Laura Rifo

Full Bayesian Analysis for a Class of Jump-Diffusion Models

The Full Bayesian Significance Test (FBST) is adjusted for jump detection in a diffusion process. Under a natural parameterization, pure diffusion can be seen as a precise hypothesis. The evidence measure defined by FBST deals with absolutely continuous posterior distributions, when posterior rates for precise hypotheses are not appropriate. Applications to simulated and real data are shown.

Comparative Estimation for Discrete Fractional Ornstein-Uhlenbeck Process

We compare, theoretically and numerically, the maximum likelihood and the Bayes estimators for discretely observed fractional diffusions.

Full Bayesian Analysis for a Model of Tail Dependence

The family of the asymmetric logistic copulas appears naturally in modeling tail dependence. Within this family, some well-known models, as independence and logistic dependence, define precise hypotheses, having zero posterior probability for an absolute continuous posterior distribution. We show that the e-value associated to the Full Bayesian Significance Test has a good performance in non standard dependence problems, obtaining posterior estimates and predictive distributions. The analysis proposed is illustrated with two examples: (1) monthly sea level maxima at Newlyn and Sheerness, England (1990–2005) and (2) AIDS rates related to an educational indicator in U.S. Census Bureau (2007). We validate the inferences obtained through simulated data.

Long-range dependence and approximate Bayesian computation

ABSTRACT In this work, we propose a method for estimating the Hurst index, or memory parameter, of a stationary process with long memory in a Bayesian fashion. Such approach provides an approximation for the posterior distribution for the memory parameter and it is based on a simple application of the so-called approximate Bayesian computation (ABC), also known as likelihood-free method. Some popular existing estimators are reviewed and compared to this method for the fractional Brownian motion, for a long-range binary process and for the Rosenblatt process. The performance of our proposal is remarkably efficient.

Coding and decoding schemes tailor made for image transmission

In this work we explore possibilities for coding and decoding tailor made for image transmission. To do so, we introduce a loss function that expresses the overall performance of a coding scheme for discrete channels and exchange the usual goal of minimizing the error probability to that of minimizing the expected loss. In this environment we explore the possibilities of using poset-decoders to make a message-wise unequal error protection (UEP), where the most valuable information is protected by placing in its proximity information words that differ by small valued information. We give explicit examples, done for scale-of-gray images, including visual simulations for the BSMC.

Full Bayesian significance test for extremal distributions

A new Bayesian measure of evidence is used for model choice within the generalized extreme value family of distributions, given an absolutely continuous posterior distribution on the related parametric space. This criterion allows quantitative measurement of evidence of any sharp hypothesis, with no need of a prior distribution assignment to it. We apply this methodology to the testing of the precise hypothesis given by the Gumbel model using real data. Performance is compared with usual evidence measures, such as Bayes factor, Bayesian information criterion, deviance information criterion and descriptive level for deviance statistic.

A Simulation-Based Study on Bayesian Estimators for the Skew Brownian Motion

In analyzing a temporal data set from a continuous variable, diffusion processes can be suitable under certain conditions, depending on the distribution of increments. We are interested in processes where a semi-permeable barrier splits the state space, producing a skewed diffusion that can have different rates on each side. In this work, the asymptotic behavior of some Bayesian inferences for this class of processes is discussed and validated through simulations. As an application, we model the location of South American sea lions (Otaria flavescens) on the coast of Calbuco, southern Chile, which can be used to understand how the foraging behavior of apex predators varies temporally and spatially.

Interdisciplinary Bayesian Statistics

What About the Posterior Distributions When the Model is Non-dominated.- Bayesian Learning of Material Density Function by Multiple Sequential Inversions of 2-D Images in Electron Microscopy.- Problems with Constructing Tests to Accept the Null Hypothesis.- Cognitive-Constructivism, Quine, Dogmas of Empiricism, and Munchhausens Trilemma.- A maximum entropy approach to learn Bayesian networks from incomplete data.- Bayesian Inference in Cumulative Distribution Fields.- MCMC-Driven Adaptive Multiple Importance Sampling.- Bayes Factors for comparison of restricted simple linear regression coefficients.- A Spanning Tree Hierarchical Model for Land Cover Classification.- Nonparametric Bayesian regression under combinations of local shape constraints.- A Bayesian Approach to Predicting Football Match Outcomes Considering Time Effect Weight.- Homogeneity tests for 22 contingency tables.- Combining Optimization and Randomization Approaches for the Design of Clinical Trials.- Factor analysis with mixture modeling to evaluate coherent patterns in microarray data.

A Note on Bayesian Inference for Long-Range Dependence of a Stationary Two-State Process

In this work we propose a Bayesian approach for selecting the range of a stationary process with two states. The analysis is based on approximate posterior distributions of the Hurst index obtained from a likelihood-free method. Our empirical study shows that a main advantage of our approach, along with its of simplicity, is the possibility of obtaining an approximate sample of the posterior distribution on the Hurst index, thus providing better estimates. Furthermore, there is no need for Gaussian nor asymptotic assumptions.

Bayes decoding for discrete linear channels with semantic value of information

In this work we explore the decoding process when information words have different semantic values. In that setting, we introduce a convenient loss function that allows us to express the overall performance of a decoding scheme for discrete channels, switching the usual goal of minimizing the error probability to that of minimizing the expected loss.