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Search Results: 1 - 10 of 232875 matches for " Matthew R. Schofield "
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Putting Markov Chains Back into Markov Chain Monte Carlo
Richard J. Barker,Matthew R. Schofield
Advances in Decision Sciences , 2007, DOI: 10.1155/2007/98086
Abstract: Markov chain theory plays an important role in statistical inference both in the formulation of models for data and in the construction of efficient algorithms for inference. The use of Markov chains in modeling data has a long history, however the use of Markov chain theory in developing algorithms for statistical inference has only become popular recently. Using mark-recapture models as an illustration, we show how Markov chains can be used for developing demographic models and also in developing efficient algorithms for inference. We anticipate that a major area of future research involving mark-recapture data will be the development of hierarchical models that lead to better demographic models that account for all uncertainties in the analysis. A key issue is determining when the chains produced by Markov chain Monte Carlo sampling have converged.
Hierarchical Modeling of Abundance in Closed Population Capture-Recapture Models Under Heterogeneity
Matthew R. Schofield,Richard J. Barker
Statistics , 2010,
Abstract: Hierarchical modeling of abundance in space or time using closed-population mark-recapture under heterogeneity (model M$_{h}$) presents two challenges: (i) finding a flexible likelihood in which abundance appears as an explicit parameter and (ii) fitting the hierarchical model for abundance. The first challenge arises because abundance not only indexes the population size, it also determines the dimension of the capture probabilities in heterogeneity models. A common approach is to use data augmentation to include these capture probabilities directly into the likelihood and fit the model using Bayesian inference via Markov chain Monte Carlo (MCMC). Two such examples of this approach are (i) explicit trans-dimensional MCMC, and (ii) superpopulation data augmentation. The superpopulation approach has the advantage of simple specification that is easily implemented in BUGS and related software. However, it reparameterizes the model so that abundance is no longer included, except as a derived quantity. This is a drawback when hierarchical models for abundance, or related parameters, are desired. Here, we analytically compare the two approaches and show that they are more closely related than might appear superficially. We exploit this relationship to specify the model in a way that allows us to include abundance as a parameter and that facilitates hierarchical modeling using readily available software such as BUGS. We use this approach to model trends in grizzly bear abundance in Yellowstone National Park from 1986-1998.
Full Open Population Capture-Recapture Models with Individual Covariates
Matthew R. Schofield,Richard J. Barker
Statistics , 2010,
Abstract: Traditional analyses of capture-recapture data are based on likelihood functions that explicitly integrate out all missing data. We use a complete data likelihood (CDL) to show how a wide range of capture-recapture models can be easily fitted using readily available software JAGS/BUGS even when there are individual-specific time-varying covariates. The models we describe extend those that condition on first capture to include abundance parameters, or parameters related to abundance, such as population size, birth rates or lifetime. The use of a CDL means that any missing data, including uncertain individual covariates, can be included in models without the need for customized likelihood functions. This approach also facilitates modeling processes of demographic interest rather than the complexities caused by non-ignorable missing data. We illustrate using two examples, (i) open population modeling in the presence of a censored time-varying individual covariate in a full robust-design, and (ii) full open population multi-state modeling in the presence of a partially observed categorical variable.
Connecting the latent multinomial
Matthew R. Schofield,Simon J. Bonner
Statistics , 2015, DOI: 10.1111/biom.12333
Abstract: Link et al. (2010) define a general framework for analyzing capture-recapture data with potential misidentifications. In this framework, the observed vector of counts, $y$, is considered as a linear function of a vector of latent counts, $x$, such that $y = A x$, with $x$ assumed to follow a multinomial distribution conditional on the model parameters, $\theta$. Bayesian methods are then applied by sampling from the joint posterior distribution of both $x$ and $\theta$. In particular, Link et al. (2010) propose a Metropolis-Hastings algorithm to sample from the full conditional distribution of $x$, where new proposals are generated by sequentially adding elements from a basis of the null space (kernel) of $A$. We consider this algorithm and show that using elements from a simple basis for the kernel of $A$ may not produce an irreducible Markov chain. Instead, we require a Markov basis, as defined by Diaconis and Sturmfels (1998). We illustrate the importance of Markov bases with three capture-recapture examples. We prove that a specific lattice basis is a Markov basis for a class of models including the original model considered by Link et al. (2010) and confirm that the specific basis used by Link et al. (2010) for their example with two sampling occasions is a Markov basis. The constructive nature of our proof provides an immediate method to obtain a Markov basis for any model in this class.
A Model-Based Approach to Climate Reconstruction Using Tree-Ring Data
Matthew R. Schofield,Richard J. Barker,Andrew Gelman,Edward R. Cook,Keith R. Briffa
Statistics , 2015,
Abstract: Quantifying long-term historical climate is fundamental to understanding recent climate change. Most instrumentally recorded climate data are only available for the past 200 years, so proxy observations from natural archives are often considered. We describe a model-based approach to reconstructing climate defined in terms of raw tree-ring measurement data that simultaneously accounts for non-climatic and climatic variability. In this approach we specify a joint model for the tree-ring data and climate variable that we fit using Bayesian inference. We consider a range of prior densities and compare the modeling approach to current methodology using an example case of Scots pine from Tornetrask, Sweden to reconstruct growing season temperature. We describe how current approaches translate into particular model assumptions. We explore how changes to various components in the model-based approach affect the resulting reconstruction. We show that minor changes in model specification can have little effect on model fit but lead to large changes in the predictions. In particular, the periods of relatively warmer and cooler temperatures are robust between models, but the magnitude of the resulting temperatures are highly model dependent. Such sensitivity may not be apparent with traditional approaches because the underlying statistical model is often hidden or poorly described.
Extending the Latent Multinomial Model with Complex Error Processes and Dynamic Markov Bases
Simon J Bonner,Matthew R Schofield,Patrik Noren,Steven J Price
Statistics , 2015,
Abstract: The latent multinomial model (LMM) model of Link et al. (2010) provided a general framework for modelling mark-recapture data with potential errors in identification. Key to this approach was a Markov chain Monte Carlo (MCMC) scheme for sampling possible configurations of the counts true capture histories that could have generated the observed data. This MCMC algorithm used vectors from a basis for the kernel of the linear map between the true and observed counts to move between the possible configurations of the true data. Schofield and Bonner (2015) showed that a strict basis was sufficient for some models of the errors, including the model presented by Link et al. (2010), but a larger set called a Markov basis may be required for more complex models. We address two further challenges with this approach: 1) that models with more complex error mechanisms do not fit easily within the LMM and 2) that the Markov basis can be difficult or impossible to compute for even moderate sized studies. We address these issues by extending the LMM to separately model the capture/demographic process and the error process and by developing a new MCMC sampling scheme using dynamic Markov bases. Our work is motivated by a study of Queen snakes (Regina septemvittata) in Kentucky, USA, and we use simulation to compare the use of PIT tags, with perfect identification, and brands, which are prone to error, when estimating survival rates.
Relationship between the EQ-5D index and measures of clinical outcomes in selected studies of cardiovascular interventions
Goldsmith Kimberley,Dyer Matthew,Schofield Peter,Buxton Martin
Health and Quality of Life Outcomes , 2009,
Abstract: Background The EuroQoL 5D (EQ-5D) has been widely used in studies of cardiac disease, but its measurement properties in this group are not well established. The study aimed to quantify the relationship between measures commonly used in studies of cardiac disease and the EQ-5D index across different levels of disease severity. Methods Patient-level data from 7 studies of cardiac interventions were used, which included randomised trials and observational studies. Relationships between the EQ-5D index and commonly used cardiac measures, Canadian Cardiovascular Society (CCS) angina severity class, treadmill exercise time (ETT) and scales of the Seattle Angina Questionnaire (SAQ) were examined. Mixed effects linear regression was used to assess these relationships, with the EQ-5D index as the response. Results Study sample sizes ranged from 68 to 2419. Mean baseline EQ-5D index ranged from 0.77 in patients at diagnosis (95% CI 0.75, 0.78) to 0.43 in patients with advanced disease (95% CI 0.39, 0.48) and differed significantly across studies (p < 0.001). There was evidence of a ceiling effect in patients at diagnosis. The minimum clinically important difference of a one minute increase in ETT was associated with a 0.019 (95% CI 0.014, 0.025) increase in EQ-5D index. One class increase in CCS was associated with a 0.11 (95% CI 0.09, 0.13) decrease in EQ-5D index. A 10 unit increase in SAQ scales was associated with increases between 0.04 and 0.07 in EQ-5D index (95% CIs 0.03, 0.05 and 0.05, 0.08). Tests of heterogeneity indicated the EQ-5D-covariate relationships were consistent across levels of disease severity for ETT and the treatment satisfaction scale of the SAQ, but heterogeneous for age, gender, CCS angina class and other scales of the SAQ. Conclusion The EQ-5D index varies with coronary disease severity. The relationship between the EQ-5D index and an outcome measure used in cardiac intervention studies, ETT, was consistent across disease severity levels, but the relationship between demographic variables, CCS angina class and most of the SAQ scales and the EQ-5D index was heterogeneous for patients with different levels of coronary disease. Differences in the EQ-5D index associated with clinically important differences in cardiac measures can be quantified and vary between three important examples - angina class, ETT and SAQ.
The SMS Chaum Mix  [PDF]
Matthew Rothmeyer, Dale R. Thompson, Matthew Moccaro
Journal of Computer and Communications (JCC) , 2014, DOI: 10.4236/jcc.2014.24010
Abstract:

Mobile devices such as smartphones are prime candidates for the application of mixing techniques to provide anonymity for small groups of individuals numbering 30 to 40 members. In this work, a Chaum mix inspired, smartphone based network that uses the Short Message Service (SMS) is proposed. This system leverages both techniques used by current anonymity networks as well as knowledge gained from current and past research to make messages private and untraceable. Previously published attacks to anonymous systems are addressed as well as mitigation techniques.

Cholinergic and Non-Cholinergic Projections from the Pedunculopontine and Laterodorsal Tegmental Nuclei to the Medial Geniculate Body in Guinea Pigs
Susan D. Motts,Brett R. Schofield
Frontiers in Neuroanatomy , 2010, DOI: 10.3389/fnana.2010.00137
Abstract: The midbrain tegmentum is the source of cholinergic innervation of the thalamus and has been associated with arousal and control of the sleep/wake cycle. In general, the innervation arises bilaterally from the pedunculopontine tegmental nucleus (PPT) and the laterodorsal tegmental nucleus (LDT). While this pattern has been observed for many thalamic nuclei, a projection from the LDT to the medial geniculate body (MG) has been questioned in some species. We combined retrograde tracing with immunohistochemistry for choline acetyltransferase (ChAT) to identify cholinergic projections from the brainstem to the MG in guinea pigs. Double-labeled cells (retrograde and immunoreactive for ChAT) were found in both the PPT (74%) and the LDT (26%). In both nuclei, double-labeled cells were more numerous on the ipsilateral side. About half of the retrogradely labeled cells were immunonegative, suggesting they are non-cholinergic. The distribution of these immunonegative cells was similar to that of the immunopositive ones: more were in the PPT than the LDT and more were on the ipsilateral than the contralateral side. The results indicate that both the PPT and the LDT project to the MG, and suggest that both cholinergic and non-cholinergic cells contribute substantially to these projections.
Quasi-linear magnetoresistance in an almost 2D band structure
A. J. Schofield,J. R. Cooper
Physics , 1997, DOI: 10.1103/PhysRevB.62.10779
Abstract: We present a theoretical study of the orbital magnetoresistance in a unixial anisotropic metal within the relaxation-time approximation. The appearance of a new dimensionless scale, delta=4t_perp/epsilon_F, allows the possibility of a new region at intermediate fields where the magnetoresistance is linear in applied magnetic field for currents flowing along the unixial direction. (Here, t_perp characterizes the bandwidth along the unixial direction.) In the limit of large anisotropy (small delta), corresponding to a quasi-two-dimensional metal made up of weakly coupled layers, we obtain an analytic expression for the magnetoresistance valid for all magnetic fields. We test our analytic results numerically and we compare our expressions with the c-axis magnetoresistance of Sr_2RuO_4.
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