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- Genre: Masters Thesis
Description
Research methods based on the frequentist philosophy use prior information in a priori power calculations and when determining the necessary sample size for the detection of an effect, but not in statistical analyses. Bayesian methods incorporate prior knowledge into the statistical analysis in the form of a prior distribution. When prior information about a relationship is available, the estimates obtained could differ drastically depending on the choice of Bayesian or frequentist method. Study 1 in this project compared the performance of five methods for obtaining interval estimates of the mediated effect in terms of coverage, Type I error rate, empirical power, interval imbalance, and interval width at N = 20, 40, 60, 100 and 500. In Study 1, Bayesian methods with informative prior distributions performed almost identically to Bayesian methods with diffuse prior distributions, and had more power than normal theory confidence limits, lower Type I error rates than the percentile bootstrap, and coverage, interval width, and imbalance comparable to normal theory, percentile bootstrap, and the bias-corrected bootstrap confidence limits. Study 2 evaluated if a Bayesian method with true parameter values as prior information outperforms the other methods. The findings indicate that with true values of parameters as the prior information, Bayesian credibility intervals with informative prior distributions have more power, less imbalance, and narrower intervals than Bayesian credibility intervals with diffuse prior distributions, normal theory, percentile bootstrap, and bias-corrected bootstrap confidence limits. Study 3 examined how much power increases when increasing the precision of the prior distribution by a factor of ten for either the action or the conceptual path in mediation analysis. Power generally increases with increases in precision but there are many sample size and parameter value combinations where precision increases by a factor of 10 do not lead to substantial increases in power.
ContributorsMiocevic, Milica (Author) / Mackinnon, David P. (Thesis advisor) / Levy, Roy (Committee member) / West, Stephen G. (Committee member) / Enders, Craig (Committee member) / Arizona State University (Publisher)
Created2014
Description
Sound localization can be difficult in a reverberant environment. Fortunately listeners can utilize various perceptual compensatory mechanisms to increase the reliability of sound localization when provided with ambiguous physical evidence. For example, the directional information of echoes can be perceptually suppressed by the direct sound to achieve a single, fused auditory event in a process called the precedence effect (Litovsky et al., 1999). Visual cues also influence sound localization through a phenomenon known as the ventriloquist effect. It is classically demonstrated by a puppeteer who speaks without visible lip movements while moving the mouth of a puppet synchronously with his/her speech (Gelder and Bertelson, 2003). If the ventriloquist is successful, sound will be “captured” by vision and be perceived to be originating at the location of the puppet. This thesis investigates the influence of vision on the spatial localization of audio-visual stimuli. Participants seated in a sound-attenuated room indicated their perceived locations of either ISI or level-difference stimuli in free field conditions. Two types of stereophonic phantom sound sources, created by modulating the inter-stimulus time interval (ISI) or level difference between two loudspeakers, were used as auditory stimuli. The results showed that the light cues influenced auditory spatial perception to a greater extent for the ISI stimuli than the level difference stimuli. A binaural signal analysis further revealed that the greater visual bias for the ISI phantom sound sources was correlated with the increasingly ambiguous binaural cues of the ISI signals. This finding suggests that when sound localization cues are unreliable, perceptual decisions become increasingly biased towards vision for finding a sound source. These results support the cue saliency theory underlying cross-modal bias and extend this theory to include stereophonic phantom sound sources.
ContributorsMontagne, Christopher (Author) / Zhou, Yi (Thesis advisor) / Buneo, Christopher A (Thesis advisor) / Yost, William A. (Committee member) / Arizona State University (Publisher)
Created2015
Description
In this work, I present a Bayesian inference computational framework for the analysis of widefield microscopy data that addresses three challenges: (1) counting and localizing stationary fluorescent molecules; (2) inferring a spatially-dependent effective fluorescence profile that describes the spatially-varying rate at which fluorescent molecules emit subsequently-detected photons (due to different illumination intensities or different local environments); and (3) inferring the camera gain. My general theoretical framework utilizes the Bayesian nonparametric Gaussian and beta-Bernoulli processes with a Markov chain Monte Carlo sampling scheme, which I further specify and implement for Total Internal Reflection Fluorescence (TIRF) microscopy data, benchmarking the method on synthetic data. These three frameworks are self-contained, and can be used concurrently so that the fluorescence profile and emitter locations are both considered unknown and, under some conditions, learned simultaneously. The framework I present is flexible and may be adapted to accommodate the inference of other parameters, such as emission photophysical kinetics and the trajectories of moving molecules. My TIRF-specific implementation may find use in the study of structures on cell membranes, or in studying local sample properties that affect fluorescent molecule photon emission rates.
ContributorsWallgren, Ross (Author) / Presse, Steve (Thesis advisor) / Armbruster, Hans (Thesis advisor) / McCulloch, Robert (Committee member) / Arizona State University (Publisher)
Created2019
Description
Bayesian Additive Regression Trees (BART) is a non-parametric Bayesian model
that often outperforms other popular predictive models in terms of out-of-sample error. This thesis studies a modified version of BART called Accelerated Bayesian Additive Regression Trees (XBART). The study consists of simulation and real data experiments comparing XBART to other leading algorithms, including BART. The results show that XBART maintains BART’s predictive power while reducing its computation time. The thesis also describes the development of a Python package implementing XBART.
that often outperforms other popular predictive models in terms of out-of-sample error. This thesis studies a modified version of BART called Accelerated Bayesian Additive Regression Trees (XBART). The study consists of simulation and real data experiments comparing XBART to other leading algorithms, including BART. The results show that XBART maintains BART’s predictive power while reducing its computation time. The thesis also describes the development of a Python package implementing XBART.
ContributorsYalov, Saar (Author) / Hahn, P. Richard (Thesis advisor) / McCulloch, Robert (Committee member) / Kao, Ming-Hung (Committee member) / Arizona State University (Publisher)
Created2019