Abstract: Generative Adversarial Net (GAN) has proved to be a powerful machine learning tool in image data analysis and generation. In this paper, we propose to use Conditional Generative Adversarial Net (CGAN) to learn and simulate time series data. The conditions include both categorical and continuous variables with different auxiliary information. Our simulation studies show that CGAN has the capability to learn different types of normal and heavy-tailed distributions, as well as dependent structures of different time series. It also has the capability to generate conditional predictive distributions consistent with training data distributions. We also provide an in-depth discussion on the rationale behind GAN and the neural networks as hierarchical splines to establish a clear connection with existing statistical methods of distribution generation. In practice, CGAN has a wide range of applications in market risk and counterparty risk analysis: it can be applied to learn historical data and generate scenarios for the calculation of Value-at-Risk (VaR) and Expected Shortfall (ES), and it can also predict the movement of the market risk factors. We present a real data analysis including a backtesting to demonstrate that CGAN can outperform Historical Simulation (HS), a popular method in market risk analysis to calculate VaR. CGAN can also be applied in economic time series modeling and forecasting. In this regard, we have included an example of hypothetical shock analysis for economic models and the generation of potential CCAR scenarios by CGAN at the end of the paper.
Abstract: Quality measurement and reporting systems are used in healthcare internationally. In Australia, the Australian Council on Healthcare Standards records and reports hundreds of clinical indicators (CIs) nationally across the healthcare system. These CIs are measures of performance in the clinical setting, and are used as a screening tool to help assess whether a standard of care is being met. Existing analysis and reporting of these CIs incorporate Bayesian methods to address sampling variation; however, such assessments are retrospective in nature, reporting upon the previous six or twelve months of data. The use of Bayesian methods within statistical process control for monitoring systems is an important pursuit to support more timely decision-making. Our research has developed and assessed a new graphical monitoring tool, similar to a control chart, based on the beta-binomial posterior predictive (BBPP) distribution to facilitate the real-time assessment of health care organizational performance via CIs. The BBPP charts have been compared with the traditional Bernoulli CUSUM (BC) chart by simulation. The more traditional “central” and “highest posterior density” (HPD) interval approaches were each considered to define the limits, and the multiple charts were compared via in-control and out-of-control average run lengths (ARLs), assuming that the parameter representing the underlying CI rate (proportion of cases with an event of interest) required estimation. Preliminary results have identified that the BBPP chart with HPD-based control limits provides better out-of-control run length performance than the central interval-based and BC charts. Further, the BC chart’s performance may be improved by using Bayesian parameter estimation of the underlying CI rate.
Abstract: In this paper, we present the human action recognition method using the variational Bayesian HMM with the Dirichlet process mixture (DPM) of the Gaussian-Wishart emission model (GWEM). First, we define the Bayesian HMM based on the Dirichlet process, which allows an infinite number of Gaussian-Wishart components to support continuous emission observations. Second, we have considered an efficient variational Bayesian inference method that can be applied to drive the posterior distribution of hidden variables and model parameters for the proposed model based on training data. And then we have derived the predictive distribution that may be used to classify new action. Third, the paper proposes a process of extracting appropriate spatial-temporal feature vectors that can be used to recognize a wide range of human behaviors from input video image. Finally, we have conducted experiments that can evaluate the performance of the proposed method. The experimental results show that the method presented is more efficient with human action recognition than existing methods.
Abstract: We present probabilistic multinomial Dirichlet
classification model for multidimensional data and Gaussian process
priors. Here, we have considered efficient computational method that
can be used to obtain the approximate posteriors for latent variables
and parameters needed to define the multiclass Gaussian process
classification model. We first investigated the process of inducing a
posterior distribution for various parameters and latent function by
using the variational Bayesian approximations and important sampling
method, and next we derived a predictive distribution of latent
function needed to classify new samples. The proposed model is
applied to classify the synthetic multivariate dataset in order to verify
the performance of our model. Experiment result shows that our model
is more accurate than the other approximation methods.
Abstract: In this talk, we introduce a newly developed quantile
function model that can be used for estimating conditional
distributions of financial returns and for obtaining multi-step ahead
out-of-sample predictive distributions of financial returns. Since we
forecast the whole conditional distributions, any predictive quantity
of interest about the future financial returns can be obtained simply
as a by-product of the method. We also show an application of the
model to the daily closing prices of Dow Jones Industrial Average
(DJIA) series over the period from 2 January 2004 - 8 October 2010.
We obtained the predictive distributions up to 15 days ahead for
the DJIA returns, which were further compared with the actually
observed returns and those predicted from an AR-GARCH model.
The results show that the new model can capture the main features
of financial returns and provide a better fitted model together with
improved mean forecasts compared with conventional methods. We
hope this talk will help audience to see that this new model has the
potential to be very useful in practice.
Abstract: A comprehensive Bayesian analysis has been carried out in the context of informative and non-informative priors for the shape parameter of the Burr type X distribution under different symmetric and asymmetric loss functions. Elicitation of hyperparameter through prior predictive approach is also discussed. Also we derive the expression for posterior predictive distributions, predictive intervals and the credible Intervals. As an illustration, comparisons of these estimators are made through simulation study.
Abstract: The article is concerned with analysis of failure rate (shape parameter) under the Topp Leone distribution using a Bayesian framework. Different loss functions and a couple of noninformative priors have been assumed for posterior estimation. The posterior predictive distributions have also been derived. A simulation study has been carried to compare the performance of different estimators. A real life example has been used to illustrate the applicability of the results obtained. The findings of the study suggest that the precautionary loss function based on Jeffreys prior and singly type II censored samples can effectively be employed to
obtain the Bayes estimate of the failure rate under Topp Leone distribution.