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Focused on empirical methods and their applications to corporate finance, this innovative text equips students with the knowledge to analyse and critically evaluate quantitative research methods in corporate finance, and conduct computer-aided statistical analyses on various types of datasets. Chapters demonstrate the application of basic econometric models in corporate finance (as opposed to derivations or theorems), backed up by relevant research. Alongside practical examples and mini case studies, computer lab exercises enable students to apply the theories of corporate finance and make stronger connections between theory and practice, while developing their programming skills. All of the Stata code is provided (with corresponding Python and R code available online), so students of all programming abilities can focus on understanding and interpreting the analyses.
ML methods are increasingly being used in (corporate) finance studies, with impressive applications. ML methods can be applied with the aim of reducing prediction error in the models, but can also be used to extend the existing traditional econometric methods. The performance of the ML models depends on the quality of the input data and the choice of model. There are many ML models, but all come with their own specific details. It is therefore essential to select accurate model(s) for the analysis. This chapter briefly reviews some broad types of ML methods. It covers supervised learning, which tends to achieve superior prediction performance by using more flexible functional forms than OLS in the prediction model. It explains unsupervised learning methods that derive and learn structural information from conventional data. Finally, the chapter also discusses some limitations and drawbacks of ML, as well as potential remedies.
Prediction in the motor domain, but perhaps also in the cognitive domain, is a universal function of the human cerebellum. The cerebellum contains and maintains two internal models of the world to coordinate and control behavior: an inverse model to generate motor commands and a forward prediction model; as well as an error detection mechanism and a learning process that corrects the prediction errors.
The brain does not passively register sensory input but actively predicts it. The activity of the sensory input is ‘explained away’ and only activity that was not predicted remains. This remaining activity is treated as an error signal that is used to update the predictive coding system. Learning is predictive coding.
This study tests whether prediction error underlies structural priming in a later-learnt L2 across two visual world eye-tracking priming experiments. Experiment 1 investigates priming when learners encounter verbs biased to double-object-datives (DO, “pay”) or prepositional-object-datives (PO, “send”) in the other structure in prime sentences. L1-German–L2-English learners read prime sentences crossing verb bias and structure (DO/PO). Subsequently, they heard target sentences – with unbiased verbs (“show”) – while viewing visual scenes. In line with implicit learning models, gaze data revealed priming and prediction-error effects, namely, more predictive looks consistent with PO following PO primes with DO-bias verbs. Priming in comprehension persisted into (unprimed) production, indicating that priming by prediction error leads to longer-term learning. Experiment 2 investigates the effects of target verb bias on error-based priming. Priming and prediction-error effects were reduced for targets with non-alternating verbs (“donate”) that only allow PO structures, suggesting learners’ knowledge of the L2 grammar modulates prediction-error-based priming.
Altered reinforcement learning (RL) and decision-making have been implicated in the pathophysiology of anorexia nervosa. To determine whether deficits observed in symptomatic anorexia nervosa are also present in remission, we investigated RL in women remitted from anorexia nervosa (rAN).
Methods:
Participants performed a probabilistic associative learning task that involved learning from rewarding or punishing outcomes across consecutive sets of stimuli to examine generalization of learning to new stimuli over extended task exposure. We fit a hybrid RL and drift diffusion model of associative learning to model learning and decision-making processes in 24 rAN and 20 female community controls (cCN).
Results:
rAN showed better learning from negative outcomes than cCN and this was greater over extended task exposure (p < .001, ηp2 = .30). rAN demonstrated a reduction in accuracy of optimal choices (p = .007, ηp2 = .16) and rate of information extraction on reward trials from set 1 to set 2 (p = .012, ηp2 = .14), and a larger reduction of response threshold separation from set 1 to set 2 than cCN (p = .036, ηp2 = .10).
Conclusions:
rAN extracted less information from rewarding stimuli and their learning became increasingly sensitive to negative outcomes over learning trials. This suggests rAN shifted attention to learning from negative feedback while slowing down extraction of information from rewarding stimuli. Better learning from negative over positive feedback in rAN might reflect a marker of recovery.
Depression is characterized by abnormalities in emotional processing, but the specific drivers of such emotional abnormalities are unknown. Computational work indicates that both surprising outcomes (prediction errors; PEs) and outcomes (values) themselves drive emotional responses, but neither has been consistently linked to affective disturbances in depression. As a result, the computational mechanisms driving emotional abnormalities in depression remain unknown.
Methods
Here, in 687 individuals, one-third of whom qualify as depressed via a standard self-report measure (the PHQ-9), we use high-stakes, naturalistic events – the reveal of midterm exam grades – to test whether individuals with heightened depression display a specific reduction in emotional response to positive PEs.
Results
Using Bayesian mixed effects models, we find that individuals with heightened depression do not affectively benefit from surprising, good outcomes – that is, they display reduced affective responses to positive PEs. These results were highly specific: effects were not observed to negative PEs, value signals (grades), and were not related to generalized anxiety. This suggests that the computational drivers of abnormalities in emotion in depression may be specifically due to positive PE-based emotional responding.
Conclusions
Affective abnormalities are core depression symptoms, but the computational mechanisms underlying such differences are unknown. This work suggests that blunted affective reactions to positive PEs are likely mechanistic drivers of emotional dysregulation in depression.
Inverse probability adaptation effects (the finding that encountering a verb in an unexpected structure increases long-term priming for that structure) have been observed in both L1 and L2 speakers. However, participants in these studies all had established representations of the syntactic structures to be primed. It therefore remains an open question whether inverse probability adaptation effects could take place with newly encountered L2 structures. In a pre-registered experiment, we exposed participants (n = 84) to an artificial language with active and passive constructions. Training on Day 1 established expectations for specific co-occurrence patterns between verbs and structures. On Day 2, established patterns were violated for the surprisal group (n = 42), but not for the control group (n = 42). We observed no immediate priming effects from exposure to high-surprisal items. On Day 3, however, we observed an effect of input variation on comprehension of verb meaning in an auditory grammaticality judgment task. The surprisal group showed higher accuracy for passive structures in both tasks, suggesting that experiencing variation during learning had promoted the recognition of optionality in the target language.
Individuals with cocaine use disorder or gambling disorder demonstrate impairments in cognitive flexibility: the ability to adapt to changes in the environment. Flexibility is commonly assessed in a laboratory setting using probabilistic reversal learning, which involves reinforcement learning, the process by which feedback from the environment is used to adjust behavior.
Aims
It is poorly understood whether impairments in flexibility differ between individuals with cocaine use and gambling disorders, and how this is instantiated by the brain. We applied computational modelling methods to gain a deeper mechanistic explanation of the latent processes underlying cognitive flexibility across two disorders of compulsivity.
Method
We present a re-analysis of probabilistic reversal data from individuals with either gambling disorder (n = 18) or cocaine use disorder (n = 20) and control participants (n = 18), using a hierarchical Bayesian approach. Furthermore, we relate behavioural findings to their underlying neural substrates through an analysis of task-based functional magnetic resonanceimaging (fMRI) data.
Results
We observed lower ‘stimulus stickiness’ in gambling disorder, and report differences in tracking expected values in individuals with gambling disorder compared to controls, with greater activity during reward expected value tracking in the cingulate gyrus and amygdala. In cocaine use disorder, we observed lower responses to positive punishment prediction errors and greater activity following negative punishment prediction errors in the superior frontal gyrus compared to controls.
Conclusions
Using a computational approach, we show that individuals with gambling disorder and cocaine use disorder differed in their perseverative tendencies and in how they tracked value neurally, which has implications for psychiatric classification.
Sequential decisions from sampling are common in daily life: we often explore alternatives sequentially, decide when to stop such exploration process, and use the experience acquired during sampling to make a choice for what is expected to be the best option. In decisions from experience, theories of sampling and experiential choice are unable to explain the decision of when to stop the sequential exploration of alternatives. In this chapter, we propose a mechanism to inductively generate stopping decisions, and we demonstrate its plausibility in a large and diverse human data set of the binary choice sampling paradigm. Our proposed stopping mechanism relies on the choice process of a theory of experiential choice, Instance-Based Learning Theory (IBLT). The new stopping mechanism tracks the relative prediction errors of the two options during sampling, and stops when such difference is close to zero. Our results from simulation are able to accurately predict human stopping decisions distributions in the dataset. This model provides an integrated theoretical account of decisions from experience, where the stopping decisions are generated inductively from the sampling process.
This chapter provides a selective review of the issues that have dominated computational models of associative learning in recent decades. Associative learning research concerns the simplest and most fundamental processes by which humans and other animals come to predict events in their environment based on past experience. It has far-reaching implications for understanding adaptive and maladaptive human behavior. With a focus on Pavlovian conditioning and adjacent subdisciplines, this chapter explores how the prediction error learning algorithm has shaped understanding of competitive learning, selective attention, stimulus representation, and learning about absent events. A number of alternative computational approaches will be introduced, along with some remaining challenges in the computational modeling of human and animal associative learning.
Delusions are false and incorrigible beliefs. They have yet to yield to psychological or neurobiological explanation. Contemporary theories attempt to bridge these levels of explanation. However, they differ in the allowable directions of influence between brain regions and psychological processes. More recently, beliefs and belief updating have fallen under the lens of social network theories. Uniting individual level accounts with those that incorporate the influence of others on ones’ beliefs may yield new avenues for treatment, that leverage key nodes in an individual’s extant social network, or that reconfigure networks to facilitate more healthful and appropriate belief formation and updating.
Eating disorders fundamentally involve disturbances in the experience of the physical sensations in one’s body based on internal signals, referred to as interoception. Interoceptive prediction errors (mismatch between anticipation and experience of physical sensation) may relate to anticipatory anxiety, avoidant behavior, and difficulty learning from experience. Deficits in making sense of brain signals related to internal body experience suggest a reliance on external signals is needed as a means to achieve recovery.
Anorexia nervosa (AN) is associated with altered sensitivity to reward and punishment. Few studies have investigated whether this results in aberrant learning. The ability to learn from rewarding and aversive experiences is essential for flexibly adapting to changing environments, yet individuals with AN tend to demonstrate cognitive inflexibility, difficulty set-shifting and altered decision-making. Deficient reinforcement learning may contribute to repeated engagement in maladaptive behavior.
Methods:
This study investigated learning in AN using a probabilistic associative learning task that separated learning of stimuli via reward from learning via punishment. Forty-two individuals with Diagnostic and Statistical Manual of Mental Disorders (DSM)-5 restricting-type AN were compared to 38 healthy controls (HCs). We applied computational models of reinforcement learning to assess group differences in learning, thought to be driven by violations in expectations, or prediction errors (PEs). Linear regression analyses examined whether learning parameters predicted BMI at discharge.
Results:
AN had lower learning rates than HC following both positive and negative PE (p < .02), and were less likely to exploit what they had learned. Negative PE on punishment trials predicted lower discharge BMI (p < .001), suggesting individuals with more negative expectancies about avoiding punishment had the poorest outcome.
Conclusions:
This is the first study to show lower rates of learning in AN following both positive and negative outcomes, with worse punishment learning predicting less weight gain. An inability to modify expectations about avoiding punishment might explain persistence of restricted eating despite negative consequences, and suggests that treatments that modify negative expectancy might be effective in reducing food avoidance in AN.
I comment on a new overview of the treatment of delusional infestation. I focus on the challenges of communicating with a patient who has delusions and evaluate practical advice. I look at philosophical models to explain those communication problems as well as theories of delusional formation, and examine how these may help clinicians to understand and overcome those challenges.
We consider some advances in relational and affective neuroscience and related disciplines that attempt to resolve some fundamental aspects of the mind–brain problem. We consider the key role of affect in generating consciousness and in meeting our essential survival needs; the neural correlates of relating; how self and other are represented in the brain and awareness of self and other is generated through interoceptive predictive processes. We describe some leading models of the generation and purpose of consciousness, linking theories of affective and cognitive consciousness. We discuss psychiatric and psychotherapeutic innovations arising from this research, new integrated biopsychosocial interventions and the obstacles to be overcome in applying these models in practice.
With world population senescence and globalization, more present-day older adults will evince cognitive aging that is influenced over a longer life span by a wide range of social practices and motivational beliefs from cultural groups across the world. Although there is no dispute that brain structure and function aggregate biological and experiential influences, a useful framework is still needed regarding the specific neural mechanisms underlying the exchange between biology and experience with age, and the effect on cognition. We introduce a predictive coding framework of the aging cognitive brain that views the older brain as making predictions about the environment based on a lifetime of experience in it. The influence of cultural experiences in shaping the aging predictive brain then reflects individual differences in processing social signals about appropriate or inappropriate behaviors and cognitive styles amid neural resources changes. We briefly annotate relevant findings on age effects and cultural differences in neurocognitive processing. We further review findings showing that cultural cognitive differences are present in children, persist in young adulthood, and are either maintained or accentuated in older adulthood. Finally, we consider that the predictive aging brain is an enculturated one, reflecting the accumulation of a lifetime of experiences that have fortified culture-specific modes of thought and neural processing in older adults.
Depressive episodes experienced in unipolar (UD) and bipolar (BD) disorders are characterized by anhedonia and have been associated with abnormalities in reward processes related to reward valuation and error prediction. It remains however unclear whether these deficits are associated with familial vulnerability to mood disorders.
Methods
In a functional magnetic resonance imaging study, we evaluated differences in the expected value (EV) and reward prediction error (RPE) signals in ventral striatum (VS) and prefrontal cortex between three groups of monozygotic twins: affected twins in remission for either UD or BD (n = 53), their high-risk unaffected co-twins (n = 34), and low-risk twins with no family history of mood disorders (n = 25).
Results
Compared to low-risk twins, affected twins showed lower EV signal bilaterally in the frontal poles and lower RPE signal bilaterally in the VS, left frontal pole and superior frontal gyrus. The high-risk group did not show a significant change in the EV or RPE signals in frontostriatal regions, yet both reward signals were consistently lower compared with low-risk twins in all regions where the affected twins showed significant reductions.
Conclusion
Our findings strengthen the notion that reduced valuation of expected rewards and reduced error-dependent reward learning may underpin core symptom of depression such as loss of interest in rewarding activities. The trend reduction in reward-related signals in unaffected co-twins warrants further investigation of this effect in larger samples and prospective follow-up to confirm possible association with increased familial vulnerability to mood disorders.
Computational neuroscience uses formal models of brain function to characterize the mechanisms behind behavioral problems. The production of false beliefs and their behavioral consequences are a central issue in such models. Hopelessness and suicidal thoughts are examples of such false beliefs that commonly lead to suicidal behavior as a consequence. In normal everyday life, people update their beliefs based on what they perceive: bottom-up sensory inputs are compared with top-down beliefs, and mismatches are signaled as prediction errors. Neurobiological correlates of belief updating are increasingly demonstrated. Cortical activations as demonstrated in functional neuroimaging studies, such as those reported in Chapter 6, thus reflect the production of prediction errors that signal a mismatch between beliefs and perceptual information. These errors can be minimized in several ways: beliefs can be updated, or sensory input can be minimized by withdrawal into oneself or escape from this world. If something goes wrong in this process of belief updating, false beliefs may develop and persist despite perceptual proof of the opposite. This chapter will describe a predictive coding model of suicidal behavior, in which findings from neurocognitive, neuroimaging, and neurobiological studies can be integrated. This model leads to a new understanding of suicide and, consequently, to new approaches to prevention.
The significant proportion of schizophrenia patients refractory to treatment, primarily directed at the dopamine system, suggests that multiple mechanisms may underlie psychotic symptoms. Reinforcement learning tasks have been employed in schizophrenia to assess dopaminergic functioning and reward processing, but these have not directly compared groups of treatment-refractory and non-refractory patients.
Methods
In the current functional magnetic resonance imaging study, 21 patients with treatment-resistant schizophrenia (TRS), 21 patients with non-treatment-resistant schizophrenia (NTR), and 24 healthy controls (HC) performed a probabilistic reinforcement learning task, utilizing emotionally valenced face stimuli which elicit a social bias toward happy faces. Behavior was characterized with a reinforcement learning model. Trial-wise reward prediction error (RPE)-related neural activation and the differential impact of emotional bias on these reward signals were compared between groups.
Results
Patients showed impaired reinforcement learning relative to controls, while all groups demonstrated an emotional bias favoring happy faces. The pattern of RPE signaling was similar in the HC and TRS groups, whereas NTR patients showed significant attenuation of RPE-related activation in striatal, thalamic, precentral, parietal, and cerebellar regions. TRS patients, but not NTR patients, showed a positive relationship between emotional bias and RPE signal during negative feedback in bilateral thalamus and caudate.
Conclusion
TRS can be dissociated from NTR on the basis of a different neural mechanism underlying reinforcement learning. The data support the hypothesis that a favorable response to antipsychotic treatment is contingent on dopaminergic dysfunction, characterized by aberrant RPE signaling, whereas treatment resistance may be characterized by an abnormality of a non-dopaminergic mechanism – a glutamatergic mechanism would be a possible candidate.