arXiv subjects

Thomas Fung

Publications and source records attributed to Thomas Fung.

8 recordsLinked to original sources

arXiv2026

Mind or Message? Auditing Theory of Mind in Multi-Agent Social Simulation

Language model agents are increasingly used to simulate social interaction, and the resulting transcripts read as though the agents understand one another. We ask whether that appearance rests on a model of the partner's mind or on the surface record of what the partner said. We build a social simulation in which both questions have exact answers: 40 multi-issue negotiations whose hidden preference weights and whose full Pareto frontier are known by construction. Two model families negotiate across 160 dyads, every transcript is frozen before any measurement, and 2880 counterfactual probes then hold the evidence byte identical while moving one factor at a time: the reader's own stake, the partner's tone, an identity label, and the order of recursion. The agents are socially fluent and economically poor. They reach agreement in 96.2% of dyads with 0 protocol failures, yet only 0.7% of deals land on the Pareto frontier, they leave 20.5% of the available joint value unclaimed, and they miss the one issue on which their interests are perfectly aligned in 76.6% of deals; on the frontier and on that aligned issue, a package drawn at random from the set both sides would accept does as well. The probes locate the failure. Swapping only the reader's own payoff sheet, while the partner's words and offers stay identical, moves the inferred top priority by 15.0 percentage points, which is egocentric projection rather than inference, while a tone rewrite moves it by 5.3 percentage points and an identity label by 0.0. Most tellingly, an agent predicts what its partner believes about it 72.5% of the time while that partner's belief is itself correct only 51.2% of the time: the agents track the conversation far better than they track the mind behind it.

cs.LG↗

arXiv2022

Tail asymptotics for the bivariate skew normal in the general case

The present paper is a sequel to and generalization of Fung and Seneta (2016) whose main result gives the asymptotic behaviour as $ u \to 0^{+}$ of $λ_L(u) = P(X_1 \leq F_1^{-1}(u) | X_2 \leq F_2^{-1}(u)),$ when $\bf{X} \sim SN_2(\boldsymbolα, R)$ with $α_1 = α_2 = α,$ that is: for the bivariate skew normal distribution in the equi-skew case, where $R$ is the correlation matrix, with off-diagonal entries $ρ,$ and $F_i(x), i=1,2$ are the marginal cdf's of $\textbf{X}$. A paper of Beranger et al. (2017) enunciates an upper-tail version which does not contain the constraint $α_1=α_2= α$ but requires the constraint $0 <ρ<1$ in particular. The proof, in their Appendix A.3, is very condensed. When translated to the lower tail setting of Fung and Seneta (2016), we find that when $α_1=α_2= α$ the exponents of $u$ in the regularly varying function asymptotic expressions do agree, but the slowly varying components, always of asymptotic form $const (-\log u)^τ$, are not asymptotically equivalent. Our general approach encompasses the case $ -1 <ρ< 0$, and covers all possibilities.

math.ST↗

arXiv2021

Consistent second-order discrete kernel smoothing using dispersed Conway-Maxwell-Poisson kernels

The histogram estimator of a discrete probability mass function often exhibits undesirable properties related to zero probability estimation both within the observed range of counts and outside into the tails of the distribution. To circumvent this, we formulate a novel second-order discrete kernel smoother based on the recently developed mean-parametrized Conway--Maxwell--Poisson distribution which allows for both over- and under-dispersion. Two automated bandwidth selection approaches, one based on a simple minimization of the Kullback--Leibler divergence and another based on a more computationally demanding cross-validation criterion, are introduced. Both methods exhibit excellent small- and large-sample performance. Computational results on simulated datasets from a range of target distributions illustrate the flexibility and accuracy of the proposed method compared to existing smoothed and unsmoothed estimators. The method is applied to the modelling of somite counts in earthworms, and the number of development days of insect pests on the Hura tree.

stat.ME↗

arXiv2020

Tail asymptotics for the bivariate equi-skew Variance-Gamma distribution

We derive the asymptotic rate of decay to zero of the tail dependence of the bivariate skew Variance Gamma (VG) distribution under the equal-skewness condition, as an explicit regularly varying function. Our development is in terms of a slightly more general bivariate skew Generalized Hyperbolic (GH) distribution. Our initial reduction of the bivariate problem to a univariate one is motivated by our earlier study of tail dependence rate for the bivariate skew normal distribution

math.ST↗

arXiv2017

Quantile function expansion using regularly varying functions

We present a simple result that allows us to evaluate the asymptotic order of the remainder of a partial asymptotic expansion of the quantile function $h(u)$ as $u\to 0^+$ or $1^-$. This is focussed on important univariate distributions when $h(\cdot)$ has no simple closed form, with a view to assessing asymptotic rate of decay to zero of tail dependence in the context of bivariate copulas. The Introduction motivates the study in terms of the standard Normal. The Normal, Skew-Normal and Gamma are used as initial examples. Finally, we discuss approximation to the lower quantile of the Variance-Gamma and Skew-Slash distributions.

math.ST↗

arXiv2016

Semiparametric generalized linear models for time-series data

Time-series data in population health and epidemiology often involve non-Gaussian responses. In this note, we propose a semiparametric generalized linear models framework for time-series data that does not require specification of a working conditional response distribution for the data. Instead, the underlying response distribution is treated as an infinite-dimensional parameter which is estimated simultaneously with the usual finite-dimensional parameters via a maximum empirical likelihood approach. A general consistency result for the resulting estimators is given. Simulations suggest that both estimation and inferences using the proposed method can perform as well as correctly-specified parametric models even for moderate sample sizes, but can be more robust than parametric methods under model misspecification. The method is used to analyse the Polio dataset from Zeger (1988) and a recent Kings Cross assault dataset from Menendez et al. (2015).

stat.ME↗

arXiv2015

Tail dependence convergence rate for the bivariate skew normal under the equal-skewness condition

We derive the rate of decay of the tail dependence of the bivariate skew normal distribution under the equal-skewness condition θ1 = θ2,= θ, say. The rate of convergence depends on whether θ > 0 or θ < 0. The latter case gives rate asymp- totically identical with the case θ = 0. The asymptotic behaviour of the quantile function for the univariate skew normal is part of the theoretical development.

math.ST↗

arXiv2013

Convergence rate to a lower tail dependence coefficient of a skew-t distribution

We examine the rate of decay to the limit of the tail dependence coefficient of a bivariate skew t distribution which always displays asymptotic tail dependence. It contains as a special case the usual bivariate symmetric t distribution, and hence is an appropriate (skew) extension. The rate is asymptotically power-law. The second-order structure of the univariate quantile function for such a skew-t distribution is a central issue.

math.ST↗