ability_eap

def ability_eap(dataset, difficulty, discrimination, options=None):
    """Estimates the abilities for dichotomous models.

    Estimates the ability parameters (theta) for dichotomous models via
    expaected a posterior likelihood estimation.

    Args:
        dataset: [n_items, n_participants] (2d Array) of measured responses
        difficulty: (1d Array) of difficulty parameters for each item
        discrimination: (1d Array) of disrimination parameters for each item
        options: dictionary with updates to default options

    Returns:
        abilities: (1d array) estimated abilities

    Options:
        * distribution: callable
        * quadrature_bounds: (float, float)
        * quadrature_n: int

    """
    options = validate_estimation_options(options)
    quad_start, quad_stop = options['quadrature_bounds']
    quad_n = options['quadrature_n']

    if np.atleast_1d(discrimination).size == 1:
        discrimination = np.full(dataset.shape[0], discrimination,
                                 dtype='float')

    the_sign = convert_responses_to_kernel_sign(dataset)

    theta = _get_quadrature_points(quad_n, quad_start, quad_stop)
    partial_int = _compute_partial_integral(
        theta, difficulty, discrimination, the_sign)

    # Weight by the input ability distribution
    partial_int *= options['distribution'](theta)

    # Compute the denominator
    denominator = integrate.fixed_quad(
        lambda x: partial_int, quad_start, quad_stop, n=quad_n)[0]

    # compute the numerator
    partial_int *= theta

    numerator = integrate.fixed_quad(
        lambda x: partial_int, quad_start, quad_stop, n=quad_n)[0]

    return numerator / denominator