ability_map

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

    Estimates the ability parameters (theta) for dichotomous models via
    maximum 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: 

    Notes:
        If distribution is uniform, please use ability_mle instead. A large set 
        of probability distributions can be found in scipy.stats
        https://docs.scipy.org/doc/scipy/reference/stats.html
    """
    options = validate_estimation_options(options)
    distribution = options['distribution']

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

    n_takers = dataset.shape[1]
    the_sign = convert_responses_to_kernel_sign(dataset)
    thetas = np.zeros((n_takers,))

    for ndx in range(n_takers):
        # pylint: disable=cell-var-from-loop
        scalar = the_sign[:, ndx] * discrimination

        def _theta_min(theta):
            otpt = 1.0 / (1.0 + np.exp(scalar * (theta - difficulty)))

            return -(np.log(otpt).sum() + np.log(distribution(theta)))

        # Solves for the ability for each person
        thetas[ndx] = fminbound(_theta_min, -6, 6)

    return thetas