Events

Optimal supermartingales for anytime-valid sequential testing

Statistical testing is`anytime-valid’ if the decision to stop or continue an experiment can depend on anything that has been observed so far, without compromising statistical error guarantees. For instance, suppose that a promising but inconclusive study receives funding to gather additional data. Then standard p-value analysis is invalidated, but anytime-valid testing is not. A recent approach to anytime-valid testing views a test statistic as a bet against the null hypothesis. These bets are constrained to be supermartingales - hence unprofitable - under the null, but designed to be profitable under the relevant alternative hypotheses. This perspective opens the door to using tools from financial mathematics. In this talk I will explain how notions such as supermartingale measures, fork-convexity, the optional decomposition theorem, and universal portfolios can be used to design optimal supermartingales for anytime-valid sequential testing. (This talk is based on ongoing work with Aaditya Ramdas (CMU) and Johannes Ruf (LSE).) 

Please Note: This talk will be given through Webex. To join, please click here: Department seminar by Martin Larsson

Insurance Risk Analysis of Financial Networks

We conduct a quantitative risk analysis of non-core insurance business of selling financial products to protect financial firms  against investment losses due to a shock. To achieve the goal, we construct a static structural model composed of a network of firms who cross-hold each other, multiple primitive assets that are vulnerable to a shock, and an insurer who resides external to the network and speculates in selling protection to financial firms. Assume that each firm in the network is rational and able to decide how much protection to purchase to optimize its portfolio according to the mean-variance principle. As a result, the shock may impact the insurer but indirectly through the network, and thus both the network integration and the shock are risk factors of this non-core insurance business. Our study focuses on describing their interactive role in the insurance risk. Depending on the shock size, an increase in the network integration (which refers to the level of exposures of firms to each other) may help reduce the insurance risk, or drive the insurer to a more profitable position, or hinder the insurer from making profit.

Please Note: This talk will be given on Webex. Click here to join: Seminar by Qihe Tang. 

Network Response Regression for Modeling Population of Networks with Covariates

Multiple-network data are fast emerging in recent years, where a separate network over a common set of nodes is measured for each individual subject, along with rich subject covariates information. Existing network analysis methods have primarily focused on modeling a single network, and are not directly applicable to multiple networks with subject covariates.

In this talk, we present a new network response regression model, where the observed networks are treated as matrix-valued responses, and the individual covariates as predictors. The new model characterizes the population-level connectivity pattern through a low-rank intercept matrix, and the parsimonious effects of subject covariates on the network through a sparse slope tensor. We formulate the parameter estimation as a non-convex optimization problem, and develop an efficient alternating gradient descent algorithm. We establish the non-asymptotic error bound for the actual estimator from our optimization algorithm. Built upon this error bound, we derive the strong consistency for network community recovery, as well as the edge selection consistency. We demonstrate the efficacy of our method through intensive simulations and two brain connectivity studies.

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Passcode: 318995

On the profitability of selfish blockchain mining under consideration of ruin

Mining blocks on a blockchain equipped with a proof of work consensus protocol is known to be resource-consuming. A miner bears the operational cost, mainly electricity consumption and IT gear, of mining, and is compensated by a capital gain when a block is discovered. In this talk we quantify the profitability of mining when the possible event of ruin is also taken into consideration. This is done by formulating a tractable stochastic model and using tools from actuarial ruin theory and analysis, including the explicit solution of a certain type of advanced functional differential equation. The expected profit at a future time point is determined for the situation when the miner follows the protocol as well as when he/she withholds blocks.  The obtained explicit expressions allow to analyze the sensitivity with respect to the different model ingredients and to identify conditions under which selfish mining is a strategic advantage. The talk is based on joint work with P.O. Goffard.

Please Note: This talk will be hosted on Webex.  To join please the following link: Department Seminar by Hansjoerg Albrecher

A new framework for modeling sparse networks that makes sense (and can actually be fit!)

Latent position models are a versatile tool when working with network data. Applications include clustering entities, network visualization, and controlling for unobserved causal confounding. In traditional treatments of the latent position model, the nodes’ latent positions are viewed as independent and identically distributed random variables. This assumption implies that the average node degree grows linearly with the number of nodes in the network, making it inappropriate when the network is sparse. In the first part of this talk, I will propose an alternative assumption—that the latent positions are generated according to a Poisson point process—and show that it is compatible with various levels of network sparsity. I will also provide theory establishing that the nodes’ latent positions can be consistently estimated, provided that the network isn't too sparse.  In the second part of the talk, I will consider the computational challenge of fitting latent position models to large datasets. I will describe a new Markov chain Monte Carlo strategy—based on a combination of split Hamiltonian Monte Carlo and Firefly Monte Carlo—that is much more efficient than the standard Metropolis-within-Gibbs algorithm for inferring the latent positions. Throughout the talk, I will use an advice-sharing network of elementary school teachers within a school district as a running example.

Please note: This talk will be hosted on Webex. To join please click on the following link: Department seminar by Neil Spencer.

De Finetti's optimal dividends problem with linearly bounded payment rates

Aiming for more realistic optimal dividend policies, we consider a stochastic control problem with linearly bounded control rates using a performance function given by the expected present value of dividend payments made up to ruin. In a Brownian model, we prove the optimality of a member of a new family of control strategies called delayed linear control strategies, for which the controlled process is a refracted diffusion process. For some parameters specifications, we retrieve the strategy initially proposed by Avanzi & Wong (2012) to regularize dividend payments, which is more consistent with actual practice.

Please Note: This talk will be hosted on Webex. To join please the following link: Department Seminar by Jean-Francois Renaud

Please Note: This seminar will be given online.

Unified Principal Component Analysis for Sparse and Dense Functional Data under Spatial Dependency

What are the contributions that international development can make in addressing COVID-19? What does the future hold for international development? Please join us for a conversation between international development practitioners and policy makers on the implications the global community faces in the COVID-19 era, the security challenges, and the future of international development projects during a global pandemic.

See the full details on the Waterloo International event page.

Please Note: This seminar will be given online.

Data-Adaptive Regression Modeling in High Dimensions

Please Note: This seminar will be given online.

Analysis of Prescription Drug Utilization with Beta Regression Models