14,318 research outputs found
Multi-species population indices for sets of species including rare, disappearing or newly occurring species
NI is funded by Natural Environment Research Council award NE/R016429/1 as part of the UK-SCAPE programme delivering National Capability.Multi-species indices (MSI) are widely used as ecological indicators and as instruments to inform environmental policies. Many of these indices combine species-specific estimates of relative population sizes using the geometric mean. Because the geometric mean is not defined when values of zero occur, usually only commoner species are included in MSIs and zero values are replaced by a small non-zero value. The latter can exhibit an arbitrary influence on the geometric mean MSI. Here, we show how the compound Poisson and the negative binomial model can be used in such cases to obtain an MSI that has similar features to the geometric mean, including weighting halving and doubling of a species’ population equally. In contrast to the geometric mean, these two statistical models can handle zero values in population sizes and thus accommodate newly occurring and temporarily or permanently disappearing species in the MSI. We compare the MSIs obtained by the two statistical models with the geometric mean MSI and measure sensitivity to changes in evenness and to population trends in rare and abundant species. Additionally, we outline sources of uncertainty and discuss how to measure them. We found that, in contrast to the geometric mean and the negative binomial MSI, the compound Poisson MSI is less sensitive to changes in evenness when total abundance is constant. Further, we found that the compound Poisson model can be influenced more than the other two methods by trends of species showing a low interannual variance. The negative binomial MSI is less sensitive to trends in rare species compared with the other two methods, and similarly sensitive to trends in abundant species as the geometric mean. While the two new MSIs have the advantage that they are not arbitrarily influenced by rare, newly appearing and disappearing species, both do not weight all species equally. We recommend replacing the geometric mean MSI with either compound Poisson or negative binomial when there are species with a population size of zero in some years having a strong influence on the geometric mean MSI. Further, we recommend providing additional information alongside the MSIs. For example, it is particularly important to give an evenness index in addition to the compound Poisson MSI and to indicate the number of disappearing and newly occurring species alongside the negative binomial MSI.Publisher PDFPeer reviewe
Some distributional properties of a class of counting distributions with claims analysis applications
We discuss a class of counting distributions motivated by a problem in discrete surplus analysis, and special cases of which have applications in stop-loss, discrete Tail value at risk (TVaR) and claim count modelling. Explicit formulas are developed, and the mixed Poisson case is considered in some detail. Simplifications occur for some underlying negative binomial and related models, where in some cases compound geometric distributions arise naturally. Applications to claim count and aggregate claims models are then given.published_or_final_versio
Analytical models of probability distribution and excess noise factor of Solid State Photomultiplier signals with crosstalk
Silicon Photomultipliers (SiPM), also so-called Solid State Photomultipliers
(SSPM), are based on Geiger mode avalanche breakdown limited by strong negative
feedback. SSPM can detect and resolve single photons due to high gain and
ultra-low excess noise of avalanche multiplication in this mode. Crosstalk and
afterpulsing processes associated with the high gain introduce specific excess
noise and deteriorate photon number resolution of the SSPM. Probabilistic
features of these processes are widely studied because of its high importance
for the SSPM design, characterization, optimization and application, but the
process modeling is mostly based on Monte Carlo simulations and numerical
methods. In this study, crosstalk is considered to be a branching Poisson
process, and analytical models of probability distribution and excess noise
factor (ENF) of SSPM signals based on the Borel distribution as an advance on
the geometric distribution models are presented and discussed. The models are
found to be in a good agreement with the experimental probability distributions
for dark counts and a few photon spectrums in a wide range of fired pixels
number as well as with observed super-linear behavior of crosstalk ENF.Comment: 10 pages, 2 tables, 3 figures, Reported at 6th International
Conference on "New Developments In Photodetection - NDIP11
Compound Poisson and signed compound Poisson approximations to the Markov binomial law
Compound Poisson distributions and signed compound Poisson measures are used
for approximation of the Markov binomial distribution. The upper and lower
bound estimates are obtained for the total variation, local and Wasserstein
norms. In a special case, asymptotically sharp constants are calculated. For
the upper bounds, the smoothing properties of compound Poisson distributions
are applied. For the lower bound estimates, the characteristic function method
is used.Comment: Published in at http://dx.doi.org/10.3150/09-BEJ246 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
Random effects compound Poisson model to represent data with extra zeros
This paper describes a compound Poisson-based random effects structure for
modeling zero-inflated data. Data with large proportion of zeros are found in
many fields of applied statistics, for example in ecology when trying to model
and predict species counts (discrete data) or abundance distributions
(continuous data). Standard methods for modeling such data include mixture and
two-part conditional models. Conversely to these methods, the stochastic models
proposed here behave coherently with regards to a change of scale, since they
mimic the harvesting of a marked Poisson process in the modeling steps. Random
effects are used to account for inhomogeneity. In this paper, model design and
inference both rely on conditional thinking to understand the links between
various layers of quantities : parameters, latent variables including random
effects and zero-inflated observations. The potential of these parsimonious
hierarchical models for zero-inflated data is exemplified using two marine
macroinvertebrate abundance datasets from a large scale scientific bottom-trawl
survey. The EM algorithm with a Monte Carlo step based on importance sampling
is checked for this model structure on a simulated dataset : it proves to work
well for parameter estimation but parameter values matter when re-assessing the
actual coverage level of the confidence regions far from the asymptotic
conditions.Comment: 4
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