Characterization of a robust probabilistic framework for brain magnetic resonance image data distributions

Probabilistic characterisation of image data for accurate prognosis and treatment planning remains a long-standing problem in medical research, especially when the data distribution depicts flat-top and high-order contact. Such flat-top distributions are quite common in brain magnetic resonance (MR) image data, where the density drops sharply beyond the flat interval. Intuitively, it would indicate a bipartition of data into positive region containing observations definitely belonging to the image class and boundary region with observations possibly belonging to it. The flat peak would also imply that multiple values are equally most likely to belong to that class. However, the popular probability distributions used in such cases are unimodal, creating ambiguity about the positive region. In this work, we study the statistical properties and develop likelihood-based iterative estimation method for the parameters of a novel class of platykurtic probability distributions containing normal, called the stomped normal distribution, that provides more accurate modelling to the flat-top data distributions. The robustness of the proposed stomped normal model has been illustrated with six simulated and nine real brain MR volumes. Our analysis shows substantial improvement in explaining a variety of shapes of data distributions using the proposed probability model

Non-Stationary Stochastic Volatility Model for Dynamic Feedback and Skewness

In this paper I present a new single factor stochastic volatility model for asset return observed in discrete time and its latent volatility. This model unites the feedback effect and return skewness using a common factor for return and its volatility. Further, it generalizes the existing stochastic volatility framework with constant feedback to one with time varying feedback and as a consequence time varying skewness. However, presence of dynamic feedback effect violates the weak-stationarity assumption usually considered for the latent volatility process. The concept of bounded stationarity has been proposed in this paper to address the issue of non-stationarity. A characterization of the error distributions for returns and volatility is provided on the basis of existence of conditional moments. Finally, an application of the model has been explained using S&P100 daily returns under the assumption of Normal error and half Normal common factor distribution

Product market performance and capital structure: A Hierarchical Bayesian semi-parametric panel regression model

The relationship between product market performance of a firm and its capital structure has drawn considerable amount of attention recently amongst corporate finance researchers. The same was established to be non-monotonic in the context of a developed market. The non-monotonicity in the functional form could be expressed by pieces of straight lines joined at different values of debt (or knots). In this paper we address the issue of estimating the slopes of different line segments along with the positions of the knots from a panel of firms using an adaptive hierarchical Bayesian semi-parametric regression model. Further,keeping in mind that such a relationship is less investigated in emerging economies where the debt market dynamics may be different we investigate the same for an emerging economy. In the process we provide the economic rationale for varying sign and magnitude of the slopes of the line segments discussed above

Deep deterministic uncertainty: a new simple baseline

Reliable uncertainty from deterministic single-forward pass models is sought after because conventional methods of uncertainty quantification are computationally expensive. We take two complex single-forward-pass uncertainty approaches, DUQ and SNGP, and examine whether they mainly rely on a well-regularized feature space. Crucially, without using their more complex methods for estimating uncertainty, we find that a single softmax neural net with such a regularized feature-space, achieved via residual connections and spectral normalization, outperforms DUQ and SNGP's epistemic uncertainty predictions using simple Gaussian Discriminant Analysis post-training as a separate feature-space density estimator-without fine-tuning on OoD data, feature ensembling, or input pre-procressing. Our conceptually simple Deep Deterministic Uncertainty (DDU) baseline can also be used to disentangle aleatoric and epistemic uncertainty and performs as well as Deep Ensembles, the state-of-the art for uncertainty prediction, on several OoD bench-marks (CIFAR-10/100 vs SVHN/Tiny-ImageNet, ImageNet vs ImageNet-O), active learning settings across different model architectures, as well as in large scale vision tasks like semantic segmentation, while being computationally cheaper