´¡²ú²õ³Ù°ù²¹³¦³Ù:Ìý The relationship between confidence intervals and null hypothesis significance testing is well known and is a topic taught in introductoryÌýstatistics. In contrast, within the Bayesian paradigm, the relationship between the Bayes factor and credible intervals is not well known.ÌýWe examined the relationship between the Bayes factor and the separation of credible intervals in between- and within-subject designsÌýunder a range of effect and sample sizes. For the within-subject case, we considered five intervals: (1) the within-subject confidenceÌýinterval of Loftus and Masson (1994), (2) the within-subject Bayesian interval developed by Nathoo, Kilshaw, and Masson (2018), whoseÌýderivation conditions on estimated random effects, (3) and (4) two modifications of (2) based on a proposal by Heck (2019) to allow forÌýshrinkage and account for uncertainty in the estimation of random effects, and (5) the standard Bayesian highest-density interval. WeÌýderived and observed through simulations a clear and consistent relationship between the Bayes factor and the separation of credibleÌýintervals. Remarkably, this relationship, for a given sample size, is well described by a simple quadratic exponential curve and is mostÌýprecise in case (4). This observation is formalized through a limiting theorem for the case of between-subject designs with two conditions.

Abstract:Ìý The Random Subspace Method (RSM) is anÌýensemble procedure in which each constituent learner isÌýconstructed using a randomly chosen subset of the dataÌýfeatures. Regression trees are ideal candidate learnersÌýin RSM ensembles. By constructing trees upon differentÌýfeature subsets, RSM reduces correlation between treesÌýresulting in a stronger ensemble. Furthermore, it lessensÌýcomputational burden by only considering a subset ofÌýthe features when building each tree.ÌýDespite its apparent advantages, RSM has a notableÌýdrawback. In some instances a randomly chosen subspaceÌýÌýmay lack informative features. This is especiallyÌýtrue in situations in which the number of trulyÌýinformative variables is small relative to the total numberÌýof variables. Trees that are constructed using featureÌýsubsets lacking informative features can be damagingÌýto the ensemble.

Here we present Grafted Random Subspaces (GRS)Ìýand Vanishing Random Subspaces (VRS), two novelÌýÌýensemble procedures designed to remedy theÌýaforementioned drawback by reusing information across trees.ÌýBoth techniques borrow from RSM by growing individualÌýtrees on randomly selected feature subsets. For eachÌýtree in a GRS ensemble, the most important variableÌýis identified and guaranteed inclusion into the next qÌýfeature subsets. This allows GRS to recycle a promisingÌýfeature from one tree across several successive trees, effectively grafting the variable into the next q activeÌýsubsets. In the VRS procedure the least importantÌýfeature is guaranteed exclusion from the next q featureÌýsubsets. This creates a more enriched pool of candidateÌývariables from which the successive feature subsets areÌýdrawn.

´¡²ú²õ³Ù°ù²¹³¦³Ù:Ìý The Southern Resident killer whale (SRKW) is anÌýendangeredÌýÌýpopulation of whales found inÌýthe northeast Pacific. They have a vocal dialect unique from other killerÌýwhales, having a repertoireÌýof distinct stereotyped calls. A framework forÌýdistinguishing SRKW call types using the frequency traces of the amplitudeÌýridges from their spectrograms (termed frequency ridges) is proposed.ÌýThe firstÌýstep is the extraction of these frequency ridges of SRKW calls using anÌýSequential Monte Carlo (SMC) approach. Next, these frequency ridges areÌýconverted into functional data usingÌýB-spline functions. They are analysed withÌýa functional principal component (FPC) analysis to characterise the intrinsicÌývariability of frequency ridges within a call type. The FPCs are able toÌýcapture the general patterns in the frequency ridges of the different SRKW callÌýtypes. The FPCs are also used as the basis for call classification. ThisÌýframework proves to be successful forÌýclassification with some call typesÌýcorrectly classified almost 80\% of the time, while other calls are less wellÌýdiscriminated. On balance, this approach showed reasonable performance givenÌýthe small sample size available.

´¡²ú²õ³Ù°ù²¹³¦³Ù:Ìý Clustering trajectories of diseaseÌýprogression can help in understanding the variability of disease pathways.ÌýRecently, a latent class mixedÌýeffect models (LCMM) approach was developed andÌýhas been applied to a wide range of progressive diseases to discover the underlyingÌýpatterns of deterioration in function. Often, biological and medical data haveÌýcomplicated structures and substantial noise. Therefore, we useÌýsimulationÌýstudies to explore the ability of LCMMs to accurately classify individuals forÌýa wide range of noise and variability in trajectories and toÌýprovide guidelinesÌýfor model specification when using this technique. Datasets were simulated fromÌý24 scenarios covering different dataÌýstructures and variability levels. We findÌýthat LCMMs can reliably recover trajectory subgroups and model parameters evenÌýfor datasets thatÌýcontain unbalanced subgroups and in which subjects areÌýfollowed irregularly with different and short follow-up times, if the ratio ofÌýthe between-individual and total variance is relatively small. When the variabilityÌýis high in the data, LCMMs have difficulty classifying individuals into theÌýcorrect subgroups and thus should be applied with caution.

This work is done in collaboration with JiachenÌýChen, Joanne M. Murabito, and Kathryn L. Lunetta.

Abstract.ÌýWe introduce the partial loop erasure (PLE) procedure, under which loops are erased only when the Markov chain enters a subset of the state space. We will prove an equality in law of the usual loop-erased random walk (LERW) and the simple path obtained through an integrated PLE procedure. The equality has applications on some fractal spaces, including the existence of the scaling limits of LERW on the Sierpinski gasket and on (planar) Sierpinski carpets. For simplicity, I will the Sierpinski gasket as a concrete example. And, I will review the construction of the Brownian motion on the Sierpinski gasket for necessary backgrounds at the beginning of the talk.
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Topic: Nov 4, 2022 – Statistics & Probability Seminar
Time: Nov 4, 2022 02:45 PM America/Toronto

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Talk titled: Introducing Actuarial Science.

´¡²ú²õ³Ù°ù²¹³¦³Ù:Ìý I plan to discuss about the actuarial profession, the similarities and differences of the two societies (CAS and SOA), and the CAS examination process.Ìý The remaining of the time, I will answer any questions the students may have.