Reply to determining structural identifiability of parameter learning machines

The paper Ran and Hu (2014, Neurocomputing) examines identifiability and parameter redundancy in classes of models used in machine learning. This note discusses the results on global identifiability and also clarifies that the paper's results on parameter redundancy already exist in the paper Cole et al. (2010, Mathematical Biosciences)

A note on the identifiability of certain latent class models

Wiering (2005, Statistics and Probability Letters, 75, 211-218) provides conditions for the identifiability of a class of latent models. Here we derive an alternative more general method of proving this result, which is based on standard identi¯ability methods involving forming Jacobians

Parameter Redundancy and Identifiability in Hidden Markov Models

Hidden Markov models are a flexible class of models that can be used to describe time series data which depends on an unobservable Markov process. As with any complex model, it is not always obvious whether all the parameters are identifiable, or if the model is parameter redundant; that is, the model can be reparameterised in terms of a smaller number of parameters. This paper considers different methods for detecting parameter redundancy and identifiability in hidden Markov models. We examine both numerical methods and methods that involve symbolic algebra. These symbolic methods require a unique representation of a model, known as an exhaustive summary. We provide an exhaustive summary for hidden Markov models and show how it can be used to investigate identifiability

Using Super-Imposition by Translation And Rotation (SITAR) to relate pubertal growth to bone health in later life:the Medical Research Council (MRC) National Survey of Health and Development

BACKGROUND: To explore associations between pubertal growth and later bone health in a cohort with infrequent measurements, using another cohort with more frequent measurements to support the modelling, data from the Medical Research Council (MRC) National Survey of Health and Development (2-26 years, 4901/30 004 subjects/measurements) and the Avon Longitudinal Study of Parents And Children (ALSPAC) (5-20 years) (10 896/74 120) were related to National Survey of Health and Development (NSHD) bone health outcomes at 60-64 years. METHODS: NSHD data were analysed using Super-Imposition by Translation And Rotation (SITAR) growth curve analysis, either alone or jointly with ALSPAC data. Improved estimation of pubertal growth parameters of size, tempo and velocity was assessed by changes in model fit and correlations with contemporary measures of pubertal timing. Bone outcomes of radius [trabecular volumetric bone mineral density (vBMD) and diaphysis cross-sectional area (CSA)] were regressed on the SITAR parameters, adjusted for current body size. RESULTS: The NSHD SITAR parameters were better estimated in conjunction with ALSPAC, i.e. more strongly correlated with pubertal timing. Trabecular vBMD was associated with early height tempo, whereas diaphysis CSA was related to weight size, early tempo and slow velocity, the bone outcomes being around 15% higher for the better vs worse growth pattern. CONCLUSIONS: By pooling NSHD and ALSPAC data, SITAR more accurately summarized pubertal growth and weight gain in NSHD, and in turn demonstrated notable associations between pubertal timing and later bone outcomes. These associations give insight into the importance of the pubertal period for future skeletal health and osteoporosis risk

Parameter redundancy in Jolly-Seber tag loss models

Capture–recapture experiments are conducted to estimate population parameters such as population size, survival rates, and capture rates. Typically, individuals are captured and given unique tags, then recaptured over several time periods with the assumption that these tags are not lost. However, for some populations, tag loss cannot be assumed negligible. The Jolly‐Seber tag loss model is used when the no‐tag‐loss assumption is invalid. Further, the model has been extended to incorporate group heterogeneity, which allows parameters to vary by group membership. Many mark–recapture models become overparameterized resulting in the inability to independently estimate parameters. This is known as parameter redundancy. We investigate parameter redundancy using symbolic methods. Because of the complex structure of some tag loss models, the methods cannot always be applied directly. Instead, we develop a simple combination of parameters that can be used to investigate parameter redundancy in tag loss models. The incorporation of tag loss and group heterogeneity into Jolly‐Seber models does not result in further parameter redundancies. Furthermore, using hybrid methods we studied the parameter redundancy caused by data through case studies and generated tag histories with different parameter values. Smaller capture and survival rates are found to cause parameter redundancy in these models. These problems resolve when applied to large populations

Statistical Development of Animal Density Estimation Using Random Encounter Modelling

Camera trapping is widely used in ecological studies to estimate animal density, although these studies are largely restricted to animals that can be identified to the individual level. The random encounter model, developed by Rowcliffe et al. (J Anal Ecol 45(4):1228–1236, 2008), estimates animal density from camera-trap data without the need to identify animals. Although the REM can provide reliable density estimates, it lacks the potential to account for the multiple sources of variance in the modelling process. The density estimator in REM is a ratio, and since the variance of a ratio estimator is intractable, we examine and compare the finite sample performance of many approaches for obtaining confidence intervals via simulation studies. We also propose an integrated random encounter model as a parametric alternative, which is flexible and can incorporate covariates and random effects. A data example from Whipsnade Wild Animal Park, Bedfordshire, south England, is used to demonstrate the application of these methods

Size- and stage-dependence in cause-specific mortality of migratory brown trout

Evidence‐based management of natural populations under strong human influence frequently requires not only estimates of survival but also knowledge about how much mortality is due to anthropogenic vs. natural causes. This is the case particularly when individuals vary in their vulnerability to different causes of mortality due to traits, life history stages, or locations. Here, we estimated harvest and background (other cause) mortality of landlocked migratory salmonids over half a century. In doing so, we quantified among‐individual variation in vulnerability to cause‐specific mortality resulting from differences in body size and spawning location relative to a hydropower dam. We constructed a multistate mark–recapture model to estimate harvest and background mortality hazard rates as functions of a discrete state (spawning location) and an individual time‐varying covariate (body size). We further accounted for among‐year variation in mortality and migratory behaviour and fit the model to a unique 50‐year time series of mark–recapture–recovery data on brown trout (Salmo trutta ) in Norway. Harvest mortality was highest for intermediate‐sized trout, and outweighed background mortality for most of the observed size range. Background mortality decreased with body size for trout spawning above the dam and increased for those spawning below. All vital rates varied substantially over time, but a trend was evident only in estimates of fishers' reporting rate, which decreased from over 50% to less than 10% throughout the study period. We highlight the importance of body size for cause‐specific mortality and demonstrate how this can be estimated using a novel hazard rate parameterization for mark–recapture models. Our approach allows estimating effects of individual traits and environment on cause‐specific mortality without confounding, and provides an intuitive way to estimate temporal patterns within and correlation among different mortality sources

Temporally varying natural mortality: Sensitivity of a virtual population analysis and an exploration of alternatives

Cohort reconstructions (CR) currently applied in Pacific salmon management estimate temporally variant exploitation, maturation, and juvenile natural mortality rates but require an assumed (typically invariant) adult natural mortality rate (dA), resulting in unknown biases in the remaining vital rates. We explored the sensitivity of CR results to misspecification of the mean and/or variability of dA, as well as the potential to estimate dA directly using models that assumed separable year and age/cohort effects on vital rates (separable cohort reconstruction, SCR). For CR, given the commonly assumed dA = 0.2, the error (RMSE) in estimated vital rates is generally small (? 0.05) when annual values of dA are low to moderate (? 0.4). The greatest absolute errors are in maturation rates, with large relative error in the juvenile survival rate. The ability of CR estimates to track temporal trends in the juvenile natural mortality rate is adequate (Pearson's correlation coefficient > 0.75) except for high dA (? 0.6) and high variability (CV > 0.35). The alternative SCR models allowing estimation of time-varying dA by assuming additive effects in natural mortality, fishing mortality, and/or maturation rates did not outperform CR across all simulated scenarios, and are less accurate when additivity assumptions are violated. Nevertheless an SCR model assuming additive effects on fishing and natural (juvenile and adult) mortality rates led to nearly unbiased estimates of all quantities estimated using CR, along with borderline acceptable estimates of the mean dA under multiple sets of conditions conducive to CR. Adding an assumption of additive effects on the maturation rates allowed nearly unbiased estimates of the mean dA as well. The SCR models performed slightly better than CR when the vital rates covaried as assumed. These separable models could serve as a partial check on the validity of CR assumptions about the adult natural mortality rate, or even a preferred alternative if there is strong reason to believe the vital rates, including juvenile and adult natural mortality rates, covary strongly across years or age classes as assumed

VLT/NACO near-infrared imaging and spectroscopy of N88A in the SMC

We present near-infrared imaging and spectroscopic high spatial resolution observations of the SMC region N88 containing the bright, excited, extincted and compact H II region N88A of size ~ 1 pc. To investigate its stellar content and reddening, N88 was observed using spectroscopy and imagery in the JHKs- and L'-band at a spatial resolution of ~ 0.1-0.3", using the VLT UT4 equipped with the NAOS adaptive optics system. In order to attempt to establish if the origin of the infra-red (IR) excess is due to bright nebulosity, circumstellar material and/or local dust, we used Ks vs J-K colour-magnitude (CM) and JHK colour-colour (CC) diagrams, as well as L' imagery.Our IR-data reveal in the N88 area an IR-excess fraction of geq 30 per cent of the detected stars,as well as an unprecedently detailed morphology of N88A. It consists of an embedded cluster of ~3.5" (~ 1 pc) in diameter, of at least thirteen resolved stars superposed with an unusual bright continuum centered on a very bright star. The four brightest stars in this cluster lie red-ward of H-K geq 0.45 mag, and could be classified as young stellar object (YSO) candidates. Four other probable YSO candidates are also detected in N88 along a south-north bow-shaped thin H2 filament at ~ 7" east of the young central bright star. At 0.2" east of this star, a heavily embedded core is detected that could be a massive class I protostar candidate. The 2.12 mu H2 image of N88A resembles a shell of diameter ~ 3" ~ 0.9 pc) centered on the bright star. The line ratios of H2 2-1 S(1) and 1-0 S(0) relative to 1-0 S(1), as well as the presence of high v lines, are indicative of photodissociation regions, rather than shocks.Comment: 15 pages, 14 figures, accepted by Astronomy and Astrophysics, uses pdflatex, aa.cl