We apply a Bayesian hierarchical Poisson spatial interaction model to the paper trail left by patent citations between high-technology patents in Europe to identify and measure spatial separation effects of interregional knowledge flows.... more
We apply a Bayesian hierarchical Poisson spatial interaction model to the paper trail left by patent citations between high-technology patents in Europe to identify and measure spatial separation effects of interregional knowledge flows. The model introduced here is novel in that it allows for spatially structured origin and destination effects for the regions. Estimation of the model is carried out
Received academic wisdom holds that human judgment is characterized by unrealistic optimism, the tendency to underestimate the likelihood of negative events and overestimate the likelihood of positive events. With recent questions being... more
Received academic wisdom holds that human judgment is characterized by unrealistic optimism, the tendency to underestimate the likelihood of negative events and overestimate the likelihood of positive events. With recent questions being raised over the degree to which the majority of this research genuinely demonstrates optimism, attention to possible mechanisms generating such a bias becomes ever more important. New studies have now claimed that unrealistic optimism emerges as a result of biased belief updating with distinctive neural correlates in the brain. On a behavioral level, these studies suggest that, for negative events, desirable information is incorporated into personal risk estimates to a greater degree than undesirable information (resulting in a more optimistic outlook). However, using task analyses, simulations and experiments we demonstrate that this pattern of results is a statistical artifact. In contrast with previous work, we examined participants’ use of new information with reference to the normative, Bayesian standard. Simulations reveal the fundamental difficulties that would need to be overcome by any robust test of optimistic updating. No such test presently exists, so that the best one can presently do is perform analyses with a number of techniques, all of which have important weaknesses. Applying these analyses to five experiments shows no evidence of optimistic updating. These results clarify the difficulties involved in studying human ‘bias’ and cast additional doubt over the status of optimism as a fundamental characteristic of healthy cognition.
We introduce a fast Markov Chain Monte Carlo (MCMC) exploration of the astrophysical parameter space using a modified version of the publicly available code CIGALE (Code Investigating GALaxy emission). The original CIGALE builds a grid of... more
We introduce a fast Markov Chain Monte Carlo (MCMC) exploration of the astrophysical parameter space using a modified version of the publicly available code CIGALE (Code Investigating GALaxy emission). The original CIGALE builds a grid of theoretical Spectral Energy Distribution (SED) models and fits to photometric fluxes from Ultraviolet (UV) to Infrared (IR) to put contraints on parameters related to both formation and evolution of galaxies. Such a grid-based method can lead to a long and challenging parameter extraction since the computation time increases exponentially with the number of parameters considered and results can be dependent on the density of sampling points, which must be chosen in advance for each parameter. Markov Chain Monte Carlo methods, on the other hand, scale approximately linearly with the number of parameters, allowing a faster and more accurate exploration of the parameter space by using a smaller number of efficiently chosen samples. We test our MCMC version of the code CIGALE (called CIGALEMC) with simulated data. After checking the ability of the code to retrieve the input parameters used to build the mock sample, we fit theoretical SEDs to real data from the well known and studied SINGS sample. We discuss constraints on the parameters and show the advantages of our MCMC sampling method in terms of accuracy of the results and optimization of CPU time.
A Gaussian conditional autoregressive (CAR) formulation is presented that permits the modelling of the spatial dependence and the dependence between multivariate random variables at irregularly spaced sites so capturing some of the... more
A Gaussian conditional autoregressive (CAR) formulation is presented that permits the modelling of the spatial dependence and the dependence between multivariate random variables at irregularly spaced sites so capturing some of the modelling advantages of the geostatistical approach. The model benefits not only from the explicit availability of the full conditionals but also from the computational simplicity of the precision
Given discrete time observations over a fixed time interval, we study a nonparametric Bayesian approach to estimation of the volatility coefficient of a stochastic differential equation. We postulate a histogram-type prior on the... more
Given discrete time observations over a fixed time interval, we study a nonparametric Bayesian approach to estimation of the volatility coefficient of a stochastic differential equation. We postulate a histogram-type prior on the volatility with piecewise constant realisations on bins forming a partition of the time interval. The values on the bins are assigned an inverse Gamma Markov chain (IGMC) prior. Posterior inference is straightforward to implement via Gibbs sampling, as the full conditional distributions are available explicitly and turn out to be inverse Gamma. We also discuss in detail the hyperparameter selection for our method. Our nonparametric Bayesian approach leads to good practical results in representative simulation examples. Finally, we apply it on a classical data set in change-point analysis: weekly closings of the Dow-Jones industrial averages.
In this article we present a Bayesian hierarchical modeling approach for imaging genetics, where the interest lies in linking brain connectivity across multiple individuals to their genetic information.We have available data from a... more
In this article we present a Bayesian hierarchical modeling approach for imaging genetics, where the interest lies in linking brain connectivity across multiple individuals to their genetic information.We have available data from a functional magnetic resonance imaging (fMRI) study on schizophrenia. Our goals are to identify brain regions of interest (ROIs) with discriminating activation patterns between schizophrenic patients and healthy controls, and to relate the ROIs’ activations with available genetic information from single nucleotide polymorphisms (SNPs) on the subjects. For this task, we develop a hierarchical mixture model that includes several innovative characteristics: it incorporates the selection of ROIs that discriminate the subjects into separate groups; it allows the mixture components to depend on selected covariates; it includes prior models that capture structural dependencies among the ROIs. Applied to the schizophrenia dataset, the model leads to the simultaneous selection of a set of discriminatory ROIs and the relevant SNPs, together with the reconstruction of the correlation structure of the selected regions. To the best of our knowledge, our work represents the first attempt at a rigorous modeling strategy for imaging genetics data that incorporates all such features.
A two-phase Monte Carlo simulation (TPMCS) uncertainty analysis framework is used to analyze epistemic and aleatory uncertainty associated with simulated exceedances of an in-stream fecal coliform (FC) water quality criterion when using... more
A two-phase Monte Carlo simulation (TPMCS) uncertainty analysis framework is used to analyze epistemic and aleatory uncertainty associated with simulated exceedances of an in-stream fecal coliform (FC) water quality criterion when using the Hydrological Simulation Program–FORTRAN (HSPF). The TPMCS framework is compared with a single-phase or standard Monte Carlo simulation (SPMCS) analysis. Both techniques are used to assess two total maximum daily load (TMDL) pollutant allocation scenarios. The application of TPMCS illustrates that cattle directly depositing FC in the stream is a greater source of epistemic uncertainty than FC loading from cropland overland runoff, the two sources specifically targeted for reduction in the allocation scenario. This distinction is not possible using SPMCS. Although applying the TPMCS framework involves subjective decisions about how selected model parameters are considered within the framework, this uncertainty analysis approach is transparent and the results provide information that can be used by decision makers when considering pollution control measure implementation alternatives, including quantifying the level of confidence in achieving applicable water quality standards.
Surface assemblages represent the most accessible, representative sample of the archaeological record for the study of human socio-ecological systems at regional scales. However, the difficulty in developing suitable chronological... more
Surface assemblages represent the most accessible, representative sample of the archaeological record for the study of human socio-ecological systems at regional scales. However, the difficulty in developing suitable chronological frameworks from surface assemblages has limited their use. Additionally, surface scatters are composed of artifacts that can accumulate across multiple occupational episodes. A challenge to chronology building in such surface contexts is the necessity to assess the probability of occupation during each time period. We describe a new method of dating surface lithic assemblages using empirical Bayesian methods, with an example from northeastern Spain. We use Bayesian methods to estimate the probability of occupation during 11 temporal periods (c.13,000-4,200 cal BP) for a sample of 25 lithic surface. A Bayesian approach allows us to combine prior knowledge, with different degrees of uncertainty, about the temporal sensitivity of projectile forms statistically derived from a regional calibration data set of 35 dated assemblages to estimate the age of each surface collections probabilistically. This approach provides new insight into the settlement history of the Maestrat in the first half of the Holocene, during the transition from foraging to food production and offers a powerful tool to archaeologists for the dating of surface collections.
Markov chain Monte Carlo (MCMC) techniques revolutionized statistical practice in the 1990s by providing an essential toolkit for making the rigor and flexibility of Bayesian analysis computationally practical. At the same time the... more
Markov chain Monte Carlo (MCMC) techniques revolutionized statistical practice in the 1990s by providing an essential toolkit for making the rigor and flexibility of Bayesian analysis computationally practical. At the same time the increasing prevalence of massive datasets and the expansion of the field of data mining has created the need for statistically sound methods that scale to these large problems. Except for the most trivial examples, current MCMC methods require a complete scan of the dataset for each iteration eliminating their candidacy as feasible data mining techniques. In this article we present a method for making Bayesian analysis of massive datasets computationally feasible. The algorithm simulates from a posterior distribution that conditions on a smaller, more manageable portion of the dataset. The remainder of the dataset may be incorporated by reweighting the initial draws using importance sampling. Computation of the importance weights requires a single scan of the remaining observations. While importance sampling increases efficiency in data access, it comes at the expense of estimation efficiency. A simple modification, based on the “rejuvenation” step used in particle filters for dynamic systems models, sidesteps the loss of efficiency with only a slight increase in the number of data accesses. To show proof-of-concept, we demonstrate the method on two examples. The first is a mixture of transition models that has been used to model web traffic and robotics. For this example we show that estimation efficiency is not affected while offering a 99% reduction in data accesses. The second example applies the method to Bayesian logistic regression and yields a 98% reduction in data accesses.
We apply a reversible-jump Markov chain Monte Carlo method to sample the Bayesian pos- terior model probability density function of 2-D seafloor resistivity as constrained by marine controlled source electromagnetic data. This density... more
We apply a reversible-jump Markov chain Monte Carlo method to sample the Bayesian pos- terior model probability density function of 2-D seafloor resistivity as constrained by marine controlled source electromagnetic data. This density function of earth models conveys infor- mation on which parts of the model space are illuminated by the data. Whereas conventional gradient-based inversion approaches require subjective regularization choices to stabilize this highly non-linear and non-unique inverse problem and provide only a single solution with no model uncertainty information, the method we use entirely avoids model regularization. The result of our approach is an ensemble of models that can be visualized and queried to provide meaningful information about the sensitivity of the data to the subsurface, and the level of res- olution of model parameters. We represent models in 2-D using a Voronoi cell parametrization. To make the 2-D problem practical, we use a source–receiver common midpoint approximation with 1-D forward modelling. Our algorithm is transdimensional and self-parametrizing where the number of resistivity cells within a 2-D depth section is variable, as are their positions and geometries. Two synthetic studies demonstrate the algorithm’s use in the appraisal of a thin, segmented, resistive reservoir which makes for a challenging exploration target. As a demonstration example, we apply our method to survey data collected over the Scarborough gas field on the Northwest Australian shelf.
