Statistics / BRG

Room 4192, Earth Sciences Building (2207 Main Mall)

Thu 28th July 2016Room 4192, Earth Sciences Building (2207 Main Mall)

4:00pm

Inferring Brain Signals Synchronicity from a Sample of EEG Readings

Show Abstract
Inferring patterns of synchronous brain activity from a heterogeneous sample of electroencephalograms (EEG) is scientifically and methodologically challenging. While it is statistically appealing to rely on readings from more than one individual in order to highlight patterns of coordinated brain activities, pooling information across subjects presents with non trivial methodological problems. We discuss some of the scientific issues associated with the understanding of synchronized neuronal activity and propose a methodological framework for statistical inference from a sample of EEG readings. Our work builds on classical contributions in time-series, cluster and functional data analysis, in an effort to reframe a challenging inferential problem in the context of familiar analytical techniques. Some attention is paid to computational issues, with a proposal based on the hybrid combination of machine learning and Bayesian techniques.

Statistics

Room 4192, Earth Sciences Building (2207 Main Mall)

Tue 19th July 2016Room 4192, Earth Sciences Building (2207 Main Mall)

11:00am

Some mechanisms leading to underdispersion of count data

Show Abstract
The theory of Poisson-overdispersed count models has been developed in deep, and consequently there are many known "physical mechanisms" leading to overdispersion. For instance, the general families of Mixed Poisson and Compound Poisson distributions are always overdispersed. These physical mechanisms can be interpreted and successfully used for health sciences and biological modelling. There are also some mechanisms leading to underdispersion but they are not very known. In this talk we are going to review some of them and present new methods and applications. The first mechanism considered is a Poisson-type process where the waiting times are not exponentially distributed. Barlow and Proschan in the 1960s showed that Increasing (Decreasing) Failure Rate distributions for the waiting times produce under(over)-dispersed count distributions. Examples of this mechanism are the models of Winkelmann (1995) using Gamma and Weibull waiting times. The second mechanism is the extended Poisson process of Faddy and Bosch (2001) based on the fact that any count distribution can be represented as a pure birth process with non-constant rates. This representation not always has a simple and meaningful interpretation. The third mechanism is provided by the limiting distribution of a M/M/1 queuing model, where the service time depends of the number of individuals in the queue. An example of this is the original development of the COM-Poisson distribution. This mechanism allows to construct new distributions capable to explain the behaviour of the counts of chromosomal aberrations under high doses of radiation (see Pujol et al., 2014). Finally we will introduce some new mechanisms based on the binomial subsampling operation (p-thinning). It is known that the Poisson distribution is closed under p-thinnings, but if p depends of the number of Poisson realizations the resulting distribution can be underdispersed. Several examples of application will be analyzed and discussed.

References

[1] Faddy, MJ. and Bosch RJ. (2001). Likelihood-Based Modeling and Analysis of Data Underdispersed Relative to the Poisson Distribution. Biometrics, 57, 620-624.

[2] Pujol M., Barquinero JF., Puig P., Puig R., Caballin MR., Barrios L. (2014). A New Model of Biodosimetry to Integrate Low and High Doses. PLoSONE, 9(12):e114137.

[3] Winkelmann, R.(1995). Duration Dependence and Dispersion in Count-Data Models. Journal of Business and Economic Statistics, 13(4), 467-474.

Statistics

Room 4192, Earth Sciences Building (2207 Main Mall)

Thu 14th July 2016Room 4192, Earth Sciences Building (2207 Main Mall)

11:00am

Multivariate investigations in ecology: The search for significance

Show Abstract
Ecosystems are composed of multiple layers of interactions within and among biotic communities and their environments, leading to multivariate ecological studies. One of the fundamental questions in ecology is why biodiversity arose, and how it is maintained. Namely, why are species in a particular location, why and how do these species persist, and how do these species affect one another? My area of interest lies in trophic interactions, such as predator-prey dynamics, considering the flow of energy among various organisms as one of the main drivers of ecosystem function. Identifying the “true” ecological factors from a suite of possibilities is challenging, thus the tendency to rely on tests that produce a measure of statistical significance. As examples, I will draw on my research experiences with examining sponge composition on Caribbean coral reefs, and the spatial distribution of exploited seahorse populations in Southeast Asia. Because statistical significance does not always denote a significant ecological effect, I combined statistical outcomes with probable or confirmed mechanistic pathways. This allows for a fuller understanding of my study systems, a useful and necessary step for real-world applications, such as ecosystem-based fisheries management.

Statistics

Room 4192, Earth Sciences Building (2207 Main Mall)

Thu 7th July 2016Room 4192, Earth Sciences Building (2207 Main Mall)

4:00pm

Improved nonparametric estimation of the number of zeros and illustrations

Show Abstract
In this talk we present some lower bounds for the probability of zero for the class of count distributions having a log-convex probability generating function, which includes Compound and Mixed Poisson distributions. These lower bounds allow to construct non-parametric estimators of the non-observed number of zeros, which are useful in capture-recapture models. Some of these bounds lead to the well known Chao's and Turing's estimators. Several examples of application are analyzed and discussed.

Statistics

Room 4192, Earth Sciences Building (2207 Main Mall)

Tue 5th July 2016Room 4192, Earth Sciences Building (2207 Main Mall)

11:00am

Vincent Zhai, PhD Student, UBC Statistics

Stochastic Processes, Statistical Inference and Efficient Algorithms for Phylogenetic Inference

Show Abstract
Phylogenetic inference aims to reconstruct the evolutionary history of populations or species. With the rapid expansion of genetic data available, statistical methods play an increasingly important role in phylogenetic inference. In this talk, we present new evolutionary models, statistical inference methods and efficient algorithms for reconstructing phylogenetic trees at the level of populations using single nucleotide polymorphism data and at the level of species using multiple sequence alignment data.

At the level of populations, we introduce a new inference method to estimate evolutionary distances for any two populations to their most recent common ancestral population using single-nucleotide polymorphism allele frequencies. Our method is based on a new evolutionary model for both drift and fixation. To scale this method to large numbers of populations, we introduce the asymmetric neighbor-joining algorithm, an efficient method for reconstructing rooted bifurcating trees.

At the level of species, we introduce a continuous time stochastic process, the geometric Poisson indel process, that allows indel rates to vary across sites. We design an efficient algorithm for computing the probability of a given multiple sequence alignment based on our new indel model. We describe a method to construct phylogeny estimates from a fixed alignment using neighbor-joining.