In Sweden, reporting is voluntary for most common felled game, and the number of voluntary reports can vary between hunting teams, HMP, and counties. In 2020, an improved harvest estimation model was developed, which reduced the sensitivity to low reporting. However, there were still some limits to the model, where large, credible intervals were estimated. Therefore, additional variables were considered as the model does not take into account landcover among HMPs, [2] the impact of climate, [4] wildlife accidents, and [4] geographical distribution, creating the covariate model. This study aimed to compare the new model with the covariate model to see if covariates would reduce the large, credible intervals. Two hypothesis tests were performed: evaluation of predictive performance using leave one out cross-validation and evaluation of the 95 % credible interval. Evaluation of predictive performance was performed by examining the difference in expected log-pointwise predictive density (ELPD) and standard error (SE) for each species and model. The results show that the covariates model ranked highest for all ten species, and out of the ten species, six had an (ELPD) difference of two to four, which implies that there is support that the covariate model will be a better predictor for other datasets than this one. At least one covariate had an apparent effect on harvest estimates for nine out of ten species. Finally, the covariate model reduced the large uncertainties, which was an improvement of the null model, indicating that harvest estimates can be improved by taking covariates into account.

Bayesian inference is particularly challenging on hierarchical statistical models as computational complexity becomes a significant issue. Sampling-based methods like the popular Markov Chain Monte Carlo (MCMC) can provide accurate solutions, but they likely suffer a high computational burden. An attractive alternative is the Integrated Nested Laplace Approximations (INLA) approach, which is faster when applied to the broad class of Latent Gaussian Models (LGMs). The method computes fast and empirically accurate deterministic posterior marginal approximations of the model's unknown parameters. In the first part of this thesis, we discuss how to extend the software's applicability to a joint posterior inference by constructing a new class of joint posterior approximations, which also add marginal corrections for location and skewness. As these approximations result from a combination of a Gaussian Copula and internally pre-computed accurate Gaussian Approximations, we name this class Skew Gaussian Copula (SGC). By computing moments and correlation structure of a mixture representation of these distributions, we achieve new fast and accurate deterministic approximations for linear combinations in a subset of the model's latent field. The same mixture approximates a full joint posterior density through a Monte Carlo sampling on the hyperparameter set. We set highly skewed examples based on Poisson and Binomial hierarchical models and verify these new approximations using INLA and MCMC. The new skewness correction from the Skew Gaussian Copula is more consistent with the outcomes provided by the default INLA strategies. In the last part, we propose an extension of the parametric fit employed by the Simplified Laplace Approximation strategy in INLA when approximating posterior marginals. By default, the strategy matches log derivatives from a third-order Taylor expansion of each Laplace Approximation marginal with those derived from Skew Normal distributions. We consider a fourth-order term and adapt an Extended Skew Normal distribution to produce a more accurate approximation fit when skewness is large. We set similarly skewed data simulations with Poisson and Binomial likelihoods and show that the posterior marginal results from the new extended strategy are more accurate and coherent with the MCMC ones than its original version.

Seismic hazard analysis is concerned with estimating risk to human populations due to earthquakes and the other natural disasters that they cause. In many parts of the world, earthquake-generated tsunamis are especially dangerous. Assessing the risk for seismic disasters relies on historical data that indicate which fault zones are capable of supporting significant earthquakes. Due to the nature of geologic time scales, the era of seismological data collection with modern instruments has captured only a part of the Earth's seismic hot zones. However, non-instrumental records, such as anecdotal accounts in newspapers, personal journals, or oral tradition, provide limited information on earthquakes that occurred before the modern era. Here, we introduce a method for reconstructing the source earthquakes of historical tsunamis based on anecdotal accounts. We frame the reconstruction task as a Bayesian inference problem by making a probabilistic interpretation of the anecdotal records. Utilizing robust models for simulating earthquakes and tsunamis provided by the software package GeoClaw, we implement a Metropolis-Hastings sampler for the posterior distribution on source earthquake parameters. In this work, we present our analysis of the 1852 Banda Arc earthquake and tsunami as a case study for the method. Our method is implemented as a Python package, which we call tsunamibayes. It is available, open-source, on GitHub: https://github.com/jwp37/tsunamibayes.

This thesis consists of two papers studying structure learning in probabilistic graphical models for both undirected graphs anddirected acyclic graphs (DAGs). Paper A, presents a novel family of graph theoretical algorithms, called the junction tree expanders, that incrementally construct junction trees for decomposable graphs. Due to its Markovian property, the junction tree expanders are shown to be suitable for proposal kernels in a sequential Monte Carlo (SMC) sampling scheme for approximating a graph posterior distribution. A simulation study is performed for the case of Gaussian decomposable graphical models showing efficiency of the suggested unified approach for both structural and parametric Bayesian inference. Paper B, develops a novel prior distribution over DAGs with the ability to express prior knowledge in terms of graph layerings. In conjunction with the prior, a search and score algorithm based on the layering property of DAGs, is developed for performing structure learning in Bayesian networks. A simulation study shows that the search and score algorithm along with the prior has superior performance for learning graph with a clearly layered structure compared with other priors. / <p>QC 20160111</p>

The purpose of this thesis is to find how we can use Bayesian statistics in analysis of sociological data and to compare outcomes of frequentist and Bayesian approach. Bayesian statistics uses probability distributions on statistical parameters. In the beginning of the analysis in Bayesian approach a prior probability (that is chosen on the basis of relevant information) is attached to the parameters. After combining prior probability and our observed data, posterior probability is computed. Because of the posterior probability we can make statistical conclusions. Comparison of approaches was made from the view of theoretical foundations and procedures and also by means of analysis of sociological data. Point estimates, interval estimates, hypothesis testing (on the example of two-sample t-test) and multiple linear regression analysis were compared. The outcome of this thesis is that considering its philosophy and thanks to the interpretational simplicity the Bayesian analysis is more suitable for sociological data analysis than common frequentist approach. Comparison showed that there is no difference between outcomes of frequentist and objective Bayesian analysis regardless of the sample size. For hypothesis testing we can use Bayesian credible intervals. Using subjective Bayesian analysis on...

Seismic hazard analysis is concerned with estimating risk to human populations due to earthquakes and the other natural disasters that they cause. In many parts of the world, earthquake-generated tsunamis are especially dangerous. Assessing the risk for seismic disasters relies on historical data that indicate which fault zones are capable of supporting significant earthquakes. Due to the nature of geologic time scales, the era of seismological data collection with modern instruments has captured only a part of the Earth's seismic hot zones. However, non-instrumental records, such as anecdotal accounts in newspapers, personal journals, or oral tradition, provide limited information on earthquakes that occurred before the modern era. Here, we introduce a method for reconstructing the source earthquakes of historical tsunamis based on anecdotal accounts. We frame the reconstruction task as a Bayesian inference problem by making a probabilistic interpretation of the anecdotal records. Utilizing robust models for simulating earthquakes and tsunamis provided by the software package GeoClaw, we implement a Metropolis-Hastings sampler for the posterior distribution on source earthquake parameters. In this work, we present our analysis of the 1852 Banda Arc earthquake and tsunami as a case study for the method. Our method is implemented as a Python package, which we call tsunamibayes. It is available, open-source, on GitHub: https://github.com/jwp37/tsunamibayes.

We experience the world through our senses. But we can only make sense of the incoming information because it is weighted and interpreted against our perceptual experience which we gather throughout our lives. In this thesis I present several approaches we used to investigate the learning of prior-experience and its utilization for prediction-based computations in decision making. Teaching participants new categories is a good example to demonstrate how new information is used to learn about, and to understand the world. In the first study I present, we taught participants new visual categories using a reinforcement learning paradigm. We recorded their brain activity before, during, and after prolonged learning over 24 sessions. This allowed us to show that initial learning of categories occurs relatively late during processing, in prefrontal areas. After extended learning, categorization occurs early during processing and is likely to occur in temporal structures. One possible computational mechanism to express prior information is the prediction of future input. In this thesis, I make use of a prominent theory of brain function, predictive coding. We performed two studies. In the first, we showed that expectations of the brain can surpass the reliability of incoming information: In a perceptual decision making task, a percept based on fill-in from the physiological blind spot is judged as more reliable to an identical percept from veridical input. In the second study, we showed that expectations occur between eye movements. There, we measured brain activity while peripheral predictions were violated over eye movements. We found two sets of prediction errors early and late during processing. By changing the reliability of the stimulus using the blind spots, we in addition confirm an important theoretical idea: The strength of prediction-violation is modified based on the reliability of the prediction. So far, we used eye-movements as they are useful to understand the interaction between the current information state of the brain and expectations of future information. In a series of experiments we modulated the amount of information the visual system is allowed to extract before a new eye movement is made. We developed a new paradigm that allows for experimental control of eye-movement trajectories as well as fixation durations. We show that interrupting the extraction of information influences the planning of new eye movements. In addition, we show that eye movement planning time follow Hick's law, a logarithmic increase of saccadic reaction time with increasing number of possible targets. Most of the studies presented here tried to identify causal effects in human behavior or brain-computations. Often direct interventions in the system, like brain stimulation or lesions, are needed for such causal statements. Unfortunately, not many methods are available to directly control the neurons of the brain and even less the encoded expectations. Recent developments of the new optogenetic agent Melanopsin allow for direct activation and silencing of neuronal cells. In cooperation with researchers from the field of optogenetics, we developed a generative Bayesian model of Melanopsin, that allows to integrate physiological data over multiple experiments, include prior knowledge on bio-physical constraints and identify differences between proteins. After discussing these projects, I will take a meta-perspective on my field and end this dissertation with a discussion and outlook of open science and statistical developments in the field of cognitive science.

When an outbreak of an infectious disease occurs, public health officials need to understand the dynamics of disease transmission in order to launch an effective response. Two quantities that are often used to describe transmission are the basic reproductive number and the distribution of the serial interval. The basic reproductive number, R0, is the average number of secondary cases a primary case will infect, assuming a completely susceptible population. The serial interval (SI) provides a measure of temporality, and is defined as the time between symptom onset between a primary case and its secondary case. Investigators typically collect outbreak data in the form of an epidemic curve that displays the number of cases by each day (or other time scale) of the outbreak. Occasionally the epidemic curve data is more expansive and includes demographic or other information. A contact trace sample may also be collected, which is based on a sample of the cases that have their contact patterns traced to determine the timing and sequence of transmission. In addition, numerous large scale social mixing surveys have been administered in recent years to collect information about contact patterns and infection rates among different age groups. These are readily available and are sometimes used to account for population heterogeneity. In this dissertation, we modify the methods presented in White and Pagano (2008) to account for additional data beyond the epidemic curve to estimate R0 and SI. We present two approaches that incorporate these data through the use of a Bayesian framework. First, we consider informing the prior distribution of the SI with contact trace data and examine implications of combining data that are in conflict. The second approach extends the first approach to account for heterogeneity in the estimation of R0. We derive a modification to the White and Pagano likelihood function and utilize social mixing surveys to inform the prior distributions of R0. Both approaches are assessed through a simulation study and are compared to alternative approaches, and are applied to real outbreak data from the 2003 SARS outbreak in Hong Kong and Singapore, and the influenza A(H1N1)2009pdm outbreak in South Africa.

Un problème central contribuant à la grande difficulté du traitement du langage naturel par des méthodes statistiques est celui de la parcimonie des données, à savoir le fait que dans un corpus d'apprentissage donné, la plupart des évènements linguistiques n'ont qu'un nombre d'occurrences assez faible, et que par ailleurs un nombre infini d'évènements permis par une langue n'apparaitront nulle part dans le corpus. Les modèles neuronaux ont déjà contribué à partiellement résoudre le problème de la parcimonie en inférant des représentations continues de mots. Ces représentations continues permettent de structurer le lexique en induisant une notion de similarité sémantique ou syntaxique entre les mots. Toutefois, les modèles neuronaux actuellement les plus répandus n'offrent qu'une solution partielle au problème de la parcimonie, notamment par le fait que ceux-ci nécessitent une représentation distribuée pour chaque mot du vocabulaire, mais sont incapables d'attribuer une représentation à des mots hors vocabulaire. Ce problème est particulièrement marqué dans des langues morphologiquement riches, ou des processus de formation de mots complexes mènent à une prolifération des formes de mots possibles, et à une faible coïncidence entre le lexique observé lors de l’entrainement d’un modèle, et le lexique observé lors de son déploiement. Aujourd'hui, l'anglais n'est plus la langue majoritairement utilisée sur le Web, et concevoir des systèmes de traduction automatique pouvant appréhender des langues dont la morphologie est très éloignée des langues ouest-européennes est un enjeu important. L’objectif de cette thèse est de développer de nouveaux modèles capables d’inférer de manière non-supervisée les processus de formation de mots sous-jacents au lexique observé, afin de pouvoir de pouvoir produire des analyses morphologiques de nouvelles formes de mots non observées lors de l’entraînement. / A crucial issue in statistical natural language processing is the issue of sparsity, namely the fact that in a given learning corpus, most linguistic events have low occurrence frequencies, and that an infinite number of structures allowed by a language will not be observed in the corpus. Neural models have already contributed to solving this issue by inferring continuous word representations. These continuous representations allow to structure the lexicon by inducing semantic or syntactic similarity between words. However, current neural models only partially solve the sparsity issue, due to the fact that they require a vectorial representation for every word in the lexicon, but are unable to infer sensible representations for unseen words. This issue is especially present in morphologically rich languages, where word formation processes yield a proliferation of possible word forms, and little overlap between the lexicon observed during model training, and the lexicon encountered during its use. Today, several languages are used on the Web besides English, and engineering translation systems that can handle morphologies that are very different from western European languages has become a major stake. The goal of this thesis is to develop new statistical models that are able to infer in an unsupervised fashion the word formation processes underlying an observed lexicon, in order to produce morphological analyses of new unseen word forms.

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