Bayes Model Selection with Path Sampling: Factor Models and Other Examples

We prove a theorem justifying the regularity conditions which are needed for Path Sampling in Factor Models. We then show that the remaining ingredient, namely, MCMC for calculating the integrand at each point in the path, may be seriously flawed, leading to wrong estimates of Bayes factors. We provide a new method of Path Sampling (with Small Change) that works much better than standard Path Sampling in the sense of estimating the Bayes factor better and choosing the correct model more often. When the more complex factor model is true, PS-SC is substantially more accurate. New MCMC diagnostics is provided for these problems in support of our conclusions and recommendations. Some of our ideas for diagnostics and improvement in computation through small changes should apply to other methods of computation of the Bayes factor for model selection.Comment: Published in at http://dx.doi.org/10.1214/12-STS403 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Hierarchical Feature Learning

The success of many tasks depends on good feature representation which is often domain-specific and hand-crafted requiring substantial human effort. Such feature representation is not general, i.e. unsuitable for even the same task across multiple domains, let alone different tasks.To address these issues, a multilayered convergent neural architecture is presented for learning from repeating spatially and temporally coincident patterns in data at multiple levels of abstraction. The bottom-up weights in each layer are learned to encode a hierarchy of overcomplete and sparse feature dictionaries from space- and time-varying sensory data. Two algorithms are investigated: recursive layer-by-layer spherical clustering and sparse coding to learn feature hierarchies. The model scales to full-sized high-dimensional input data and to an arbitrary number of layers thereby having the capability to capture features at any level of abstraction. The model learns features that correspond to objects in higher layers and object-parts in lower layers.Learning features invariant to arbitrary transformations in the data is a requirement for any effective and efficient representation system, biological or artificial. Each layer in the proposed network is composed of simple and complex sublayers motivated by the layered organization of the primary visual cortex. When exposed to natural videos, the model develops simple and complex cell-like receptive field properties. The model can predict by learning lateral connections among the simple sublayer neurons. A topographic map to their spatial features emerges by minimizing the wiring length simultaneously with feature learning.The model is general-purpose, unsupervised and online. Operations in each layer of the model can be implemented in parallelized hardware, making it very efficient for real world applications

Search for chaos in neutron star systems: Is Cyg X-3 a black hole?

The accretion disk around a compact object is a nonlinear general relativistic system involving magnetohydrodynamics. Naturally the question arises whether such a system is chaotic (deterministic) or stochastic (random) which might be related to the associated transport properties whose origin is still not confirmed. Earlier, the black hole system GRS 1915+105 was shown to be low dimensional chaos in certain temporal classes. However, so far such nonlinear phenomena have not been studied fairly well for neutron stars which are unique for their magnetosphere and kHz quasi-periodic oscillation (QPO). On the other hand, it was argued that the QPO is a result of nonlinear magnetohydrodynamic effects in accretion disks. If a neutron star exhibits chaotic signature, then what is the chaotic/correlation dimension? We analyze RXTE/PCA data of neutron stars Sco X-1 and Cyg X-2, along with the black hole Cyg X-1 and the unknown source Cyg X-3, and show that while Sco X-1 and Cyg X-2 are low dimensional chaotic systems, Cyg X-1 and Cyg X-3 are stochastic sources. Based on our analysis, we argue that Cyg X-3 may be a black hole.Comment: 9 pages including 6 figures; to appear in The Astrophysical Journa

Predicting the Spatial Distribution of Rain-Induced Shallow Landslides by applying GIS and Geocomputational Techniques: A Case Study from North East India

This study presents a case of statistical modelling, by applying GIS and geocomputational techniques, to predict areas that are susceptible to future rain-induced shallow landslides. The statistical prediction model is based on the observed relationships between the spatial distribution of past landslideevents and environmental (causal) factors that are associated with such phenomena. The study also evaluates the predictive performance of a nonlinear regression model, namely the Generalized Additive Model(GAM),applied for the analysis. The study area comprises a residual hill of ? 6 Km2 area situated in the heart of Guwahati (capital city of Assam in NE India). We exploited the geoprocessing functions of SAGA GIS to derive nine different terrain attributesfrom a digital elevation model (DEM) processed by synthetic aperture radar interferometry (InSAR). The terrain attributes along with land use classes, in raster grid format, constitute the predictor variables. An inventory of the locations of eighty-two past occurrences of shallow landslide events constitutes the response. We performed the modelling and statistical geocomputation entirely in the open-source R language and software environment. The procedure comprises the following three steps: (1) Collinearityanalysis to discard redundant predictors. (2) 100-fold bootstrap resampling to fit the GAM by a random selection of 2/3 of the landslide pixels ("training" subset) and validate the GAM by the remaining 1/3 ("test" subset). (3) Estimate model accuracy (true error rates) by a repeated 100-fold 'hold-out validation' method and evaluate the predictive performance of the model by the Area under the ROC curve (AUROC) computed for 100 independently trained models. The mean and standard deviation of accuracy on training sets are 0.80 and 0.01, and that on test sets are 0.79 and 0.02 respectively. The AUROC corresponding to the meanof landslide probabilities is 0.87, and that of the 95% Confidence Intervals (CI) is between 0.86 and 0.88. Thevalues of these quality measures indicate that a data-driven model, such as the GAM, is efficient regarding its predictive performance, to highlight the unstable areas in the study area. We subsequently used the mean values of the landslide probability (susceptibility) estimates corresponding to each mapping unit (grid cell) to construct the landslide susceptibility map, which can be used for land use planning and hazard mitigation