P.N. Jones

Fitting Mixture-Models to Grouped and Truncated Data Via the Em Algorithm

The fitting of finite mixture models via the EM algorithm is considered for data which are available only in grouped form and which may also be truncated. A practical example is presented where a mixture of two doubly truncated log-normal distributions is adopted to model the distribution of the volume of red blood cells in cows during recovery from anemia.

Bycatch diversity and variation in a tropical Australian penaeid fishery; the implications for monitoring

Abstract The composition of teleost and elasmobranch bycatch in two tropical Australian penaeid prawn fisheries was examined using scientific surveys. These covered the major fishing grounds in February and October 1997. On average 82% of the bycatch was teleosts and elasmobranchs, resulting in a high proportion of the bycatch which is unlikely to survive capture. The bycatch is highly diverse (over 350 species of teleosts and elasmobranchs) and dominated by species which occur rarely (75% of species occurred in Overall the general catch characteristics (e.g. total bycatch weight, catch rate of teleosts and elasmobranchs), bycatch composition and individual species abundances showed significant variation among the regions and between February and October. The variation due to regional differences was much greater than between the two times of year. The inclusion of covariates (depth, acoustic measures of seabed roughness and hardness, commercial prawn catch and commercial fishing effort) explained some of the observed variation but there was still significant regional variation present. The primary implication of the results is the clear need for future monitoring strategies to be stratified with respect to region. Monitoring from a single region or time is unlikely to be representative of the fishery.

Pressure treatment of meat: Effects on thermal transitions and shear values

The effects of pressure treatment (150 MN m(-2) for 3 h at 0°C) on the pH, thermal transitions, ultrastructure and Warner-Bratzler shear values of post-rigor beef semimembranosus and longissimus dorsi muscles have been investigated. Pressure treatment resulted in a slight but significant increase in pH. Differential scanning calorimetry revealed large changes in the thermograms of muscle samples as a result of pressure treatment, in particular a transition attributed to F-actin was absent in the pressure-treated sample. Examination of the ultrastructure also revealed extensive change as a result of pressure treatment, particularly in the I-band and M-line region. Pressure treatment either did not change shear values or increased them, according to whether the muscle was in the stretched or contracted state, respectively. The results are thought to support a theory for contraction state toughness proposed by Voyle (1969) in which increasing toughness is caused by an increasing incidence of sarcomeres in which thick filaments have been compressed onto the Z-line, thus removing the I-band as a zone of weakness.

Binding of comminuted meat: Effect of high pressure.

Patties prepared from comminuted meat were pressure-treated at up to 150 MPa at 0-3°C and the cohesion between meat particles in the cooked patty investigated from tensile strength measurements. Pressure treatment increased tensile strength, the magnitude of the increase depending upon the intensity and duration of pressure treatment, the concentration of salt in the patty and pH value. The effect was most pronounced in patties of pH 5 to 6 and with 1% salt in the aqueous phase. Under these conditions cooking losses were reduced. When compared with the effect of addition of 0·5% tetrasodium pyrophosphate in a patty with 1% salt, pressure treatment retained its effect at lower pH values.

The relationship between animal age and the thermal stability and cross-link content of collagen from five goat muscles.

The thermal stability of intramuscular collagen, as determined using differential scanning calorimetry, was measured in five muscles from 75 goats with known birth dates ranging in age from one day to 13 years. The collagen cross-link pyridinoline, and the collagen-associated, and putative cross-link, Ehrlich Chromogen were also measured. Five different muscles were examined and the effects of age compared to those found in the tendon of the longissimus dorsi muscle. The differences between intramuscular collagen and tendon collagen were found to be much greater than those between the intramuscular collagens of different muscles. Intramuscular collagen is more thermally stable than tendon collagen due to higher levels of heat-stable cross-links. However the increase in thermal stability of intramuscular collagen with age could not be explained simply in terms of the cross-links measured.

Algorithm AS 254: maximum likelihood estimation from grouped and truncated data with finite normal mixture models

Description and Purpose Data are often collected in the form of frequencies of observations falling in fixed class intervals. A further feature that is often encountered is truncation in the data; observations below and above certain readings are often not available. Subroutine MGT fits a mixture of a specified number of normal distributions to data collected in this manner. The subroutine can also be used where the data are grouped but not truncated. The fitting procedure uses the EM algorithm (Dempster et al., 1977).

Laplace-normal mixtures fitted to wind shear data

A mixture model with Laplace and normal components is fitted to wind shear data available in grouped form. A set of equations is presented for iteratively estimating the parameters of the model using an application of the EM algorithm. Twenty-four sets of data are examined with this technique, and the model is found to give a good fit to the data. Some hypotheses about the parameters in the model are discussed in light of the estimates obtained.

A comparison of fish bycatch communities between areas open and closed to prawn trawling in an Australian tropical fishery

The bycatch fish community was compared between areas open and closed to prawn trawling in Australia’s Northern Prawn Fishery to investigate the impacts of the fishery. Two regions of a large (� 6648 km 2 ) closure were compared, with three areas in each region, one closed to trawling (Closed) and two open to trawling, one near the closure (Near) and one farther from the closure (Far). Sampling was undertaken both day and night. The two regions and two times were analysed separately using both multivariate and univariate analyses to examine changes in overall community structure and differences in individual species. Overall the results were equivocal with respect to the impact of trawling. The multivariate and univariate analyses showed that in both regions, during both day and night, the bycatch fish community of the Far open area differed from the Near and Closed areas, while the latter were similar. This at least partly reflected differences in depth and sediment. For individual species, most showed no significant difference between the areas open and closed to trawling. Of the significant results there was no consistent tendency for species to be more likely to occur inside the closure or be at a higher density or larger size within the closure. Benthic and demersal species, those more susceptible to capture by prawn trawls, were not consistently less likely to occur or at a lower biomass in the open areas. The lack of a strong contrast in the fish community between the open and closed areas is probably due to the comparatively low effort in the fishery, the highly aggregated nature of the trawling and the fact the fishery does not target the bycatch species. These factors may reduce the potential impact of trawling on the fish bycatch.

Improving the convergence rate of the EM algorithm for a mixture model fitted to grouped truncated data

A method is provided for computing the standard errors for estimated parameters of a normal mixture model fitted to grouped truncated data. An estimate of the information matrix is obtained in terms of quantities computed during an implementation of the EM algorithm. This estimated information matrix is also used to enhance the convergence rate of the EM algorithm using a Newton-type step procedure. A comparison is made of this enhanced procedure with the original procedure using two sets of data each involving a two component mixture, one having mixing proportions almost equal, and the other with the mixing proportions in a ratio close to four to one.

Modelling mass-size particle data by finite mixtures

A minimum distance procedure, analogous to maximum likelihood for multinomial data, is employed to fit mixture models to mass-size relative frequencies recorded for some clay soils of southeastern Australia. Log hyperbolic component distributions are considered initially and it is shown how they can be fitted satisfactorily at least to ungrouped data using a generalized EM algorithm. A computationally more convenient model with log skew Laplace components is subsequently shown to suffice. It is demonstrated how it can be fitted to the data in their original grouped form. Consideration is given also to the provision of standard errors using the idea of a quasi-sample size.