In this paper, we examine the feasibility of extending the Akaike information criterion (AIC) for deterministic systems as a potential model selection criteria for stochastic models. We discuss the implementation method for three different classes of stochastic models: continuous time Markov chains (CTMC), stochastic differential equations (SDE), and random differential equations (RDE). The effectiveness and limitations of implementing the AIC for comparison of stochastic models is demonstrated using simulated data from the three types of models and then applied to experimental longitudinal growth data for algae.

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The study of neural and behavioural mechanisms of perceptual decision making is often done by experimental tasks involving the categorization of sensory stimuli. Among the key perceptual tasks that decision neuroscience researchers use are motion discrimination paradigms that include tracking and specifying the net direction of a single dot or a group of moving dots. These motion discrimination paradigms, such as the random-dot motion task, allow the measurement of the participant's perceptual decision making abilities in multiple task difficulty levels by varying the amount of noise in the sensory stimuli. Computational models of perceptual decision making, such as the drift-diffusion model, are widely used to analyze the behavioural measurements from these motion discrimination experiments. However, the standard drift-diffusion model can only analyze the average measures like reaction times or the proportion of correct decisions to explain the behavioural data. In the past decade, an emerging computational modeling approach was introduced to analyze the choice behaviour based on precise noise patterns in the sensory stimuli. These computational models that use spatiotemporal stimulus details have shown promise in the single-trial analysis of motion discrimination behaviour. In this thesis, I further develop the advanced computational models of perceptual decision making that use spatiotemporal dynamics of motion stimuli to provide detailed explanations of perceptual choice behaviour. First, I demonstrate the usefulness of equipping an extended Bayesian Model, equivalent to the extended drift-diffusion model, with trial-wise stimulus information leading to a significantly better explanation of behavioural data from a single-dot tracking experiment. Second, I show that the extended drift-diffusion model constrained by spatiotemporal stimulus details can explain the consistent biased choice behaviour in response to stochastic motion stimuli. Based on this model-based analysis, I provide evidence that the source of the observed biased choice behaviour is the presence of subtle motion information in the sensory stimuli. These results further emphasize the effectiveness of using spatiotemporal details of stochastic stimuli in detailed model-based analyses of the experimental data and provide computational interpretations of the data related to underlying mechanisms of perceptual decision making.

The temporal specificity of functional magnetic resonance imaging (fMRI) is limited by a sluggish and locally variable hemodynamic response trailing the neural activity by seconds. Here, we demonstrate for an attention capture paradigm that it is, never the less, possible to extract information about the relative timing of regional brain activity during cognitive processes on the scale of 100 ms by comparing alternative signal models representing early versus late activation. We demonstrate that model selection is not driven by confounding regional differences in hemodynamic delay. We show, including replication, that the activity in the dorsal anterior insula is an early signal predictive of behavioral performance, while amygdala and ventral anterior insula signals are not. This specific finding provides new insights into how the brain assigns salience to stimuli and emphasizes the role of the dorsal anterior insula in this context. The general analytic approach, named “Cognitive Timing through Model Comparison” (CTMC), offers an exciting and novel method to identify functional brain subunits and their causal interactions.

Fotogrammetri är en viktig metod för att skapa 3D-representationer av terräng och strukturer, men utmaningar kvarstår när det gäller noggrannheten på grund av faktorer som bildkvalitet, kamerakalibrering och positionsdata. Användningen av drönare för byggnadsdetaljmätning möjliggör snabb och kostnadseffektiv datainsamling, men noggrannheten kan påverkas av bildkvalitet och skuggning. Avhandlingen syftar till att jämföra noggrannheten och kvaliteten hos punktmoln genererade med två olika tekniker: terrester laserskanning (TLS) och struktur-från-rörelse (SfM) fotogrammetri med drönare. För att testa båda metodernas osäkerhet och noggrannhet vid detaljmätning av bostäder. Genom att utföra mätningar på en villa har data samlats in med både TLS och drönare utrustade med 48 MP kamera, samt georeferering med markstöd (GCP). SfM-punktmoln bearbetades med Agisoft Metashape. Jämförelser gjordes mellan SfM- och TLS-punktmoln avseende täckning, lägesskillnad och lägesosäkerhet. Genom att följa riktlinjer från HMK - Terrester Laserskanning och tillämpa HMK Standardnivå 3 säkerställs hög noggrannhet i mätningarna. Kontroll av lägesosäkerhet av båda punktmolnen resulterade i en lägesosäkerhet som understeg toleranser satta enligt HMK - Terrester laserskanner Standardnivå 3.  Kontrollen av lägesosäkerheten visade att kvadratiska medelfelet(RMSE) i plan och höjd var 0.011m respektive 0.007m för TLS-punktmolnet, och 0.02m respektive 0.015m för drönar-SfM-punktmolnet, vilket låg under toleransen enligt HMK- Terrester Detaljmätning 2021. Resultaten tyder på att Structure-from-Motion fotogrammetri med drönare kan generera punktmoln med god detaljrikedom, inte lika noggrann som med terrester laserskanner på sin lägsta inställning. TLS uppvisade mindre osäkerhet enligt kontrollen av lägesosäkerhet, ungefär en halvering av RMSE i både plan och höjd. I studien framgick det att TLS presterar sämre vid svåråtkomliga ytor med skymd sikt och ogynnsamma infallsvinklar, där effekten blir en lägre punkttäthet för punktmolnet. Vid gynnsamma förhållanden erbjuder TLS en högre noggrannhet och detaljnivå jämfört med SfM punktmoln. Enligt M3C2 punktmoln analys, med TLS punktmolnet som referens, antydde det att SfM punktmolnet genererade största felen vid takfot samt vid buskage. De större felen vid takfot tyder på att SfM presterar sämre gällande detaljnivå och fel vid buskageområdet varierar inte från det som dokumenterats om fotogrammetriska fel vid mappning av vegetation. SfM kan utföra en effektiv datainsamling för större samt svåråtkomliga ytor men kräver lång bearbetningstid med diverse hjälpmedel för att uppnå hög noggrannhet. TLS kräver istället en lång datainsamlingsprocess men kan generera ett detaljerat och noggrant punktmoln direkt utan långa bearbetningsprocesser. Val av metod styrs därmed baserat på specifika projektkrav. Långsiktiga implikationer inkluderar förbättrad effektivitet och säkerhet inom bygg- och anläggningsprojekt, samt potentialen för kostnadsbesparingar och mer detaljerade inspektioner. / Photogrammetry is a crucial method for creating 3D representations of terrain and structures, yet challenges remain regarding accuracy due to factors such as image quality, camera calibration, and positional data. The use of drones for building detail measurements enables rapid and cost-effective data collection, but accuracy can be affected by image quality and shading. This thesis aims to compare the accuracy and quality of point clouds generated using two different techniques: terrestrial laser scanning (TLS) and Structure-from-Motion (SfM) photogrammetry with drones. The objective is to test the uncertainty and accuracy of both methods in residential surveying. Data collection was performed on a villa using both TLS and a drone equipped with a 48 MP camera, along with georeferencing with ground control points (GCP). SfM point clouds were processed with Agisoft Metashape. Comparisons were made between SfM and TLS point clouds in terms of coverage, positional difference, and positional uncertainty. By following guidelines from HMK - Terrester laserskanning 2021 and applying HMK Standard Level 3, high measurement accuracy was ensured. Positional uncertainty checks of both point clouds resulted in positional uncertainty within tolerances set by HMK - Terrestrial Laser Scanning Standard Level 3. The positional uncertainty, with a sample of 41 points showed that the root mean square error (RMSE) in plane and height was 0.011m and 0.007m respectively for the TLS point cloud, and 0.02m and 0.015m for the drone-SfM point cloud, both within the tolerance according to HMK - Terrestrial Detail Measurement 2021. The results suggest that Structure-from-Motion photogrammetry with drones can generate point clouds with good detail, although not as accurate as terrestrial laser scanning at its lowest setting. TLS showed less uncertainty according to the positional uncertainty check, with approximately half the RMSE in both plan and height. The study found that TLS performs worse on difficult-to-access surfaces with obstructed views and unfavorable angles, resulting in lower point cloud density. Under favorable conditions, TLS offers higher accuracy and detail compared to SfM point clouds. According to M3C2 point cloud analysis, using the TLS point cloud as a reference, SfM point clouds showed the largest errors at eaves and shrubbery. The larger errors at eaves indicate that SfM performs worse in terms of detail level, and errors in the shrubbery area are consistent with documented photogrammetric errors in vegetation mapping. SfM can effectively collect data for larger and difficult-to-access areas but requires extensive processing time with various aids to achieve high accuracy. Conversely, TLS requires a long data collection process but can generate a detailed and accurate point cloud directly without lengthy processing. The choice of method thus depends on specific project requirements. Long-term implications include improved efficiency and safety in construction and infrastructure projects, as well as potential cost savings and more detailed inspections.

This thesis consists of three chapters on economic and econometric applications of Bayesian parameter estimation and model comparison. The first two chapters study the incidental parameter problem mainly under a linear autoregressive (AR) panel data model with fixed effect. The first chapter investigates the problem from a model comparison perspective. The major finding in the first chapter is that consistency in parameter estimation and model selection are interrelated. The reparameterization of the fixed effect parameter proposed by Lancaster (2002) may not provide a valid solution to the incidental parameter problem if the wrong set of exogenous regressors are included. To estimate the model consistently and to measure its goodness of fit, the Bayes factor is found to be more preferable for model comparson than the Bayesian information criterion based on the biased maximum likelihood estimates. When the model uncertainty is substantial, Bayesian model averaging is recommended. The method is applied to study the relationship between financial development and economic growth. The second chapter proposes a correction function approach to solve the incidental parameter problem. It is discovered that the correction function exists for the linear AR panel model of order p when the model is stationary with strictly exogenous regressors. MCMC algorithms are developed for parameter estimation and to calculate the Bayes factor for model comparison. The last chapter studies how stock return's predictability and model uncertainty affect a rational buy-and-hold investor's decision to allocate her wealth for different lengths of investment horizons in the UK market. The FTSE All-Share Index is treated as the risky asset, and the UK Treasury bill as the riskless asset in forming the investor's portfolio. Bayesian methods are employed to identify the most powerful predictors by accounting for model uncertainty. It is found that though stock return predictability is weak, it can still affect the investor's optimal portfolio decisions over different investment horizons.