Papers by Woollcott Smith
Operations Research, 1972
This note studies an infinitely-many-server queue with N types of customers arriving according to... more This note studies an infinitely-many-server queue with N types of customers arriving according to a semi-Markov process. The service times are independent exponential random variables with means 1/μi, where i is the type of customer being served. The stationary distribution of the embedded Markov chain and the limiting distribution of the continuous-time process are obtained.
Journal of Agricultural, Biological, and Environmental Statistics, 2009
Estimating the number of species in a biological community based on a multinomial sample of indiv... more Estimating the number of species in a biological community based on a multinomial sample of individual organisms is a classical problem in statistical ecology. A central issue in parametric estimation is the specification of a model of the relative abundances of species given their number. A common approach to this problem is to assume that relative abundances follow a symmetric Dirichlet distribution. This is mathematically convenient but is unconnected to work by ecologists on abundance distributions in real communities. In this article we describe ML estimation based on the sequential broken stick model that has been proposed for abundances. This model is defined mechanistically, requiring that the likelihood be approximated numerically. For this to be feasible, the likelihood must be based on a small number of summary statistics. We present simulation results that show that the observed number of species and the observed number of species represented by a single individual is a reasonable set of summary statistics on which to base estimation. We apply the method to two published data sets, one involving insect species on Mount Kenya and the other involving spider species in an Appalachian forest.
A single method, the normalized expected species shared measure of similarity or NESS, is used to... more A single method, the normalized expected species shared measure of similarity or NESS, is used to measure faunal change with depth for gastropods, cumaceans* polychaetes and ophiuroids. The standard errors of NESS estimates are calculated. Each group has a characteristic pattern of zonation on the Gay Head-Bermuda transect, with gastro pods and cumaceans having much narrower depth distribu tions than either polychaetes or ophiuroids. In the polychaetes the higher similarity results from a small proportion of eurybathyal species. The greatest changes in faunal composition occur on the outer margins of the continental shelf at depths of 200 to 300 m and between upper slope and middle slope depths. These discontinuities coincide with the lower limit of the slope water at 200 to 300 m and the lower limits of temperature anomalies resulting from warm core Gulf Stream rings impinging on the bottom at slope depths. Cluster analysis methods tend to divide the samples into discrete groups or zones, even when the faunal similarity between stations appears to be a continuous function of depth. Changes in cumacean species with both depth and distance between ocean basins are compared for Eastern and Western basins of the North Atlantic.
Most distribution free nonparametric methods depend on the ranks or orderings of the individual o... more Most distribution free nonparametric methods depend on the ranks or orderings of the individual observations. This dissertation develops methods for the situation when there is only partial information about the ranks available. A random-linear-extension exact test and an empirical version of the random-linear-extension test are proposed as a new way to compare groups of data with partial orders. The basic computation procedure is to generate all possible permutations constrained by the known partial order using a randomization method similar in nature to multiple imputation. This random-linear-extension test can be simply implemented using a Gibbs Sampler to generate a random sample of complete orderings. Given a complete ordering, standard nonparametric methods, such as the Wilcoxon rank-sum test, can be applied, and the corresponding test statistics and rejection regions can be calculated. As a direct result of our new method, a single p-value is replaced by a distribution of p-v...
Obstetrics & Gynecology, 1995
To determine whether the risk of maternal overweight associated with an excessive rate of gestati... more To determine whether the risk of maternal overweight associated with an excessive rate of gestational gain needs to be balanced against the risks of impaired fetal growth associated with a low rate of gain. Rate of gestational weight gain was measured prospectively in a sample of 274 young, low-income, and primarily minority women (12-29 years old) with pregravid body mass indices (BMI) in the normal range (19.8-26.0). We defined an excessive rate of gain between 20-36 weeks' gestation as one greater than 0.68 kg/week, and a low rate of gain as one less than 0.34 kg/week. Women were followed-up at 4-6 weeks and 6 months postpartum. Rate of measured gestational gain between 20-36 weeks' gestation was associated with total weight gain based on pregravid weight, with infant birth weight and gestation duration, and with maternal overweight (BMI greater than 26) and weight retention postpartum. Infant birth weight and gestation duration were significantly reduced for women with low rates of gain, and there was no significant difference between women with excessive and moderate gains. Despite little difference in pregravid BMI, women with excessive rates of gain retained more weight overall, attained a greater postpartum BMI, and had higher levels of subcutaneous fat and overweight. Maternal anthropometric status showed little change between 4-6 weeks and 6 months postpartum. Weight gained at an excessive rate by women with a pregravid BMI in the normal range does not greatly enhance fetal growth and gestation duration, contributing instead to postpartum maternal overweight.
In this note a model for shot noise generated by a semi-Markov process is developed. The moments ... more In this note a model for shot noise generated by a semi-Markov process is developed. The moments of the shot noise process are found, and some applications of this model are briefly indicated. SEMI-MARKOV; SHOT NOISE; INFINITELY MANY SERVER QUEUE; NEURAL SPIKE TRAINS 1. A general shot noise model Before developing the shot noise model, we introduce and define some notation for semi-Markov processes. In semi-Markov processes, S-MP, as in Markov processes, each jump is a regeneration point eliminating the influence of past events. However, in the S-MP the distribution of times between jumps is arbitrary, whereas in the Markov process the sojourn time in any state is exponentially distributed. Let ti, be the time of the nth transition, n = 0, 1,2, .... Throughout this paper, we let to = 0. Let X, be the value of the S-MP after the nth transition. The process X, is a homogeneous Markov chain. The S-MP, X(t), is completely defined by a set of defective probability distributions, Gi; G, (...
Deep Sea Research Part A. Oceanographic Research Papers, 1980
The digitization error for averaging by frequency counting is analyzed for the case in which succ... more The digitization error for averaging by frequency counting is analyzed for the case in which successive recording intervals are not separated in time. It is shown that the power density of the noise spectrum is given by ~t 2 G r = A ~-(1-cos 2~z Av) where A is the length of the recording interval, ~t is the conversion factor from signal to counts defined by N = X/ct where N is counts, X is signal, and v is frequency. This result is in contrast to the white noise that results from digitization error when the recording intervals are well separated in time. * Contribution No. 4410 from the Woods Hole Oceanographic Institution.
Astrophysical Letters, 1980
OCEAN 75 Conference, 1975
Near bottom moored transponders are b e i n g u s e d f o r p r e c i s i o n n a v i g a t i o n... more Near bottom moored transponders are b e i n g u s e d f o r p r e c i s i o n n a v i g a t i o n i n t h e deep ocean.
The Journal of Prosthetic Dentistry, 1985
Journal of Physical Oceanography, 1982
Abstract The probability density function (pdf) of Richardson number in a Gaussian internal-wave ... more Abstract The probability density function (pdf) of Richardson number in a Gaussian internal-wave field is derived. It is found to compare well with available data. The pdf depends on only parameter λ, the rms stain in the field, which is very weakly dependent on depth if at all. The probability Ri<0.25 is a very sensitive function of λ, which is about λ≈0.5 in the ocean. Numerical simulations of vertical profiles Ri(z) are calculated based on a set of stochastic differential equations. The statistics of the vertical distributions of regions where Ri<0.25 is investigated and a simplified mixing model based on the stochastic differential equations is derived. We conclude that shear instability is a significant factor in the dissipation of internal waves.
Journal of Applied Probability, 1973
In this note a model for shot noise generated by a semi-Markov process is developed. The moments ... more In this note a model for shot noise generated by a semi-Markov process is developed. The moments of the shot noise process are found, and some applications of this model are briefly indicated.
Evolution, 2010
Cope's Rule refers to the tendency of body size to increase along an evolutionary lineage. This r... more Cope's Rule refers to the tendency of body size to increase along an evolutionary lineage. This rule is commonly tested by comparing size differences in pairs of taxa, one of which is assumed to be ancestral to the other. It has recently been pointed out that this approach fails to account for the unknown number of speciation events separating each pair. Here, a test that does account for this degree of separation is described and applied to some published data for dinosaurs. A by-product of the analysis is an estimate of the origination rate of dinosaur species.
Ecology, 2000
A species-accumulation curve measures the increase in the number of species encountered with incr... more A species-accumulation curve measures the increase in the number of species encountered with increased sampling. When quadrat or other kinds of area sampling designs are used, the contribution of spatial community structure to the species-accumulation curve can be investigated. This paper describes and illustrates a relatively simple index, based on a random-sampling model, that quantifies the role of spatial community structure in the species-accumulation curve.
Deep Sea Research Part II: Topical Studies in Oceanography, 2009
ABSTRACT Benthic infaunal samples collected from depths ranging from 5.9 to 2180 m, from nearshor... more ABSTRACT Benthic infaunal samples collected from depths ranging from 5.9 to 2180 m, from nearshore in Boston Harbor to offshore on the continental slope off the coast of Massachusetts, USA, were evaluated for changes in diversity with depth using expected species at a subsample size of 100, ES(100), as well as Fisher&#39;s log-series alpha. All samples were processed with fine mesh (0.3 mm) screens and identified by the same team of researchers, who provided a high and comparable level of expertise. Both measures of diversity were made at the single sample level. An analysis of the variation in these measures, based on a linear mixed model, showed that the largest source of variation was due to depth followed by stations within the same depth range. Variation between cruises/years was relatively small. Communities from the shallowest harbor stations out to 168 m at the edge of the continental shelf had a wide range of diversities, but exhibited no apparent pattern of change with depth or sediment type. The highest diversities were found at mid-slope depths (1220–1350 m). Diversities at 2065–2180 m overlapped with those from mid-slope depths, but were generally lower.
The Bulletin of Mathematical Biophysics, 1971
A stochastic model is developed for an enzyme reaction in an open linear system. The proposed mod... more A stochastic model is developed for an enzyme reaction in an open linear system. The proposed model assumes that the open system maintains the concentration of substrate and inhibitor at constant levels and that the product molecules are removed from the system by a first order reaction. Stochastic models for several enzyme reactions occurring in this open system are shown to correspond to special cases of the GI/M/~ queue. Takhcs' (1958) results for this queueing system are used to obtain the stochastic properties of the enzyme systems. A specific model we studied assumed completely competitive inhibition in an open system. The stationary distribution for the number of product molecules in the system is obtained. The enzyme reaction which incorporated the "intermediate chain hypothesis" can also be investigated by the queueing theory approach. It is shown that for this open system, if the model which incorporated the intermediate chain hypothesis has the same deterministic properties as the Michaelis-Menten model, then the latter has greater stochastic variation than the former.
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Papers by Woollcott Smith