These expectation-dependent dynamics represent a novel view of leaky, saturating, or otherwise imperfect evidence accumulation, which here may be understood as facilitating, rather than hindering, statistical inference.
This formulation allowed us to identify, for the first time, features of evidence accumulation that can underlie normative, adaptive decision-making, including expectation-dependent changes in leaky accumulation when beliefs are weak and saturating accumulation when beliefs are stronger.
The term 'integrated' is used explicitly to emphasise that the outputs of this system (i.e. decisions, actions and expectations) are dependent on an extended history of past experiences.
An offering passes the test if it meets four prongs: being an investment contract in a common enterprise with an expectation of profits dependent on a third-part promoter.
Instead of a linear model, we carry out the analysis using the nonlinear specification in Eq. 2, where the conditional expectation of the dependent binary variable is a nonlinear function that follows a Probit specification.
Binning allows us to estimate the conditional expectation of the dependent variable given the independent variable, i.e. apply equation 6.
The GEE approach, extending the idea of the generalized linear model (GLM), assumes a known function of the marginal expectation of the dependent variables [ 38].
Then the time-dependent expectation value of any observable is (6).
On the other hand, the model-dependent expectation involves a sum over all (2^K) elements of u as well as the (2^T) elements of h.
Therefore, exact computation of the data-dependent expectation is intractable because its complexity is exponential in the number of visible and hidden layer nodes.
Once sufficient number of samples are obtained with Gibbs sampling, the Monte Carlo approach can be used to approximate the model-dependent expectation specified in Eq. (14).
