement of uncertainty via theposteriors and the mixing of the analytical posteriors developed in Chapter 10.When the posterior is not analytic, one can use the bridge sampler instead, seeChapter 12. The mixing of posteriors in Ly et al. (2017a), however, implies thatthe posterior, and the marginal likelihood in particular, can be evaluated quickly.Hence, to further make Bayesian methods accessible to empirical scientist, weneed to make these sampling methods more e cient. Lastly, Chapter 13 providessome insights in the nature of statistical models and provides the empirical scien-tists with regularity conditions that allow them to formulate models in which thestandard methods are (asymptotically) valid.We hope to have made a convincing case for the use of Bayesian methods inthe empirical sciences, and the Bayes factor in particular when it comes to testing.Our advocacy for Bayesian methods in psychology is, in essence, a call to adopta principled method of learning. This call is neither new nor controversial, asBayesian methods have been adopted in fields such as econometrics, statistics andcomputer science with great success.269

UvA-DARE is a service provided by the library of the University of Amsterdam (https://dare.uva.nl)UvA-DARE (Digital Academic Repository)Bayes factors for research workersLy, A.Publication date2018Document VersionOther versionLicenseOtherLink to publicationCitation for published version (APA):Ly, A. (2018). Bayes factors for research workers. [Thesis, fully internal, Universiteit vanAmsterdam].General rightsIt is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s)and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an opencontent license (like Creative Commons).Disclaimer/Complaints regulationsIf you believe that digital publication of certain material infringes any of your rights or (privacy) interests, pleaselet the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the materialinaccessible and/or remove it from the website. Please Ask the Library: https://uba.uva.nl/en/contact, or a letterto: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. Youwill be contacted as soon as possible.Download date:09 Mar 2023Chapter 14Discussion and Future DirectionsIn this dissertation we advocate the use of Bayes factors in empirical research toreplace or complement standard null hypothesis tests based on p-values. TheseBayes factors were specifically designed to quantify the evidence for or against theexistence of an e↵ect. This was done by comparing two models with the samedistributional assumptions, where the alternative model is an extension of the nullmodel by incorporating one extra parameter. Furthermore, instead of returning adecision to “reject” or “not reject”, a Bayes factor BF10(d) returns a non-negativenumber that represents the evidence within the observed data for the model thatincludes the e↵ect. The returned number can be seen as a refinement of the binarydecision with BF10(d) = 1 and BF10(d) = 0 corresponding to definite rejectionand acceptance of the null, respectively. Moreover, the Bayes factor allows its usersto forgo the binary decision and acknowledge uncertainty, so that the evidencecan be updated continually in light of new data, directly and easily. For empiricalscientists to be able to use these Bayes factors we implemented them in Je↵reys’sAmazing Statistics Program, JASP, which is freely available and open-source (url:https://jasp-stats.org).In Chapter 8 we showed how easy it is do a Bayesian reanalysis of publishedresults in JASP. Most of the discussion centred on how Bayes factors quantifyevidence from data already observed, but future research should also focus onhow the already observed data can be used for follow-up experiments. This ideaof generalising past observations to future data underlies the replication Bayesfactor discussed in Chapter 9. Comprehensive knowledge updating requires thatthe data come from the same population, which is why we emphasised the roleof openness and transparency in Chapter 7. By making research materials anddata available, future researchers can then conduct a direct replication and buildupon previous work. In some cases, however, a replication on the same populationis not possible. For correlation and t-test Bayes factors we can nonetheless domeaningful inference by relocating the data, while for more complicated settingssuch as ANOVAs and contingency tables this is still work in progress.When no previous data are available we recommend the use of default Je↵reys’sBayes factors that are constructed from priors that adhere to the general criteria26714. Discussion and Future Directionsfor Bayesian model choice (Bayarri et al., 2012). One goal of this dissertationwas to explain, apply, and extend these general criteria to scenarios common toempirical scientists. The first extension was to Pearson’s correlation, Chapter 2,resulting in an analytic Bayes factor, which was further extended to Kendall’s ⌧in Chapter 4. By modelling the test statistic, more specifically, approximatingthe sampling distribution of the test statistic with its asymptotic normal equiv-alent, a Bayes factor was derived that leads to interpretable results and is fastto compute. In future research we plan to apply the general procedure based onthe asymptotic normal approximation and parametric yoking to other scenarios.The use of the normal approximation to the true sampling distribution, however,is not as principled as we wanted it to be and led to Bayes factors that provideless evidence for the alternative, whenever ⌧ is far from zero. This motivated usto consider di↵erent approaches and the latent normal approach in van Doornet al. (2017) in particular. Future research should further explore the relationshipbetween Kendall’s ⌧ and certain copula families as this will provide insights instatistical research on dependency.The calculations used for the analytic posteriors for Pearson’s ⇢ also led to theinformed t-test in Chapter 5. This work can easily be adapted to linear regressionand is worth exploring further.The first analytic result of Chapter 11 was used to construct a limit-consistentBayes factor for the two-sample Poisson problem in Chapter 6. In future researchwe will use the posterior for the odds ratio to formulate a Bayesian test for twoproportions, the homogeneity of the odds ratio and the test for independence inmultiple 2-by-2 tables. Chapter 6 also described our attempt to extend Je↵reys’sprinciples of testing to problems that deal with discrete random variables basedon the desideratum of limit-consistency. Further research should also focus onthe relationship between predictive matching and limit-consistency, as the lattercriterion might provide a fruitful technique to generalise Je↵reys’s ideas on testingto other settings.Je↵reys’s principles to construct Bayes factors, however, requires one of the pa-rameters to be perceived as the test-relevant one and the others as nuisance. Thismight be di cult for high-dimensional problems, but can be done for location-scaleproblems and the variable selection problem in particular. The multiplicity intro-duced can then be tackled by the method discussed by Scott and Berger (2006,2010), which have yet to be incorporated in JASP. Furthermore, Je↵reys’s con-struction also requires that we choose the distribution form of the models, whichincreases the hazard of model misspecification. Model misspecification can havedramatic e↵ects on Bayesian methods as was shown by Grünwald and van Ommen(2014). Fortunately, Grünwald (2017) and colleagues also developed a frameworkfor safe Bayesian inference and methods to detect model misspecification. Furtherresearch in this area is necessary and on the way. One goal, therefore, is to extendJe↵reys’s principled Bayes factors to nonparametric models, which in itself comeswith additional challenges of tractability and once again multiplicity.To control for multiplicity with the Bayes factors described here, we recom-mended that researchers preregister their hypotheses and the tests they perform.The reason for this is that testing is a confirmatory tool of inference concernedwith model uncertainty and that this di↵ers from an estimation problem. Esti-268mation and exploration, however, should not be undervalued as they allow for theconstruction of theories and models, which can subsequently be tested. Modelsare always simplified description of reality and can always be improved upon.Bayesian methods can help discover and improve models. For instance, byBayesian model averaging, or by exploring the posterior of fitted models usingso-called plausible values to give insights to how a hierarchical model should beformulated (e.g., Ly et al., 2017a; Marsman, 2014; Marsman et al., 2016b). Forinstance, in Ly et al. (2017a) we used plausible values to generalise the findingof Forstmann et al. (2008) based on n = 19 participants to the general popula-tion. Key to this generalisation was the acknowledgement of uncertainty via theposteriors and the mixing of the analytical posteriors developed in Chapter 10.When the posterior is not analytic, one can use the bridge sampler instead, seeChapter 12. The mixing of posteriors in Ly et al. (2017a), however, implies thatthe posterior, and the marginal likelihood in particular, can be evaluated quickly.Hence, to further make Bayesian methods accessible to empirical scientist, weneed to make these sampling methods more e cient. Lastly, Chapter 13 providessome insights in the nature of statistical models and provides the empirical scien-tists with regularity conditions that allow them to formulate models in which thestandard methods are (asymptotically) valid.We hope to have made a convincing case for the use of Bayesian methods inthe empirical sciences, and the Bayes factor in particular when it comes to testing.Our advocacy for Bayesian methods in psychology is, in essence, a call to adopta principled method of learning. This call is neither new nor controversial, asBayesian methods have been adopted in fields such as econometrics, statistics andcomputer science with great success.269

The Creation of an Expert System for Teaching Piano Lessons

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CWI's Institutional Repository

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University of Central Florida (UCF): STARS (Showcase of Text, Archives, Research & Scholarship)

International Migration, Integration and Social Cohesion online publications

International Migration, Integration and Social Cohesion online publications

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