Sung Nok Chiu

• Hong Kong Baptist University

In a recent prominent study, Worobey et al. (2022. The Huanan Seafood Wholesale Market in Wuhan was the early epicenter of the COVID-19 pandemic. Science, 377(6609), 951–959) purported to demonstrate statistically that the Huanan Seafood Wholesale Market was the epicentre of the early COVID-19 epidemic. We show that this statistical conclusion is i...

We criticize a statistical proof of the hypothesis that the Huanan seafood wholesale market was the epicenter of the COVID-19 pandemic. There are three points in the proof we consider critically: (1) The Huanan seafood wholesale market is not a data-driven location. (2) The assumption that a centroid of early case locations or another simply constr...

This work focuses on the invertibility of non-constant shape Gaussian asymmetric interpolation matrix, which includes the cases of both variable and random shape parameters. We prove a sufficient condition for that these interpolation matrices are invertible almost surely for the choice of shape parameters. The proof is then extended to the case of...

We argue and show empirically that for the Monte Carlo test, if the pseudo-random numbers are replaced by a randomized low discrepancy sequence, the actual errors in approximating the p-value are smaller and the deviations of the exact level from the nominal level have higher potential to be smaller. Hence in real applications the proposed method,...

By exploiting the meshless property of kernel-based collocation methods, we propose a fully automatic numerical recipe for solving interpolation/regression and boundary value problems adaptively. The proposed algorithm is built upon a least-squares collocation formulation on some quasi-random point sets with low discrepancy. A novel strategy is pro...

We develop a model-free isotropy test for spatial point patterns. The proposed test statistic assesses the discrepancy between the uniform distribution and the empirical normalised reduced second-order moment measure of a sector of increasing central angle. The null distribution of the test statistic is approximated by the empirical distribution ob...

The methods of computing the ridge parameters have been studied for more than four decades. However, there is still no way to compute its optimal value. Nevertheless, many methods have been proposed to yield ridge regression estimators of smaller mean squared errors than the least square estimators empirically. This paper compares the mean squared...

Electroacupuncture is a safe treatment for chronic neck pain. Nonetheless, one month after treatment, improvement of neck pain is similar to that in placebo-treated controls. This suggests that the efficacy may not be due to specific effect of the treatment procedure.

An extensive update to a classic text Stochastic geometry and spatial statistics play a fundamental role in many modern branches of physics, materials sciences, engineering, biology and environmental sciences. They offer successful models for the description of random two- and three-dimensional micro and macro structures and statistical methods fo...

For testing stationarity of a given spatial point pattern, Guan (2008) proposed a model-free statistic, based on the deviations between observed and expected counts of points in expanding regions within the sampling window. This article extends his method to a general class of statistics by incorporating also such information when points are projec...

We prove that the complete monotonicity is preserved under mixed geometric compounding, and hence show that the ruin probability, the Laplace transform of the ruin time, and the density of the tail of the joint distribution of ruin and the deficit at ruin in the Sparre Andersen model are completely monotone if the claim size distribution has a comp...

We consider the asymptotic variance of vacancy (AVV) in the high intensity small-grain Boolean model. Subjecting the grains to rotations or, more generally, linear distortions gives rise to a function which maps distortion distributions to the AVV of the corresponding Boolean model. We mainly study continuity properties of this function, where we u...

There is a paucity of knowledge on dysphagia in patients with nasopharyngeal carcinoma postradiotherapy (NPC post-RT). The purpose of this study was to establish silent aspiration occurrence, safe bolus consistency, and their relationship with swallowing physiology in patients with dysphagic NPC post-RT. Eighty-five patients with dysphagic NPC post...

The parametric bootstrap tests and the asymptotic or approximate tests for detecting difference of two Poisson means are compared. The test statistics used are the Wald statistics with and without log-transformation, the Cox F statistic and the likelihood ratio statistic. It is found that the type I error rate of an asymptotic/approximate test may...

The Gaussian kernel density estimator is known to have substantial problems for bounded random variables with high density at the boundaries. For independent and identically distributed data, several solutions have been put forward to solve this boundary ...

In this paper we compare the size distortions and powers for Pearson's [chi]2-statistic, likelihood ratio statistic LR, score statistic SC and two statistics, which we call UT and VT here, proposed by [Potthoff, R.F., Whittinghill, M., 1966. Testing for homogeneity: II. The Poisson distribution. Biometrika 53, 183-190] for testing the equality of t...

A class of statistics for testing the goodness-of-fit for any multivariate continuous distribution is proposed. These statistics consider not only the goodness-of-fit of the joint distribution but also the goodness-of-fit of all marginal distributions, and can be regarded as generalizations of the multivariate Cramér-von Mises statistic. Simulation...

Purpose This study aimed to investigate (a) the accuracy of adult reports in assessing the vocabulary knowledge of Cantonese-speaking children with hearing impairment (HI) and (b) the factors that are associated with the accuracy of those reports. Method The first participant group consisted of 47 children and their mothers. The second group consi...

A very common way of analyzing different and complicated plant behaviors is to use spatial point pattern analysis, which allows us to assess whether there is any structure present. To test the complete spatial randomness hypothesis, Diggle (1979) proposed a Monte Carlo test whose test statistic is the discrepancy between the estimated and the theor...

The generating function of a marginal distribution of the reduced Palm distribution of a spatial point process is considered. It serves as a bivariate summary function, providing more information than some other popular univariate summary functions, such as the reduced second-moment function and the nearest-neighbour distance distribution function....

As tradition Chinese herbal medicine becomes increasingly popular, there is an urgent need for efficient and accurate methods for the authentication of the Chinese Materia Medica (CMM) used in the herbal medicine. In this work, we present a denoising filter and introduce the use of chord length distribution (CLD) for the classification of starch gr...

A widely applicable edge correction method for estimating summary statistics of a spatial point pattern is proposed. We reconstruct point patterns in a larger region containing the sampling window by matching sampled and simulated kth nearest neighbour distance distributions of the given pattern and then apply plus sampling. Simulation studies show...

Using Ripley's K-function in testing spatial randomness, Koen's estimated critical values deviated notably from Ripley's approximation formula; the former, however, came from an incorrect algorithm. This paper reports new estimates, which agree very well with Ripley's approximation and recommends that the approximation formula can be used instead o...

For a spatial point pattern observed in a bounded window, we propose using discrepancies, which are measures of uniformity in the quasi-Monte Carlo method, to test the complete spatial randomness hypothesis. Tests using these discrepancies are in fact goodness-of-fit tests for uniform distribution. The discrepancies are free from edge effects and,...

Consider a risk reserve process under which the reserve can generate interest. For constants a and b such that a<b, we study the occupation time T a,b (t), which is the total length of the time intervals up to time t during which the reserve is between a and b. We first present a general formula for piecewise deterministic Markov processes, which w...

Diggle's test for complete spatial randomness of a given point pattern uses the discrepancy between the estimated and the theoretical form of a summary function as the test statistic. One commonly used discrepancy measure is the supremum of the pointwise differences over a suitably chosen range; the upper bound of the range is an arbitrary but some...

Extension of Deltheil's study on random points in a convex quadrilateral - Volume 37 Issue 3 - Richard Cowan, S. N. Chiu

The distributions of the last passage time at a given level and the joint distributions of the last passage time, the first passage time and their difference for a general spectrally negative process are derived in the form of Laplace transforms. The results are applied to risk theory.

The probability pn that n points, uniformly and independently distributed within a con- vex planar body K, have a triangular convex hull is known (at least for some values of n ≥ 3) when K is either a triangle, an ellipse, a parallelogram or a regular polygon. The apparent absence of a solution for the case when K is a general quadrilateral was of...

A general risk model that allows for stochastic return on investments as well as perturbation by diffusion is studied. Integro-differential equations for the distributions of the time of ruin, the surplus prior to ruin and the deficit at ruin of this model are established. In particular, we consider a diffusion perturbed risk model with interest fo...

A maximum likelihood procedure is given for estimating parameters in a germination–growth process, based on germination times only or on both times and locations. The process is assumed to be driven by a Poisson process whose intensity is of known analytical form. The procedure is shown to perform well on simulated data with unnormalised gamma inte...

Given a spatial point pattern, we use various characteristics of its Voronoi diagram and Delaunay tessellation to extract information of the dependence between points. In particular, we use the characteristics to construct statistics for testing complete spatial randomness. It is shown that the minimum angle of a typical Delaunay triangle is sensit...

This paper introduces a new graph constructed from a point process. The idea is to connect a point with its nearest neighbour, then to the second nearest and continue this process until the point belongs to the interior of the convex hull of these nearest neighbours. The number of such neighbours is called the degree of a point. We derive the distr...

This paper introduces a new graph constructed from a point process. The idea is to connect a point with its nearest neighbour, then to the second nearest and continue this process until the point belongs to the interior of the convex hull of these nearest neighbours. The number of such neighbours is called the degree of a point. We derive the distr...

The paper studies the joint distribution of the time of ruin, the surplus prior to ruin and the deficit at ruin for the classical risk process that is perturbed by diffusion. We prove that the expected discounted penalty satisfies an integro-differential equation of renewal type, the solution of which can be expressed as a convolution formula. The...

Studies have shown that while children acquire all Cantonese tones by age two, they are not able to label them reliably until approximately age 10. One possible explanation for the large age discrepancy may be the different methodologies used. This study aimed to (1) investigatea new research design for the collection of reliable tone perception da...

This paper investigates the first exit time and the ruin time of a risk reserve process with reserve-dependent income under the assumption that the claims arrive as a Poisson process. We show that the Laplace transform of the distribution of the first exit time from an interval satisfies an integro-differential equation. The exact solution for the...

Studies have shown that while children acquire all Cantonese tones by age two, they are not able to label them reliably until approximately age 10. One possible explanation for the large age discrepancy may be the different methodologies used. This study aimed to (1) investigate a new research design for the collection of reliable tone perception d...

A linear birth–growth process is generated by an inhomogeneous Poisson process on ℝ × [0, ∞). Seeds are born randomly according to the Poisson process. Once a seed is born, it commences immediately to grow bidirectionally with a constant speed. The positions occupied by growing intervals are regarded as covered. New seeds continue to form on the un...

Cantonese is a tone language. A change in the fundamental frequency pattern within the same phonemic segment causes a change in the lexical meaning. The present study examined the Cantonese tone perception ability of cochlear implant children in comparison with normal-hearing children. It was hypothesized that cochlear implant children follow a sim...

Baddeley and Gill (1994, 1996) have introduced an edge-corrected Kaplan–Meier type estimator of the empty space function, which is very important in point process statistics. The present paper suggests a further estimator of this function, which is based on a method used by Hanisch (1984) for unbiased edge-corrected estimation of the nearest neighb...

Seeds are randomly scattered in Rd according to an m-dependent point process. Each seed has its own potential germination time. From each seed that succeeds in germinating, a spherical inhibited region grows to prohibit germination of any seed with later potential germination time. We show that under certain conditions on the distribution of the po...

Seeds are randomly scattered in ℝ d according to an m-dependent point process. Each seed has its own potential germination time. From each seed that succeeds in germinating, a spherical inhibited region grows to prohibit germination of any seed with later potential germination time. We show that under certain conditions on the distribution of the p...

We describe a technique applicable to optimize certain quantities associated with the two-phase structure described by a model of penetrable grains. The solution is given in a form of an intensity surface that controls locations of the grains. Particular examples include maximization of the expected phase 2 volume and design of functionally graded...

Seeds are planted on the interval [0, L] at various locations. Each seed has a location x and a potential germination time t epsilon [0, infinity), and it is assumed that the collection of such (x, t) pairs forms a Poisson process in [0, L] x [0, infinity) with intensity measure dxd lambda(t). From each seed that germinates, an inhibiting region gr...

Consider the following birth-growth model in ℝ. Seeds are born randomly according to an inhomogeneous space-time Poisson process. A newly formed point immediately initiates a bi-directional coverage by sending out a growing branch. Each frontier of a branch moves at a constant speed until it meets an opposing one. New seeds continue to form on the...

Consider the following birth-growth model in R. Seeds are born randomly according to an inhomogeneous space-time Poisson process. A newly formed point immediately initiates a bi-directional coverage by sending out a growing branch. Each frontier of a branch moves at a constant speed until it meets an opposing one. New seeds continue to form on the...

We describe a technique applicable to optimise certain quantities associated with the two-phase structure described by a model of penetrable grains. The solution is given in a form of an intensity surface that controls locations of the grains. Particular examples include minimisation of the expected phase 1 volume and design of functionally graded...

Kernel smoothing methods are applied to nonparametric estimation for nonstationary Boolean models. In many applications only exposed tangent points of the models are observable rather than full realisations. Several methods are developed for estimating the distribution of the underlying Boolean model from observation of the exposed tangent points....

The prelims comprise: Properties of infinite Voronoi diagramsProperties of Poisson Voronoi diagramsUses of Poisson Voronoi diagramsSimulating Poisson Voronoi and Delaunay cellsProperties of Poisson Voronoi cellsStochastic processes induced by Poisson VoronoidiagramsSectional Voronoi diagramsAdditively weighted Poisson Voronoi diagrams: the Johnson-...

In the literature, Rivier's maximum entropy method was used to "prove" Lewis' law and a linear Aboav's law. In this paper we show that the functional forms of these two laws for a statistically equilibrated cellular network, even if such a network really exists, cannot be derived or proved by this method. For example, within the maximum entropy met...

A monotonic. pointwise unbiased and uniformly consistent estimator for the survival function of failure time under the random censorship model is proposed. This estimator is closely related to the Kaplan-Meier. the Nelson-Aalen. and the reduced sample estimator. Large sample properties of the new estimator are discussed.

A Poisson point process ψ in d-dimensional Euclidean space and in time is used to generate a birth-growth model: seeds are born randomly at locations xi in ℝd at times ti ∈ [0, ∞). Once a seed is born, it begins to create a cell by growing radially in all directions with speed v > 0. Points of ψ contained in such cells are discarded, that is, thinn...

A Poisson process in space--time is used to generate a linear Kolmogorov's birth--growth model. Points start to form on [0; L] at time zero. Each newly formed point initiates two bidirectional moving frontiers of constant speed. New points continue to form on not-yet passed over parts of [0; L]. The whole interval will eventually be passed over by...

Is the intersection between an arbitrary but fixed plane and the spatial Poisson Voronoi tessellation a planar Voronoi tessellation? In this paper a negative answer is given to this long-standing question in stochastic geometry. The answer remains negative for the intersection between a t-dimensional linear affine space and the d-dimensional Poisso...

Is the intersection between an arbitrary but fixed plane and the spatial Poisson Voronoi tessellation a planar Voronoi tessellation? In this paper a negative answer is given to this long-standing question in stochastic geometry. The answer remains negative for the intersection between a t -dimensional linear affine space and the d -dimensional Pois...

Johnson-Mehl tessellations can be considered as the results of spatial birth-growth processes. It is interesting to know when such a birth-growth process is completed within a bounded region. This paper deals with the limiting distributions of the time of completion for various models of Johnson-Mehl tessellations in ℝ d and k-dimensional sectional...

The DNA of higher animals replicates by an interesting mechanism. Enzymes recognise specific sites randomly scattered on the molecule and establish a bidirectional process of unwinding and replication from these sites. We investigate the limiting distribution of the completion time for this process by considering related coverage problems investiga...

The DNA of higher animals replicates by an interesting mechanism. Enzymes recognise specific sites randomly scattered on the molecule and establish a bidirectional process of unwinding and replication from these sites. We investigate the limiting distribution of the completion time for this process by considering related coverage problems investiga...

A brief review of Aboav's law (the relationship between the average number of edges of a randomly chosen neighboring cell of a typical n-cell and n) and Lewis' law (the relationship between the mean area of a typical n-cell and n) is presented. These two laws now play central roles in Rivier's maximum entropy theory of statistical crystallography....

The mean number of edges of a randomly chosen neighbouring cell of the typical cell in a planar stationary tessellation, under the condition that it has n edges, has been studied by physicists for more than 20 years. Experiments and simulation studies led empirically to the so- called Aboav law. This law now plays a central role in N. Rivier’s maxi...

The double-stranded molecule, DNA, has the unique property of replication and, because of this, it is the central molecule of life. The mechanism of replication for each single strand is intricate, involving enzymes which move along each of the single strands building a complementary copy. At the frontier of this action, the events have a strong st...

The double-stranded molecule, DNA, has the unique property of replication and, because of this, it is the central molecule of life. The mechanism of replication for each single strand is intricate, involving enzymes which move along each of the single strands building a complementary copy. At the frontier of this action, the events have a strong st...

Thesis (M.Phil.)--University of Hong Kong, 1993. Mode of access: World Wide Web.