arXiv subjects

Jonas Wallin

Publications and source records attributed to Jonas Wallin.

44 records · Page 3Linked to original sources

arXiv2017

Level set Cox processes

The log-Gaussian Cox process (LGCP) is a popular point process for modeling non-interacting spatial point patterns. This paper extends the LGCP model to handle data exhibiting fundamentally different behaviors in different subregions of the spatial domain. The aim of the analyst might be either to identify and classify these regions, to perform kriging, or to derive some properties of the parameters driving the random field in one or several of the subregions. The extension is based on replacing the latent Gaussian random field in the LGCP by a latent spatial mixture model. The mixture model is specified using a latent, categorically valued, random field induced by level set operations on a Gaussian random field. Conditional on the classification, the intensity surface for each class is modeled by a set of independent Gaussian random fields. This allows for standard stationary covariance structures, such as the Matérn family, to be used to model Gaussian random fields with some degree of general smoothness but also occasional and structured sharp discontinuities. A computationally efficient MCMC method is proposed for Bayesian inference and we show consistency of finite dimensional approximations of the model. Finally, the model is fitted to point pattern data derived from a tropical rainforest on Barro Colorado island, Panama. We show that the proposed model is able to capture behavior for which inference based on the standard LGCP is biased.

stat.ME↗

arXiv2016

Whole-brain substitute CT generation using Markov random field mixture models

Computed tomography (CT) equivalent information is needed for attenuation correction in PET imaging and for dose planning in radiotherapy. Prior work has shown that Gaussian mixture models can be used to generate a substitute CT (s-CT) image from a specific set of MRI modalities. This work introduces a more flexible class of mixture models for s-CT generation, that incorporates spatial dependency in the data through a Markov random field prior on the latent field of class memberships associated with a mixture model. Furthermore, the mixture distributions are extended from Gaussian to normal inverse Gaussian (NIG), allowing heavier tails and skewness. The amount of data needed to train a model for s-CT generation is of the order of 100 million voxels. The computational efficiency of the parameter estimation and prediction methods are hence paramount, especially when spatial dependency is included in the models. A stochastic Expectation Maximization (EM) gradient algorithm is proposed in order to tackle this challenge. The advantages of the spatial model and NIG distributions are evaluated with a cross-validation study based on data from 14 patients. The study show that the proposed model enhances the predictive quality of the s-CT images by reducing the mean absolute error with 17.9%. Also, the distribution of CT values conditioned on the MR images are better explained by the proposed model as evaluated using continuous ranked probability scores.

stat.AP↗

arXiv2016

Estimating the unobservable moose - converting index to population size using a Bayesian Hierarchical state space model

Indirect information on population size, like pellet counts or volunteer counts, is the main source of information in most ecological studies and applied population management situations. Often, such observations are treaded as if they were actual measurements of population size. This assumption results in incorrect conclusions about a population's size and its dynamics. We propose a model with a temporal varying link, denoted countability, between indirect observations and actual population size. We show that, when indirect measurement has high precision (for instance many observation hours) the assumption of temporal varying countability can have a crucial effect on the estimated population dynamic. We apply the model on two local moose populations in Sweden. The estimated population dynamics is found to explain 30-50 percent of the total variability in the observation data; thus, countability accounts for most of the variation. This unreliability of the estimated dynamics has a substantial negative impact on the ability to manage populations; for example, reducing (increasing) the number of animals that needs to be harvested in order to sustain the population above (below) a fixed level. Finally, large difference in countability between two study areas implies a substantial spatial variation in the countability; this variation in itself is highly worthy of study.

stat.AP↗

arXiv2016

Online estimation of driving events and fatigue damage on vehicles

Driving events, such as maneuvers at slow speed and turns, are important for durability assessments of vehicle components. By counting the number of driving events, one can estimate the fatigue damage caused by the same kind of events. Through knowledge of the distribution of driving events for a group of customers, the vehicles producers can tailor the design, of vehicles, for the group. In this article, we propose an algorithm that can be applied on-board a vehicle to online estimate the expected number of driving events occurring, and thus be used to estimate the distribution of driving events for a certain group of customers. Since the driving events are not observed directly, the algorithm uses a hidden Markov model to extract the events. The parameters of the HMM are estimated using an online EM algorithm. The introduction of the online EM is crucial for practical usage, on-board vehicles, due to that its complexity of an iteration is fixed. Typically, the EM algorithm is used to find the, fixed, parameters that maximizes the likelihood. By introducing a fixed forgetting factor in the online EM, an adaptive algorithm is acquired. This is important in practice since the driving conditions changes over time and a single trip can contain different road types such as city and highway, making the assumption of fixed parameters unrealistic. Finally, we also derive a method to online compute the expected damage.

stat.AP↗

arXiv2016

Spatially adaptive covariance tapering

Covariance tapering is a popular approach for reducing the computational cost of spatial prediction and parameter estimation for Gaussian process models. However, tapering can have poor performance when the process is sampled at spatially irregular locations or when non-stationary covariance models are used. This work introduces an adaptive tapering method in order to improve the performance of tapering in these problematic cases. This is achieved by introducing a computationally convenient class of compactly supported non-stationary covariance functions, combined with a new method for choosing spatially varying taper ranges. Numerical experiments are used to show that the performance of both kriging prediction and parameter estimation can be improved by allowing for spatially varying taper ranges. However, although adaptive tapering outperforms regular tapering, simply dividing the data into blocks and ignoring the dependence between the blocks is often a better method for parameter estimation.

stat.CO↗

arXiv2016

Efficient adaptive MCMC through precision estimation

A novel adaptive Markov chain Monte Carlo algorithm is presented. The algorithm utilizes sparsity in the partial correlation structure of a density to efficiently estimate the covariance matrix through the Cholesky factor of the precision matrix. The algorithm also utilizes the sparsity to sample efficiently from both MALA and Metropolis Hasting random walk proposals. Further, an algorithm that estimates the partial correlation structure of a density is proposed. Combining this with the Cholesky factor estimation algorithm results in an efficient black-box AMCMC method that can be used for general densities with unknown dependency structure. The method is compared with regular empirical covariance adaption for two examples. In both examples, the proposed method's covariance estimates converge faster to the true covariance matrix and the computational cost for each iteration is lower.

stat.CO↗

arXiv2015

Latent modeling of flow cytometry cell populations

Flow cytometry is a widespread single-cell measurement technology with a multitude of clinical and research applications. Interpretation of flow cytometry data is hard; the instrumentation is delicate and can not render absolute measurements, hence samples can only be interpreted in relation to each other while at the same time comparisons are confounded by inter-sample variation. Despite this, current automated flow cytometry data analysis methods either treat samples individually or ignore the variation by for example pooling the data. In this article we introduce a Bayesian hierarchical model for studying latent relations between cell populations in flow cytometry samples, thereby systematizing inter-sample variation. The model is applied to a data set containing replicated flow cytometry measurements of samples from healthy individuals, with informative priors capturing expert knowledge. It is shown that the technical variation in the inferred cell population sizes is small in comparison to the intrinsic biological variation. The large size of flow cytometry data, where a single sample can contain measurements on hundreds of thousands of cells, necessitates computationally efficient methods. To address this, we have implemented a parallel Markov Chain Monte Carlo scheme for sampling the posterior distribution.

stat.AP↗

arXiv2013

Non-Gaussian Matérn fields with an application to precipitation modeling

The recently proposed non-Gaussian Matérn random field models, generated through Stochastic Partial differential equations (SPDEs), are extended by considering the class of Generalized Hyperbolic processes as noise forcings. The models are also extended to the standard geostatistical setting where irregularly spaced observations are modeled using measurement errors and covariates. A maximum likelihood estimation technique based on the Monte Carlo Expectation Maximization (MCEM) algorithm is presented, and it is shown how the model can be used to do predictions at unobserved locations. Finally, an application to precipitation data over the United States for two month in 1997 is presented, and the performance of the non-Gaussian models is compared with standard Gaussian and transformed Gaussian models through cross-validation.

stat.AP↗