Mathematics & Statisticshttp://hdl.handle.net/10344/202020-07-07T10:25:04Z2020-07-07T10:25:04ZA multi-parameter regression model for interval censored survival dataPeng, DefenMacKenzie, GilbertBurke, Kevinhttp://hdl.handle.net/10344/89782020-07-03T00:02:31Z2020-01-01T00:00:00ZA multi-parameter regression model for interval censored survival data
Peng, Defen; MacKenzie, Gilbert; Burke, Kevin
We develop flexible multiparameter regression (MPR) survival models for interval‐censored survival data arising in longitudinal prospective studies and longitudinal randomised controlled clinical trials. A multiparameter Weibull regression survival model, which is wholly parametric, and has nonproportional hazards, is the main focus of the article. We describe the basic model, develop the interval‐censored likelihood, and extend the model to include gamma frailty and a dispersion model. We evaluate the models by means of a simulation study and a detailed reanalysis of data from the Signal Tandmobiel study. The results demonstrate that the MPR model with frailty is computationally efficient and provides an excellent fit to the data.
peer-reviewed; The full text of this article will not be available in ULIR until the embargo expires on the 24/04/2021
2020-01-01T00:00:00ZA generalization of the classical Kelly betting formula to the case of temporal correlationO'Brien, Joseph D.Burke, KevinBurke, Mark E.Barmish, Ross B.http://hdl.handle.net/10344/89742020-07-02T00:02:06Z2020-01-01T00:00:00ZA generalization of the classical Kelly betting formula to the case of temporal correlation
O'Brien, Joseph D.; Burke, Kevin; Burke, Mark E.; Barmish, Ross B.
For sequential betting games, Kelly’s theory, aimed at maximization of the logarithmic growth of one’s account value, involves optimization of the so-called betting fraction K. In this Letter, we extend the classical formulation to allow for temporal correlation among bets. To demonstrate the potential of this new paradigm, for simplicity of exposition, we mainly address the case of a coin-flipping game with even-money payoff. To this end, we solve a problem with memory depth m. By this, we mean that the outcomes of coin flips are no longer assumed to be i.i.d. random variables. Instead, the probability of heads on flip k depends on previous flips k-1,k-2,...,k-m. For the simplest case of n flips, with m=1, we obtain a closed form solution Kn for the optimal betting fraction. This generalizes the classical result for the memoryless case. That is, instead of fraction K*=2p-1 which pervades the literature for a coin with probability of heads p≥1/2, our new fraction Kn depends on both n and the parameters associated with the temporal correlation. Generalizations of these results for m>1 and numerical simulations are also included. Finally, we indicate how the theory extends to time-varying feedback and alternative payoff distributions.
peer-reviewed
2020-01-01T00:00:00ZDynamics impose limits to detectability of network structureAsllani, MalbordaCunha, Bruno RequiãoEstrada, ErnestoGleeson, James P.http://hdl.handle.net/10344/89682020-06-30T00:02:13Z2020-01-01T00:00:00ZDynamics impose limits to detectability of network structure
Asllani, Malbor; daCunha, Bruno Requião; Estrada, Ernesto; Gleeson, James P.
Networks are universally considered as complex structures of interactions of large multi-component systems. To determine the role that each node has inside a complex network, several centrality measures have been developed. Such topological features are also crucial for their role in the dynamical processes occurring in networked systems. In this paper, we argue that the dynamical activity of the nodes may strongly reshape their relevance inside the network, making centrality measures in many cases, misleading. By proposing a generalisation of the communicability function, we show that when the dynamics taking place at the local level of the node is slower than the global one between the nodes, then the system may lose track of the structural features. On the contrary, hidden global properties such as the shortest path distances can be recovered only in the limit where network-level dynamics are negligible compared to node-level dynamics. From the perspective of network inference, this constitutes an uncertainty condition, in the sense that it limits the extraction of multi-resolution information about the structure, particularly in the presence of noise. For illustration purposes, we show that for networks with different time-scale structures such as strong modularity, the existence of fast global dynamics can imply that precise inference of the community structure is impossible.
peer-reviewed
2020-01-01T00:00:00ZQuantifying uncertainty in a predictive model for popularity dynamicsO'Brien, Joseph D.Aleta, AlbertoMoreno, YamirGleeson, James P.http://hdl.handle.net/10344/89472020-06-24T00:01:36Z2020-01-01T00:00:00ZQuantifying uncertainty in a predictive model for popularity dynamics
O'Brien, Joseph D.; Aleta, Alberto; Moreno, Yamir; Gleeson, James P.
The Hawkes process has garnered attention in recent years for its suitability to describe the behavior of online information cascades. Here we present a fully tractable approach to analytically describe the distribution of the number of events in a Hawkes process, which, in contrast to purely empirical studies or simulation-based models, enables the effect of process parameters on cascade dynamics to be analyzed.We show that the presented
theory also allows predictions regarding the future distribution of events after a given number of events have been observed during a time window. Our results are derived through a differential-equation approach to attain the governing equations of a general branching process. We confirm our theoretical findings through extensive simulations of such processes. This work provides the basis for more complete analyses of the self-exciting processes that govern the spreading of information through many communication platforms, including the potential to predict cascade dynamics within confidence limits.
peer-reviewed
2020-01-01T00:00:00Z