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Jan Sprenger - One of the best experts on this subject based on the ideXlab platform.

  • Testing a Precise Null Hypothesis: The Case of Lindley’s Paradox
    Philosophy of Science, 2013
    Co-Authors: Jan Sprenger
    Abstract:

    Testing a point null hypothesis is a classical but controversial issue in statistical methodology. A prominent illustration is Lindley’s Paradox, which emerges in hypothesis tests with large sample size and exposes a salient divergence between Bayesian and frequentist inference. A close analysis of the paradox reveals that both Bayesians and frequentists fail to satisfactorily resolve it. As an alternative, I suggest Bernardo’s Bayesian Reference Criterion: (i) it targets the predictive performance of the null hypothesis in future experiments; (ii) it provides a proper decision-theoretic model for testing a point null hypothesis; (iii) it convincingly addresses Lindley’s Paradox.

  • testing a precise null hypothesis the case of lindley s paradox
    Philosophy of Science, 2013
    Co-Authors: Jan Sprenger
    Abstract:

    Testing a point null hypothesis is a classical but controversial issue in statistical methodology. A prominent illustration is Lindley’s Paradox, which emerges in hypothesis tests with large sample size and exposes a salient divergence between Bayesian and frequentist inference. A close analysis of the paradox reveals that both Bayesians and frequentists fail to satisfactorily resolve it. As an alternative, I suggest Bernardo’s Bayesian Reference Criterion: (i) it targets the predictive performance of the null hypothesis in future experiments; (ii) it provides a proper decision-theoretic model for testing a point null hypothesis; (iii) it convincingly addresses Lindley’s Paradox.

Mark Steyvers - One of the best experts on this subject based on the ideXlab platform.

  • bayesian models of cognition revisited setting optimality aside and letting data drive psychological theory
    Psychological Review, 2017
    Co-Authors: Sean Tauber, Daniel J Navarro, Amy Perfors, Mark Steyvers
    Abstract:

    Recent debates in the psychological literature have raised questions about the assumptions that underpin Bayesian models of cognition and what inferences they license about human cognition. In this paper we revisit this topic, arguing that there are 2 qualitatively different ways in which a Bayesian model could be constructed. The most common approach uses a Bayesian model as a normative standard upon which to license a claim about optimality. In the alternative approach, a descriptive Bayesian model need not correspond to any claim that the underlying cognition is optimal or rational, and is used solely as a tool for instantiating a substantive psychological theory. We present 3 case studies in which these 2 perspectives lead to different computational models and license different conclusions about human cognition. We demonstrate how the descriptive Bayesian approach can be used to answer different sorts of questions than the optimal approach, especially when combined with principled tools for model evaluation and model selection. More generally we argue for the importance of making a clear distinction between the 2 perspectives. Considerable confusion results when descriptive models and optimal models are conflated, and if Bayesians are to avoid contributing to this confusion it is important to avoid making normative claims when none are intended. (PsycINFO Database Record

  • Bayesian models of cognition revisited: Setting optimality aside and letting data drive psychological theory
    2016
    Co-Authors: Sean Tauber, Daniel J Navarro, Amy Perfors, Mark Steyvers
    Abstract:

    Recent debates in the psychological literature have raised questions about what assumptions underpin Bayesian models of cognition, and what infer-ences they license about human cognition. In this paper we revisit this topic, arguing that there are two qualitatively different ways in which a Bayesian model could be constructed. If a Bayesian model is intended to license a claim about optimality then the priors and likelihoods in the model must be constrained by reference to some external criterion. A descriptive Bayesian model need not correspond to any claim that the underlying cognition is optimal or rational, and is used solely as a tool for instantiating a sub-stantive psychological theory. We present three case studies in which these two perspectives lead to different computational models and license different conclusions about human cognition. We argue that the descriptive Bayesian approach is more useful overall, especially when combined with principled tools for model evaluation and model selection. More generally we argue for the importance of making a clear distinction between the two perspectives. Considerable confusion results when descriptive models and optimal models are conflated, and if Bayesians are to avoid contributing to this confusion it is important to avoid making normative claims when none are intended

Rianne De Heide - One of the best experts on this subject based on the ideXlab platform.

  • why optional stopping can be a problem for Bayesians
    arXiv: Methodology, 2021
    Co-Authors: Rianne De Heide, Peter Grunwald
    Abstract:

    Recently, optional stopping has been a subject of debate in the Bayesian psychology community. Rouder (2014) argues that optional stopping is no problem for Bayesians, and even recommends the use of optional stopping in practice, as do Wagenmakers et al. (2012). This article addresses the question whether optional stopping is problematic for Bayesian methods, and specifies under which circumstances and in which sense it is and is not. By slightly varying and extending Rouder's (2014) experiments, we illustrate that, as soon as the parameters of interest are equipped with default or pragmatic priors - which means, in most practical applications of Bayes factor hypothesis testing - resilience to optional stopping can break down. We distinguish between three types of default priors, each having their own specific issues with optional stopping, ranging from no-problem-at-all (Type 0 priors) to quite severe (Type II priors).

  • Why optional stopping can be a problem for Bayesians
    Psychonomic Bulletin & Review, 2020
    Co-Authors: Rianne De Heide, Peter D. Grünwald
    Abstract:

    Recently, optional stopping has been a subject of debate in the Bayesian psychology community. Rouder ( Psychonomic Bulletin & Review 21 (2), 301–308, 2014 ) argues that optional stopping is no problem for Bayesians, and even recommends the use of optional stopping in practice, as do (Wagenmakers, Wetzels, Borsboom, van der Maas & Kievit, Perspectives on Psychological Science 7 , 627–633, 2012 ). This article addresses the question of whether optional stopping is problematic for Bayesian methods, and specifies under which circumstances and in which sense it is and is not. By slightly varying and extending Rouder’s ( Psychonomic Bulletin & Review 21 (2), 301–308, 2014 ) experiments, we illustrate that, as soon as the parameters of interest are equipped with default or pragmatic priors—which means, in most practical applications of Bayes factor hypothesis testing—resilience to optional stopping can break down. We distinguish between three types of default priors, each having their own specific issues with optional stopping, ranging from no-problem-at-all (type 0 priors) to quite severe (type II priors).

  • why optional stopping is a problem for Bayesians
    arXiv: Methodology, 2017
    Co-Authors: Rianne De Heide, Peter Grunwald
    Abstract:

    Recently, optional stopping has been a subject of debate in the Bayesian psychology community. Rouder (2014) argues that optional stopping is no problem for Bayesians, and even recommends the use of optional stopping in practice, as do Wagenmakers et al. (2012). This article addresses the question whether optional stopping is problematic for Bayesian methods, and specifies under which circumstances and in which sense it is and is not. By slightly varying and extending Rouder's (2014) experiment, we illustrate that, as soon as the parameters of interest are equipped with default or pragmatic priors - which means, in most practical applications of Bayes Factor hypothesis testing - resilience to optional stopping can break down. We distinguish between four types of default priors, each having their own specific issues with optional stopping, ranging from no-problem-at-all (Type 0 priors) to quite severe (Type II and III priors).

Peter D. Grünwald - One of the best experts on this subject based on the ideXlab platform.

  • Why optional stopping can be a problem for Bayesians
    Psychonomic Bulletin & Review, 2020
    Co-Authors: Rianne De Heide, Peter D. Grünwald
    Abstract:

    Recently, optional stopping has been a subject of debate in the Bayesian psychology community. Rouder ( Psychonomic Bulletin & Review 21 (2), 301–308, 2014 ) argues that optional stopping is no problem for Bayesians, and even recommends the use of optional stopping in practice, as do (Wagenmakers, Wetzels, Borsboom, van der Maas & Kievit, Perspectives on Psychological Science 7 , 627–633, 2012 ). This article addresses the question of whether optional stopping is problematic for Bayesian methods, and specifies under which circumstances and in which sense it is and is not. By slightly varying and extending Rouder’s ( Psychonomic Bulletin & Review 21 (2), 301–308, 2014 ) experiments, we illustrate that, as soon as the parameters of interest are equipped with default or pragmatic priors—which means, in most practical applications of Bayes factor hypothesis testing—resilience to optional stopping can break down. We distinguish between three types of default priors, each having their own specific issues with optional stopping, ranging from no-problem-at-all (type 0 priors) to quite severe (type II priors).

Sean Tauber - One of the best experts on this subject based on the ideXlab platform.

  • bayesian models of cognition revisited setting optimality aside and letting data drive psychological theory
    Psychological Review, 2017
    Co-Authors: Sean Tauber, Daniel J Navarro, Amy Perfors, Mark Steyvers
    Abstract:

    Recent debates in the psychological literature have raised questions about the assumptions that underpin Bayesian models of cognition and what inferences they license about human cognition. In this paper we revisit this topic, arguing that there are 2 qualitatively different ways in which a Bayesian model could be constructed. The most common approach uses a Bayesian model as a normative standard upon which to license a claim about optimality. In the alternative approach, a descriptive Bayesian model need not correspond to any claim that the underlying cognition is optimal or rational, and is used solely as a tool for instantiating a substantive psychological theory. We present 3 case studies in which these 2 perspectives lead to different computational models and license different conclusions about human cognition. We demonstrate how the descriptive Bayesian approach can be used to answer different sorts of questions than the optimal approach, especially when combined with principled tools for model evaluation and model selection. More generally we argue for the importance of making a clear distinction between the 2 perspectives. Considerable confusion results when descriptive models and optimal models are conflated, and if Bayesians are to avoid contributing to this confusion it is important to avoid making normative claims when none are intended. (PsycINFO Database Record

  • Bayesian models of cognition revisited: Setting optimality aside and letting data drive psychological theory
    2016
    Co-Authors: Sean Tauber, Daniel J Navarro, Amy Perfors, Mark Steyvers
    Abstract:

    Recent debates in the psychological literature have raised questions about what assumptions underpin Bayesian models of cognition, and what infer-ences they license about human cognition. In this paper we revisit this topic, arguing that there are two qualitatively different ways in which a Bayesian model could be constructed. If a Bayesian model is intended to license a claim about optimality then the priors and likelihoods in the model must be constrained by reference to some external criterion. A descriptive Bayesian model need not correspond to any claim that the underlying cognition is optimal or rational, and is used solely as a tool for instantiating a sub-stantive psychological theory. We present three case studies in which these two perspectives lead to different computational models and license different conclusions about human cognition. We argue that the descriptive Bayesian approach is more useful overall, especially when combined with principled tools for model evaluation and model selection. More generally we argue for the importance of making a clear distinction between the two perspectives. Considerable confusion results when descriptive models and optimal models are conflated, and if Bayesians are to avoid contributing to this confusion it is important to avoid making normative claims when none are intended