Validating hidden Markov models for seabird behavioural inference.

Understanding animal movement and behaviour can aid spatial planning and inform conservation management. However, it is difficult to directly observe behaviours in remote and hostile terrain such as the marine environment. Different underlying states can be identified from telemetry data using hidden Markov models (HMMs). The inferred states are subsequently associated with different behaviours, using ecological knowledge of the species. However, the inferred behaviours are not typically validated due to difficulty obtaining 'ground truth' behavioural information. We investigate the accuracy of inferred behaviours by considering a unique data set provided by Joint Nature Conservation Committee. The data consist of simultaneous proxy movement tracks of the boat (defined as visual tracks as birds are followed by eye) and seabird behaviour obtained by observers on the boat. We demonstrate that visual tracking data is suitable for our study. Accuracy of HMMs ranging from 71% to 87% during chick-rearing and 54% to 70% during incubation was generally insensitive to model choice, even when AIC values varied substantially across different models. Finally, we show that for foraging, a state of primary interest for conservation purposes, identified missed foraging bouts lasted for only a few seconds. We conclude that HMMs fitted to tracking data have the potential to accurately identify important conservation-relevant behaviours, demonstrated by a comparison in which visual tracking data provide a 'gold standard' of manually classified behaviours to validate against. Confidence in using HMMs for behavioural inference should increase as a result of these findings, but future work is needed to assess the generalisability of the results, and we recommend that, wherever feasible, validation data be collected alongside GPS tracking data to validate model performance. This work has important implications for animal conservation, where the size and location of protected areas are often informed by behaviours identified using HMMs fitted to movement data.

Discussion on "The central role of the identifying assumption in population size estimation" by Serge Aleshin-Guendel, Mauricio Sadinle, and Jon Wakefield.

In this discussion response, we consider some practical implications of the authors' consideration of the no-highest-order interaction (NHOI) model for multiple systems estimation, which permits the authors to derive the explicit (albeit untestable) identifying assumption related to the unobserved (or missing) individuals. In particular, we discuss several aspects, from the standard process of model selection to potential poor predictive performance due to over-fitting and the implications of data reduction. We discuss these aspects in relation to the case study presented by the authors relating to the number of civilian casualties within the Kosovo war, and conduct further preliminary simulations to investigate these issues further. The results suggest that the NHOI models considered, despite having a potentially useful theoretical result in relation to the underlying identifying assumption, may perform poorly in practice.

The nose is not enough: Multi-site sampling is best for MRSP detection in dogs and households.

BACKGROUND: Following recovery from meticillin-resistant Staphylococcus pseudintermedius (MRSP) infection of any type, dogs may continue to carry MRSP asymptomatically on skin and mucosae, contributing to the spread of this multidrug-resistant, veterinary hospital-associated pathogen with zoonotic potential to others and into the environment. OBJECTIVES: This study determined which canine anatomic and household environmental sites are most sensitive for sampling to identify carriage and contamination. METHODS AND MATERIALS: Fifty-one dogs and 22 households, MRSP-positive on at least one tested site, were sampled on 132 and 40 occasions over time, respectively. Dogs were swabbed at six sites (mouth, nose, conjunctiva, skin, prepuce/vulva, perianal area); household environments were sampled using contact plates (mannitol salt agar [MSA] and MSA + 6 mg/L oxacillin [MS+]) on five sites. MRSP was isolated after enrichment, grown on MSA/MS+ and was confirmed by PCR. Generalized estimating equations were used for calculation of sensitivity (95% confidence interval) for each site/combination. RESULTS: Each anatomical and environmental site yielded MRSP at least once. MRSP was isolated from only a single site in 27.3% of dogs, with the buccal mucosa showing the highest sensitivity (63.8%). Multi-site sampling of a minimum of four canine anatomical or four environmental sites, respectively, was needed to achieve >95% sensitivity. CONCLUSIONS AND CLINICAL RELEVANCE: The canine buccal mucosa should be included in MRSP sampling protocols, ideally in addition to at least three other anatomical sites. Likewise, environment sampling should be of multiple household sites in cases where it is used as a part of clinical case management.

Building integral projection models with nonindependent vital rates.

Population dynamics are functions of several demographic processes including survival, reproduction, somatic growth, and maturation. The rates or probabilities for these processes can vary by time, by location, and by individual. These processes can co-vary and interact to varying degrees, e.g., an animal can only reproduce when it is in a particular maturation state. Population dynamics models that treat the processes as independent may yield somewhat biased or imprecise parameter estimates, as well as predictions of population abundances or densities. However, commonly used integral projection models (IPMs) typically assume independence across these demographic processes. We examine several approaches for modelling between process dependence in IPMs and include cases where the processes co-vary as a function of time (temporal variation), co-vary within each individual (individual heterogeneity), and combinations of these (temporal variation and individual heterogeneity). We compare our methods to conventional IPMs, which treat vital rates independent, using simulations and a case study of Soay sheep (Ovis aries). In particular, our results indicate that correlation between vital rates can moderately affect variability of some population-level statistics. Therefore, including such dependent structures is generally advisable when fitting IPMs to ascertain whether or not such between vital rate dependencies exist, which in turn can have subsequent impact on population management or life-history evolution.

eLearning significantly improves maternity professionals' knowledge of the congenital cytomegalovirus prevention guidelines.

AIMS: Cytomegalovirus (CMV) is a preventable cause of neurodevelopmental disability. Australian guidelines recommend that pregnant women are informed about CMV to reduce their risk of infection; however, less than 10% of maternity health professionals routinely provide prevention advice. The aim was to develop and evaluate the effectiveness of an eLearning course for midwives to improve knowledge and confidence about CMV. MATERIALS AND METHODS: Participants undertaking the course between March and November 2020 were invited to complete an evaluation questionnaire: before the course (T1), immediately after (T2) and three months post completion (T3). A linear mixed model was used to evaluate change in participant scores; P < 0.05 was considered statistically significant. RESULTS: Midwives (316/363, 87%), midwifery students (29/363, 8%) and nurses (18/363, 5%) participated. At T1 80% indicated they had not received education about CMV. Total adjusted mean scores for questionnaires completed between T1 (n = 363) and T2 (n = 238) increased significantly (from 17.2 to 22.8, P < 0.001). Limited available T3 scores (n = 27) (-1.7, P < 0.001), while lower than T2, remained higher than at T1 (+3.6, P < 0.001). Participants' awareness of CMV information resources improved from 10 to 97% from T1 to T2. Confidence in providing CMV advice increased from 6 to 95% between T1 and T2 (P < 0.001) and was maintained at T3. Almost all (99%) participants indicated they would recommend the course to colleagues. CONCLUSION: Participants who completed the eLearning course had significantly improved knowledge and confidence in providing advice about CMV. Programs targeting other maternity health professionals should be considered, to further support the implementation of the congenital CMV prevention guidelines.

Effect of topical antimicrobial therapy and household cleaning on meticillin-resistant Staphylococcus pseudintermedius carriage in dogs.

BACKGROUND: Meticillin-resistant Staphylococcus pseudintermedius (MRSP) is a multidrug-resistant canine pathogen with a low zoonotic potential. This study investigated MRSP carriage and clearance through topical antimicrobial therapy and household cleaning in dogs recovered from MRSP infection. METHODS: Dogs were swabbed for MRSP carriage; household contamination was assessed using contact plates. Carrier dogs were allocated randomly to receive topical fusidic acid and chlorhexidine/miconazole treatment combined with owners implementing a household hygiene protocol (H&T) or implementation of hygiene alone (H) over three weeks. Carriage-negative dogs were monitored monthly. The relatedness of isolates over time was investigated by pulsed-field gel electrophoresis (PFGE). RESULTS: At inclusion, MRSP carriage was confirmed in 31/46 (67.4%) index dogs and 16/24 (66.7%) contact dogs, and contamination was found in 18/40 (45%) environments. In dogs completing all cycles, interventions cleared carriage in 5/9 (55.6%) dogs in group H&T and 2/6 (33.3%) in group H. Environmental contamination was infrequent but associated with carrier dogs (p = 0.047). Monthly monitoring of initially negative dogs showed intermittent carriage in 9/14 dogs. PFGE-concordance was found among all 34 MRSP isolated from eight index dogs over time. CONCLUSION: MRSP carriage was common in dogs after recovery from infection. Topical antimicrobial therapy temporarily eliminated carriage but recurrence was frequent. Management efforts must include the prevention of recurrent infections and hygiene.

Parameter clustering in Bayesian functional principal component analysis of neuroscientific data.

The extraordinary advancements in neuroscientific technology for brain recordings over the last decades have led to increasingly complex spatiotemporal data sets. To reduce oversimplifications, new models have been developed to be able to identify meaningful patterns and new insights within a highly demanding data environment. To this extent, we propose a new model called parameter clustering functional principal component analysis (PCl-fPCA) that merges ideas from functional data analysis and Bayesian nonparametrics to obtain a flexible and computationally feasible signal reconstruction and exploration of spatiotemporal neuroscientific data. In particular, we use a Dirichlet process Gaussian mixture model to cluster functional principal component scores within the standard Bayesian functional PCA framework. This approach captures the spatial dependence structure among smoothed time series (curves) and its interaction with the time domain without imposing a prior spatial structure on the data. Moreover, by moving the mixture from data to functional principal component scores, we obtain a more general clustering procedure, thus allowing a higher level of intricate insight and understanding of the data. We present results from a simulation study showing improvements in curve and correlation reconstruction compared with different Bayesian and frequentist fPCA models and we apply our method to functional magnetic resonance imaging and electroencephalogram data analyses providing a rich exploration of the spatiotemporal dependence in brain time series.

Environment-sensitive mass changes influence breeding frequency in a capital breeding marine top predator.

The trade-off between survival and reproduction in resource-limited iteroparous animals can result in some individuals missing some breeding opportunities. In practice, even with the best observation regimes, deciding whether 'missed' years represent real pauses in breeding or failures to detect breeding can be difficult, posing problems for the estimation of individual reproductive output and overall population fecundity. We corrected fecundity estimates by determining whether breeding had occurred in skipped years, using long-term capture-recapture observation datasets with parallel longitudinal mass measurements, based on informative underlying relationships between individuals' mass, breeding status and environmental drivers in a capital breeding phocid, the grey seal. Bayesian modelling considered interacting processes jointly: temporal changes in a phenotypic covariate (mass); relationship of mass to breeding probability; effects of maternal breeding state and mark type on resighting. Full reproductive histories were imputed, with the status of unobserved animals estimated as breeding or non-breeding, accounting for local environmental variation. Overall fecundity was then derived for Scottish breeding colonies with contrasting pup production trends. Maternal mass affected breeding likelihood. Mothers with low body mass at the end of breeding were less likely to bear a pup the following year. Successive breeding episodes incurred a cost in reduced body mass which was more pronounced for North Rona, Outer Hebrides (NR) mothers. Skipping breeding increased subsequent pupping probability substantially for low mass females. Poor environmental conditions were associated with declines in breeding probability at both colonies. Seal mass gain between breeding seasons was (a) negatively associated with lagged North Atlantic Oscillation for seals at NR and (b) positively associated with an index of seal prey (Ammodytes spp) abundance at Isle of May, Firth of Forth (IM). Overall fecundity was marginally greater at IM (increasing/stable pup production) than at NR (decreasing). No effects of mass were detected on maternal survival. Skipping breeding in female grey seals appears to be an individual mass-dependent constraint moderated by previous reproductive output and local environmental conditions. Different demographic trends at breeding colonies were consistent with the fecundities estimated using this method, which is general and adaptable to other situations.

Assessing factors associated with changes in the numbers of birds visiting gardens in winter: Are predators partly to blame?

The factors governing the recent declines observed in many songbirds have received much research interest, in particular whether increases of avian predators have had a negative effect on any of their prey species. In addition, further discussion has centered on whether or not the choice of model formulation has an effect on model inference. The study goal was to evaluate changes in the number of 10 songbird species in relation to a suite of environmental covariates, testing for any evidence in support of a predator effect using multiple model formulations to check for consistency in the results. We compare two different approaches to the analysis of long-term garden bird monitoring data. The first approach models change in the prey species between 1970 and 2005 as a function of environmental covariates, including the abundance of an avian predator, while the second uses a change-change approach. Significant negative relationships were found between Eurasian Sparrowhawk Accipiter nisus and three of the 10 species analyzed, namely house Sparrow Passer domesticus, starling Sturnus vulgaris, and blue tit Cyanistes caeruleus. The results were consistent under both modeling approaches. It is not clear if this is a direct negative impact on the overall populations of these species or a behavioral response of the prey species to avoid feeding stations frequented by Sparrowhawks (which may in turn have population consequences, by reducing available resources). The species showing evidence of negative effects of Sparrowhawks were three of the four species most at risk to Sparrowhawk predation according to their prevalence in the predator's diet. The associations could be causal in nature, although in practical terms the reduction in the rate of change in numbers visiting gardens accredited to Sparrowhawks is relatively small, and so unlikely to be the main driver of observed population declines.

A continuous-time hidden Markov model for cancer surveillance using serum biomarkers with application to hepatocellular carcinoma.

Hepatocellular carcinoma (HCC) is the fourth most common cause of cancer deaths worldwide, and its early detection is a critical determinant of whether curative treatment is achievable. Early stage HCC is typically asymptomatic. Thus, screening programmes are used for cancer detection in patients at risk of tumour development. Radiological screening methods are limited by imperfect data, cost and associated risks, and additionally are unable to detect lesions until they have grown to a certain size. Therefore, some screening programmes use additional blood/serum biomarkers to help identify individuals in whom to target diagnostic cancer investigations. The GALAD score, combining the levels of several blood biomarkers, age and sex, has been developed to identify patients with early HCC. Here we propose a Bayesian hierarchical model for an individual's longitudinal GALAD scores whilst in HCC surveillance to identify potentially significant changes in the trend of the GALAD score, indicating the development of HCC, aiming to improve early detection compared to standard methods. An absorbent two-state continuous-time hidden Markov model is developed for the individual level longitudinal data where the states correspond to the presence/absence of HCC. The model is additionally informed by the information on the diagnosis by standard clinical practice, taking into account that HCC can be present before the actual diagnosis so that there may be false negatives within the diagnosis data. We fit the model to a Japanese cohort of patients undergoing HCC surveillance and show that the detection capability of this proposal is greater than using a fixed cut-point.

Multiple Systems Estimation (or Capture-Recapture Estimation) to Inform Public Policy.

Estimating population sizes has long been of interest, from the estimation of the human or ecological population size within regions or countries to the hidden number of civilian casualties in a war. Total enumeration of the population, for example, via a census, is often infeasible or simply impractical. However, a series of partial enumerations or observations of the population is often possible. This has led to the ideas of capture-recapture methods, which have been extensively used within ecology to estimate the size of wildlife populations, with an associated measure of uncertainty, and are most effectively applied when there are multiple capture occasions. Capture-recapture ideology can be more widely applied to multiple data-sources, by the linkage of individuals across the multiple lists. This is often referred to as Multiple Systems Estimation (MSE). The MSE approach has been preferred when estimating "capture-shy" or hard-to-reach populations, including those caught up in the criminal justice system; or homeless; or trafficked; or civilian casualties of war. Motivated by a range of public policy applications of MSE, each briefly introduced, we discuss practical problems with potentially substantial methodological implications. They include: "period" definition; "case" definition; when an observed count is not a true count of the population of interest but an upper bound due to mismatched definitions; exact or probabilistic matching of "cases" across different lists; demographic or other information about the "case" which may influence capture-propensities; required permissions to access extant-lists; list-creation by research-teams or interested parties; referrals (if presence on list A results - almost surely - in presence on list B); different mathematical models leading to widely different estimated population sizes; uncertainty in estimation; computational efficiency; external validation; hypothesis-generation; and additional independent external information. Returning to our motivational applications, we focus on whether the uncertainty which qualified their estimates was sufficiently narrow to orient public policy; and, if not, what options were available and/or taken to reduce the uncertainty or to seek external validation. We also consider whether MSE was hypothesis-generating: in the sense of having spawned new lines of inquiry.

Identifying multispecies synchrony in response to environmental covariates.

The importance of multispecies models for understanding complex ecological processes and interactions is beginning to be realized. Recent developments, such as those by Lahoz-Monfort et al. (2011), have enabled synchrony in demographic parameters across multiple species to be explored. Species in a similar environment would be expected to be subject to similar exogenous factors, although their response to each of these factors may be quite different. The ability to group species together according to how they respond to a particular measured covariate may be of particular interest to ecologists. We fit a multispecies model to two sets of similar species of garden bird monitored under the British Trust for Ornithology's Garden Bird Feeding Survey. Posterior model probabilities were estimated using the reversible jump algorithm to compare posterior support for competing models with different species sharing different subsets of regression coefficients. There was frequently good agreement between species with small asynchronous random-effect components and those with posterior support for models with shared regression coefficients; however, this was not always the case. When groups of species were less correlated, greater uncertainty was found in whether regression coefficients should be shared or not. The methods outlined in this study can test additional hypotheses about the similarities or synchrony across multiple species that share the same environment. Through the use of posterior model probabilities, estimated using the reversible jump algorithm, we can detect multispecies responses in relation to measured covariates across any combination of species and covariates under consideration. The method can account for synchrony across species in relation to measured covariates, as well as unexplained variation accounted for using random effects. For more flexible, multiparameter distributions, the support for species-specific parameters can also be measured.

Semi-Markov Arnason-Schwarz models.

We consider multi-state capture-recapture-recovery data where observed individuals are recorded in a set of possible discrete states. Traditionally, the Arnason-Schwarz model has been fitted to such data where the state process is modeled as a first-order Markov chain, though second-order models have also been proposed and fitted to data. However, low-order Markov models may not accurately represent the underlying biology. For example, specifying a (time-independent) first-order Markov process involves the assumption that the dwell time in each state (i.e., the duration of a stay in a given state) has a geometric distribution, and hence that the modal dwell time is one. Specifying time-dependent or higher-order processes provides additional flexibility, but at the expense of a potentially significant number of additional model parameters. We extend the Arnason-Schwarz model by specifying a semi-Markov model for the state process, where the dwell-time distribution is specified more generally, using, for example, a shifted Poisson or negative binomial distribution. A state expansion technique is applied in order to represent the resulting semi-Markov Arnason-Schwarz model in terms of a simpler and computationally tractable hidden Markov model. Semi-Markov Arnason-Schwarz models come with only a very modest increase in the number of parameters, yet permit a significantly more flexible state process. Model selection can be performed using standard procedures, and in particular via the use of information criteria. The semi-Markov approach allows for important biological inference to be drawn on the underlying state process, for example, on the times spent in the different states. The feasibility of the approach is demonstrated in a simulation study, before being applied to real data corresponding to house finches where the states correspond to the presence or absence of conjunctivitis.

Maximum penalized likelihood estimation in semiparametric mark-recapture-recovery models.

We discuss the semiparametric modeling of mark-recapture-recovery data where the temporal and/or individual variation of model parameters is explained via covariates. Typically, in such analyses a fixed (or mixed) effects parametric model is specified for the relationship between the model parameters and the covariates of interest. In this paper, we discuss the modeling of the relationship via the use of penalized splines, to allow for considerably more flexible functional forms. Corresponding models can be fitted via numerical maximum penalized likelihood estimation, employing cross-validation to choose the smoothing parameters in a data-driven way. Our contribution builds on and extends the existing literature, providing a unified inferential framework for semiparametric mark-recapture-recovery models for open populations, where the interest typically lies in the estimation of survival probabilities. The approach is applied to two real datasets, corresponding to gray herons (Ardea cinerea), where we model the survival probability as a function of environmental condition (a time-varying global covariate), and Soay sheep (Ovis aries), where we model the survival probability as a function of individual weight (a time-varying individual-specific covariate). The proposed semiparametric approach is compared to a standard parametric (logistic) regression and new interesting underlying dynamics are observed in both cases.

Bayesian hierarchical modelling of continuous non-negative longitudinal data with a spike at zero: An application to a study of birds visiting gardens in winter.

The development of methods for dealing with continuous data with a spike at zero has lagged behind those for overdispersed or zero-inflated count data. We consider longitudinal ecological data corresponding to an annual average of 26 weekly maximum counts of birds, and are hence effectively continuous, bounded below by zero but also with a discrete mass at zero. We develop a Bayesian hierarchical Tweedie regression model that can directly accommodate the excess number of zeros common to this type of data, whilst accounting for both spatial and temporal correlation. Implementation of the model is conducted in a Markov chain Monte Carlo (MCMC) framework, using reversible jump MCMC to explore uncertainty across both parameter and model spaces. This regression modelling framework is very flexible and removes the need to make strong assumptions about mean-variance relationships a priori. It can also directly account for the spike at zero, whilst being easily applicable to other types of data and other model formulations. Whilst a correlative study such as this cannot prove causation, our results suggest that an increase in an avian predator may have led to an overall decrease in the number of one of its prey species visiting garden feeding stations in the United Kingdom. This may reflect a change in behaviour of house sparrows to avoid feeding stations frequented by sparrowhawks, or a reduction in house sparrow population size as a result of sparrowhawk increase.

EXPANDING PRACTICE INTO AREAS. ALIGNED PHILOSOPHICALLY WITH MIDWIFERY.

The number of midwives practicing in Australia in 1999, were 11,985 and in 2014, 23,862 (Australian Institute of Health & Welfare, 2014 workforce report). Just over 3,000 are registered as a midwife only.

A default prior distribution for contingency tables with dependent factor levels.

A default prior distribution is proposed for the Bayesian analysis of contingency tables. The prior is specified to allow for dependence between levels of the factors. Different dependence structures are considered, including conditional autoregressive and distance correlation structures. To demonstrate the prior distribution, a dataset is considered which involves estimating the number of injecting drug users in the eleven National Health Service board regions of Scotland using an incomplete contingency table where the dependence structure relates to geographical regions.

Incomplete contingency tables with censored cells with application to estimating the number of people who inject drugs in Scotland.

Estimating the size of hidden or difficult to reach populations is often of interest for economic, sociological or public health reasons. In order to estimate such populations, administrative data lists are often collated to form multi-list cross-counts and displayed in the form of an incomplete contingency table. Log-linear models are typically fitted to such data to obtain an estimate of the total population size by estimating the number of individuals not observed by any of the data-sources. This approach has been taken to estimate the current number of people who inject drugs (PWID) in Scotland, with the Hepatitis C virus diagnosis database used as one of the data-sources to identify PWID. However, the Hepatitis C virus diagnosis data-source does not distinguish between current and former PWID, which, if ignored, will lead to overestimation of the total population size of current PWID. We extend the standard model-fitting approach to allow for a data-source, which contains a mixture of target and non-target individuals (i.e. in this case, current and former PWID). We apply the proposed approach to data for PWID in Scotland in 2003, 2006 and 2009 and compare with the results from standard log-linear models.

Injecting drug users in Scotland, 2006: Listing, number, demography, and opiate-related death-rates.

Using Bayesian capture-recapture analysis, we estimated the number of current injecting drug users (IDUs) in Scotland in 2006 from the cross-counts of 5670 IDUs listed on four data-sources: social enquiry reports (901 IDUs listed), hospital records (953), drug treatment agencies (3504), and recent Hepatitis C virus (HCV) diagnoses (827 listed as IDU-risk). Further, we accessed exact numbers of opiate-related drugs-related deaths (DRDs) in 2006 and 2007 to improve estimation of Scotland's DRD rates per 100 current IDUs. Using all four data-sources, and model-averaging of standard hierarchical log-linear models to allow for pairwise interactions between data-sources and/or demographic classifications, Scotland had an estimated 31700 IDUs in 2006 (95% credible interval: 24900-38700); but 25000 IDUs (95% CI: 20700-35000) by excluding recent HCV diagnoses whose IDU-risk can refer to past injecting. Only in the younger age-group (15-34 years) were Scotland's opiate-related DRD rates significantly lower for females than males. Older males' opiate-related DRD rate was 1.9 (1.24-2.40) per 100 current IDUs without or 1.3 (0.94-1.64) with inclusion of recent HCV diagnoses. If, indeed, Scotland had only 25000 current IDUs in 2006, with only 8200 of them aged 35+ years, the opiate-related DRD rate is higher among this older age group than has been appreciated hitherto. There is counter-balancing good news for the public health: the hitherto sharp increase in older current IDUs had stalled by 2006.

Flexible and practical modeling of animal telemetry data: hidden Markov models and extensions.

We discuss hidden Markov-type models for fitting a variety of multistate random walks to wildlife movement data. Discrete-time hidden Markov models (HMMs) achieve considerable computational gains by focusing on observations that are regularly spaced in time, and for which the measurement error is negligible. These conditions are often met, in particular for data related to terrestrial animals, so that a likelihood-based HMM approach is feasible. We describe a number of extensions of HMMs for animal movement modeling, including more flexible state transition models and individual random effects (fitted in a non-Bayesian framework). In particular we consider so-called hidden semi-Markov models, which may substantially improve the goodness of fit and provide important insights into the behavioral state switching dynamics. To showcase the expediency of these methods, we consider an application of a hierarchical hidden semi-Markov model to multiple bison movement paths.