In the present dissertation, we investigate two different nonparametric models; empirical Bayes model and functional deconvolution model. In the case of the nonparametric empirical Bayes estimation, we carried out a complete minimax study. In particular, we derive minimax lower bounds for the risk of the nonparametric empirical Bayes estimator for a general conditional distribution. This result has never been obtained previously. In order to attain optimal convergence rates, we use a wavelet series based empirical Bayes estimator constructed in Pensky and Alotaibi (2005). We propose an adaptive version of this estimator using Lepski’s method and show that the estimator attains optimal convergence rates. The theory is supplemented by numerous examples. Our study of the functional deconvolution model expands results of Pensky and Sapatinas (2009, 2010, 2011) to the case of estimating an (r + 1)-dimensional function or dependent errors. In both cases, we derive minimax lower bounds for the integrated square risk over a wide set of Besov balls and construct adaptive wavelet estimators that attain those optimal convergence rates. In particular, in the case of estimating a periodic (r + 1)-dimensional function, we show that by choosing Besov balls of mixed smoothness, we can avoid the ”curse of dimensionality” and, hence, obtain higher than usual convergence rates when r is large. The study of deconvolution of a multivariate function is motivated by seismic inversion which can be reduced to solution of noisy two-dimensional convolution equations that allow to draw inference on underground layer structures along the chosen profiles. The common practice in seismology is to recover layer structures separately for each profile and then to combine the derived estimates into a two-dimensional function. By studying the two-dimensional version of the model, we demonstrate that this strategy usually leads to estimators which are less accurate than the ones obtained as two-dimensional functional deconvolutions. Finally, we consider a multichannel deconvolution model with long-range dependent Gaussian errors. We do not limit our consideration to a specific type of long-range dependence, rather we assume that the eigenvalues of the covariance matrix of the errors are bounded above and below. We show that convergence rates of the estimators depend on a balance between the smoothness parameters of the response function, the iii smoothness of the blurring function, the long memory parameters of the errors, and how the total number of observations is distributed among the channels.

The human visual system gathers information about three-dimensional object shape from a wide range of sources. How effectively we can use these sources, and how they are combined to form a consistent and accurate percept of the 3D world is the focus of much research. In complex scenes inter-reflections of light between surfaces (mutual illumination) can occur, creating chromatic illumination gradients. These gradients provide a source of information about 3D object shape, but little research has been conducted into the capabilities of the visual system to use such information. The experiments described here were conducted with the aim of understanding the influence of chromatic gradients from mutual illumination on 3D shape perception. Psychophysical experiments are described that were designed to investigate: If the human visual system takes account of mutual illumination when estimating 3D object shape, and how this might occur; How colour shading cues are integrated with other shape cues; The relative influence on 3D shape perception of achromatic (luminance) shading and chromatic shading from mutual illumination. In addition, one chapter explores a selection of mathematical models of cue integration and their applicability in this case. The results of the experiments suggest that the human visual system is able to quickly assess and take account of colour mutual illuminations when estimating 3D object shape, and use chromatic gradients as an independent and effective cue. Finally, mathematical modelling reveals that the chromatic gradient cue is likely integrated with other shape cues in a way that is close to statistically optimal.

Perfectionism is a transdiagnostic process implicated in several disorders, and is defined in the literature as having standards of performance that are excessively high and often unrealistic, rigidly pursuing these standards, and subsequently measuring one’s own self-worth on their ability to meet these self-set standards (Egan et al., 2011). Perfectionism is related to many negative outcomes for physical and mental health, warranting the need to identify effective treatments that are accessible to individuals experiencing clinical perfectionism. There is a growing need for discrete, single session therapeutic interventions, and research has found that patients who were provided with a brief intervention exhibited accelerated rates of change, compared to patients whose treatment was longer (Baldwin et al., 2009; Kroska, 2018). Therefore, the purpose of this study was to examine the effects of a 90-minute, single-session ACT intervention targeting psychological flexibility for perfectionistic beliefs and behaviors on perfectionism, psychological distress, and well-being utilizing a multiple baseline across participants experimental design. Four individuals completed the following self-report measures at each time point: the Personalized Psychological Flexibility Inventory (PPFI), the Multidimensional Psychological Flexibility Inventory (MPFI), the Frost Multi-Dimensional Perfectionism Scale (FMPS), the Self-Compassion Scale (SCS), the Depression, Anxiety, and Stress Scale-21 item (DASS-21), and the Flourishing Scale (FS). These measures were completed once per week for the five-week baseline period. After baseline, participant engaged in a 90-minute single-session ACT intervention targeting the development of psychological flexibility. For follow-up, participants completed the same measures twice a week for four weeks. Researchers hypothesized that the intervention would increase psychological flexibility, flourishing, self-compassion, and progress towards an idiographic goal, and decrease perfectionism, psychological inflexibility, and psychological distress post-intervention compared to the baseline assessment. A TAR trend analysis was conducted, and Bayes Factors were computed for each individual for each outcome variable to examine within-participant results. A between-case standardized mean difference effect size for SCED was calculated for each outcome variable to examine the results across participants, resulting in a d-statistic. Within participants, while two individuals completed the study with perfectionistic concerns scores below cut offs, this outcome did not change significantly from baseline, with greater evidence for a null effect on this outcome variable for most participants. However, there was evidence for treatment effects for decreasing perfectionistic strivings, psychological distress, and psychological inflexibility and increasing psychological flexibility and flourishing. Across participants, the intervention demonstrated small to large effect sizes. There were small effects on perfectionistic concerns, perfectionistic strivings, psychological distress, and psychological flexibility towards an individual goal. There were medium effects for psychological flexibility and flourishing. Large effects were demonstrated for psychological inflexibility and self-compassion. Overall, the results demonstrate promising evidence for increasing well-being within the context of clinical perfectionism using a single session intervention.

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No / The recent development of information techniques, especially the state-of-the-art “big data” solutions, enables the extracting, gathering, and processing large amount of toxicity information from multiple sources. Facilitated by this technology advance, a framework named integrated testing strategies (ITS) has been proposed in the predictive toxicology domain, in an effort to intelligently jointly use multiple heterogeneous toxicity data records (through data fusion, grouping, interpolation/extrapolation etc.) for toxicity assessment. This will ultimately contribute to accelerating the development cycle of chemical products, reducing animal use, and decreasing development costs. Most of the current study in ITS is based on a group of consensus processes, termed weight of evidence (WoE), which quantitatively integrate all the relevant data instances towards the same endpoint into an integrated decision supported by data quality. Several WoE implementations for the particular case of toxicity data fusion have been presented in the literature, which are collectively studied in this paper. Noting that these uncertainty handling methodologies are usually not simply developed from conventional probability theory due to the unavailability of big datasets, this paper first investigates the mathematical foundations of these approaches. Then, the investigated data integration models are applied to a representative case in the predictive toxicology domain, with the experimental results compared and analysed.

Recollection is a pattern completion process that enables retrieval of arbitrarily associated information following minimal study. These attributes enable recollection to support retrieval of many kinds of mnemonic representations, from highly associative contextual information to very specific low-level representations. However, recollection is typically studied in the context of declarative memory tasks, in which participants exhibit recollection by explicitly reporting on the recollected information. Is it the case that recollection is limited to declarable representations, or is it a more general process that occurs for any representation? Two experiments and a novel analysis technique are presented to answer this question. The results suggest that recollection is not limited to declarable representations. These results argue against theories of recognition memory that restrict the representational input allowed to mnemonic processes; mnemonic processes in general may act on arbitrary representations.