Bayesian

Bayesian flexibles modelling of mixed logit models

by marcucci edoardo

Subjective Bayesianism, probability spaces, and the Sleeping Beauty problem

by Lee Elkin

draft only

My intention in this paper is to provide a two-pronged argument in response to the Sleeping Beauty puzzle. I will... more My intention in this paper is to provide a two-pronged argument in response to the Sleeping Beauty puzzle. I will first argue against Ruth Weintraub’s (2004) defense of the Thirder position by showing that the new evidence that she claims SB gains is irrelevant for updating her initial credence from 1/2 to 1/3 on the first awakening. To show this, I will use Bayesian analysis and conditionalize on the new piece of evidence that Weintraub claims that SB gains upon being awakened.

The second prong of the argument is to offer a solution to the puzzle without the need of SB acquiring new information. I believe that Thirders vacillate between probability spaces from Sunday night to Monday afternoon, and this is what causes the puzzle to arise. If we establish two distinct mathematical probability spaces independent of one another, then the probabilistic issues will resolve themselves and therefore the puzzle dissipates. Given my proposed solution to the problem, I remain neutral between Thirdism and Halfism since what I take to be relevant are the questions asked and the relevant probability spaces under consideration.   

A Bayesian mixture modeling approach for assessing the effects of correlated exposures in case-control studies

by Frank de Vocht

Frank de Vocht, Nicola Cherry, jon Wakefield

Predisposition to a disease is usually caused by cumulative effects of a multitude of exposures and lifestyle factors... more Predisposition to a disease is usually caused by cumulative effects of a multitude of exposures and lifestyle factors in combination with individual susceptibility. Failure to include all relevant variables may result in biased risk estimates and decreased power, whereas inclusion of all variables may lead to computational difficulties, especially when variables are correlated. We describe a Bayesian Mixture Model (BMM) incorporating a variable-selection prior and compared its performance with logistic multiple regression model (LM) in simulated case–control data with up to twenty exposures with varying prevalences and correlations. In addition, as a practical example we re analyzed data on male infertility and occupational exposures (Chaps-UK). BMM mean-squared errors (MSE) were smaller than of the LM, and were independent of the number of model parameters. BMM type I errors were minimal (less than or equal to1), whereas for the LM this increased with the number of parameters and correlation between exposures. The numbers of type II errors were comparable. Re analysis of Chaps-UK data demonstrated more convincingly than by using a LM that occupational exposure to glycol ethers and VOCs are likely risk factors for male infertility. This BMM proves an appealing alternative to standard logistic regression when dealing with the analysis of (correlated) exposures in case–control studies.

Kleinschmidt, D. F., Fine, A. B., & Jaeger, T. F. (2012). A belief-updating model of adaptation and cue combination in syntactic comprehension. In CogSci12

by Dave Kleinschmidt

Talk to be presented at CogSci12 in Sapporo, Japan.

We develop and evaluate a preliminary belief-updating model which links intermediate-term (i.e., over several days)... more We develop and evaluate a preliminary belief-updating model which links intermediate-term (i.e., over several days) syntactic adaptation to the joint statistics of syntactic structures and lexical cues to those structures. This model shows how subjects differentially depend on different cues to syntactic structure following changes in the reliability of those cues, as shown by Fine and Jaeger (2011). By relating syntactic adaptation and cue combination to rational inference under uncertainty, this work links learning and adaptation in sentence processing with adaptation in speech perception and non-linguistic domains.

Kleinschmidt, D. F., & Jaeger, T. F. (2012). A continuum of phonetic adaptation: Evaluating an incremental belief-updating model of recalibration and selective adaptation. In CogSci12

by Dave Kleinschmidt

Talk to be presented at CogSci12 in Sapporo, Japan.

We have previously proposed that incremental belief updating can provide a unified account of the effect of cumulative... more We have previously proposed that incremental belief updating can provide a unified account of the effect of cumulative exposure on phonetic recalibration and selective adaptation (Kleinschmidt & Jaeger, 2011). This model predicts that these are not two distinct phenomena but rather two points on a continuum. We investigate that prediction here using adaptor stimuli intermediate between those which induce recalibration and selective adaptation, and find that the quantitative predictions of the model fit the data well. We also demonstrate that with the proper controls, Mechanical Turk provides a suitable online platform for speech perception experiments

A Bayesian binaural system for 3D sound-source localisation

by João Filipe Ferreira

How Likely is Simpson's Paradox?

by Marios Pavlides

The American Statistician. August 1, 2009, 63(3): 226-233. doi:10.1198/tast.2009.09007.

What proportion of all 2×2×2 contingency tables exhibit Simpson’s Paradox? An exact answer is obtained for large... more What proportion of all 2×2×2 contingency tables exhibit Simpson’s Paradox? An exact answer is obtained for large sample sizes and extended to 2×2×ℓ tables by Monte Carlo approximation. Conditional probabilities of the occurrence of Simpson’s Paradox are also derived. If the observed cell proportions satisfy a Simpson reversal, the posterior probability that the population parameters satisfy the same reversal is obtained. This Bayesian analysis is applied to the well-known Simpson reversal of the 1995–1997 batting averages of Derek Jeter and David Justice.

Bayesian mixture modeling of gene-environment and gene-gene interactions.

by Frank de Vocht

Genet Epidemiol. 2010 Jan;34(1):16-25.

With the advent of rapid and relatively cheap genotyping technologies there is now the opportunity to attempt to... more With the advent of rapid and relatively cheap genotyping technologies there is now the opportunity to attempt to identify gene-environment and gene-gene interactions when the number of genes and environmental factors is potentially large. Unfortunately the dimensionality of the parameter space leads to a computational explosion in the number of possible interactions that may be investigated. The full model that includes all interactions and main effects can be unstable, with wide confidence intervals arising from the large number of estimated parameters. We describe a hierarchical mixture model that allows all interactions to be investigated simultaneously, but assumes the effects come from a mixture prior with two components, one that reflects small null effects and the second for epidemiologically significant effects. Effects from the former are effectively set to zero, hence increasing the power for the detection of real signals. The prior framework is very flexible, which allows substantive information to be incorporated into the analysis. We illustrate the methods first using simulation, and then on data from a case-control study of lung cancer in Central and Eastern Europe.

A Bayesian Approach to Schools' Catchment-based Performance Modelling

by Chris Brunsdon

Robotic Implementation of Biological Bayesian Models for Visuo-Inertial Image Stabilization and Gaze Control

by João Filipe Ferreira

Disagreement, Equal Weight, and Commutativity

by Alastair Wilson

Philosophical Studies 149(3):321-326, 2010.

How should we respond to cases of disagreement where two epistemic agents have the same evidence but come to different... more How should we respond to cases of disagreement where two epistemic agents have the same evidence but come to different conclusions? Adam Elga has provided a Bayesian framework for addressing this question. In this paper, I shall highlight two unfortunate consequences of this framework, which Elga does not anticipate. Both problems derive from a failure of commutativity between application of the equal weight view and updating in the light of other evidence.

A hierarchical Bayesian framework for multimodal active perception

by João Filipe Ferreira

Co-authored with M. Castelo-Branco, J. Dias, Adaptive Behavior, published online ahead of print, March 1st, 2012.

In this article, we present a hierarchical Bayesian framework for multimodal active perception, devised to be... more In this article, we present a hierarchical Bayesian framework for multimodal active perception, devised to be emergent, scalable and adaptive. This framework, while not strictly neuromimetic, finds its roots in the role of the dorsal perceptual pathway of the human brain. Its composing models build upon a common spatial configuration that is naturally fitting for the integration of readings from multiple sensors using a Bayesian approach devised in previous work. The framework presented in this article is shown to adequately model human-like active perception behaviours, namely by exhibiting the following desirable properties: high-level behaviour results from low-level interaction of simpler building blocks; seamless integration of additional inputs is allowed by the Bayesian Programming formalism; initial ‘genetic imprint’ of distribution parameters may be changed ‘on the fly’ through parameter manipulation, thus allowing for the implementation of goal-dependent behaviours (i.e. top-down influences).

Bayesian flexibles modelling of mixed logit models

by marcucci edoardo

A Bayesian approach to tracking with kernel recursive least-squares

by Steven Van Vaerenbergh

Co-authored with Miguel Lázaro-Gredilla and Ignacio Santamaría, presented at 2011IEEE International Workshop on Machine Learning for Signal Processing.

In this paper we introduce a kernel-based recursive least-squares (KRLS) algorithm that is able to track nonlinear,... more In this paper we introduce a kernel-based recursive least-squares (KRLS) algorithm that is able to track nonlinear, time-varying relationships in data. To this purpose we first derive the standard KRLS equations from a Bayesian perspective (including a principled approach to pruning) and then take advantage of this framework to incorporate forgetting in a consistent way, thus enabling the algorithm to perform tracking in non-stationary scenarios. In addition to this tracking ability, the resulting algorithm has a number of appealing properties: It is online, requires a fixed amount of memory and computation per time step and incorporates regularization in a natural manner. We include experimental results that support the theory as well as illustrate the efficiency of the proposed algorithm.

BaSTA: an R package for Bayesian estimation of age-specific survival from incomplete mark–recapture/recovery data with covariates

by Owen Jones

published in Methods In Ecology and Evolution 2012

1. Understanding age-specific survival in wild animal populations is crucial to the study of population dynamics and... more 1. Understanding age-specific survival in wild animal populations is crucial to the study of population dynamics and is therefore an essential component of several fields including evolution, management and conservation.

2. We present Bayesian survival trajectory analysis (BaSTA), a free open-source software package for estimating age-specific survival from capture–recapture/recovery data under a Bayesian framework.

3. The method copes with low recapture probabilities, unknown ages (e.g. because of left-truncation) and unknown ages at death (e.g. because of right-censoring). It estimates survival and detection parameters as well as the unknown birth and death times (i.e. latent states) while allowing users to test a range of survival models. In addition, the effect of continuous or categorical covariates can be evaluated.

4. This tool facilitates the analysis of age patterns of survival in long-term animal studies and will enable researchers to robustly infer the effect of covariates, even with large amounts of missing data.

Behavior and neural basis of near-optimal visual search

by Ronald van den Berg

WJ Ma, V Navalpakkam, JM Beck, R van den Berg, A Pouget
Nature Neuroscience, 2011

The ability to search efficiently for a target in a cluttered environment is one of the most remarkable functions of... more The ability to search efficiently for a target in a cluttered environment is one of the most remarkable functions of the nervous system. This task is difficult under natural circumstances, as the reliability of sensory information can vary greatly across space and time and is typically a priori unknown to the observer. In contrast, visual-search experiments commonly use stimuli of equal and known reliability. In a target detection task, we randomly assigned high or low reliability to each item on a trial-by-trial basis. An optimal observer would weight the observations by their trial-to-trial reliability and combine them using a specific nonlinear integration rule. We found that humans were near-optimal, regardless of whether distractors were homogeneous or heterogeneous and whether reliability was manipulated through contrast or shape. We present a neural-network implementation of near-optimal visual search based on probabilistic population coding. The network matched human performance.

Forecasting In Vector Autoregressions With Many Predictors

by Dimitris Korobilis

Bayesian real-time perception algorithms on GPU

by João Filipe Ferreira

MULTIMODAL ACTIVE EXPLORATION USING A BAYESIAN APPROACH

by João Filipe Ferreira

Bayesian models for multimodal perception of 3D structure and motion

by João Filipe Ferreira