Class
NumCosmoMathStatsVec
Description [src]
final class NumCosmoMath.StatsVec : GObject.Object
{
/* No available fields */
}An online statistics vector.
This object calculates some basic statistics (mean, variance and covariance) of a set of random variables.
The mean can be calculated online using the following formula: $$\bar{x}n = \bar{x}{n-1} + (x_n - \bar{x}_{n-1})\frac{w_n}{W_n},$$ where $\bar{x}_n$ is the mean calculated using the first $n$ elements, $x_n$ is the $n$-th element, $w_n$ the $n$-th weight and finally $W_n$ is the sum of the first $n$ weights.
Using the expressions above we obtain the variance from as following: $$M_n = M_{n-1} + (x_n - \bar{x}{n-1})^2w_n\frac{W{n-1}}{W_n},$$ where the variance of the first $n$ elements is $$V_n = \frac{M_n}{W^\text{bias}{n}}, \quad W^\text{bias}{n} \equiv \frac{W_n^2 - \sum^n_iw_i^2}{W_n}.$$ In the formula above we defined the bias corrected weight $W^\text{bias}_{n}$.
Finally, the covariance is computed through the following expression: $$N(x,y)n = N(x,y){n-1} + (x_n - \bar{x}n)(y_n - \bar{y}{n-1})w_n,$$ where the covariance of two variables $x$, $y$ is given by $$Cov(x,y)n = \frac{N(x,y)_n}{W^\text{bias}{n}}.$$
Using a NcmStatsVec.
// Creates a new one dimensional NcmStatsVec to calculates mean and variance.
NcmStatsVec *svec = ncm_stats_vec_new (1, NCM_STATS_VEC_VAR, FALSE);
// Set and update three different values of the only random variable.
ncm_stats_vec_set (svec, 0, 1.0);
ncm_stats_vec_update (svec);
ncm_stats_vec_set (svec, 0, 2.0);
ncm_stats_vec_update (svec);
ncm_stats_vec_set (svec, 0, 1.5);
ncm_stats_vec_update (svec);
{
gdouble mean = ncm_stats_vec_get_mean (svec, 0);
gdouble var = ncm_stats_vec_get_var (svec, 0);
...
}
Functions
ncm_stats_vec_clear
Decrease the reference count of svec by one, and sets the pointer *svec to
NULL.
Instance methods
ncm_stats_vec_append
Appends and updates the statistics using weight 1.0 for the vector x NcmVector of same
size NcmStatsVec:length and with continuous allocation. i.e., NcmVector:stride == 1.
ncm_stats_vec_append_data
Appends and updates the statistics using the data contained in data and weight == 1.0.
It assumes that each element of data is a NcmVector of same size NcmStatsVec:length and
with continuous allocation. i.e., NcmVector:stride == 1.
ncm_stats_vec_append_weight
Appends and updates the statistics using weight w for the vector x NcmVector of same
size NcmStatsVec:length and with continuous allocation. i.e., NcmVector:stride == 1.
ncm_stats_vec_compute_cov_robust_diag
Compute the covariance using the saved data applying a a robust scale estimator for each degree of freedom.
ncm_stats_vec_compute_cov_robust_ogk
Compute the covariance matrix employing the Orthogonalized Gnanadesikan-Kettenring (OGK) method. This method utilizes saved data and incorporates a robust scale estimator for each degree of freedom. The OGK method provides a robust and efficient approach to compute covariance, ensuring reliable estimates even in the presence of outliers or skewed distributions.
ncm_stats_vec_enable_quantile
Enables quantile calculation, it will calculate the $p$ quantile. Warning, it does not support weighted samples, the results will ignores the weights.
ncm_stats_vec_estimate_const_break
Estimate mean $\mu$ and standard deviation $\sigma$ fitting the paramater p
using robust regression. Computes the time $t_0$ where the parameter p falls
within the $\alpha\sigma$ from $\mu$, where $\alpha$ is implicitly defined by
$$ \int_\alpha^\infty\chi_1(X)\mathrm{d}X = 1/N,$$
and $N$ is the size of the sample.
ncm_stats_vec_fit_ar_model
If order is zero the value of floor $\left[10 log_{10}(s) \right]$, where $s$ is the number of points.
ncm_stats_vec_get_autocorr
Calculates the autocorrelation vector, the j-th element represent the self-correlation with lag-j.
ncm_stats_vec_get_autocorr_tau
Calculates the integrated autocorrelation time for the parameter p
using all rows of data.
ncm_stats_vec_get_cor
Return the current value of the correlation between the i-th and the j-th
variables, i.e., $$Cor_{ij} \equiv \frac{Cov_{ij}}{\sigma_i\sigma_j}.$$.
ncm_stats_vec_get_cov
Return the current value of the variance between the i-th and the j-th
variables, i.e., $Cov_{ij}$.
ncm_stats_vec_get_cov_matrix
Copy the current value of the correlation between the variables to the
matrix m starting from paramenter offset.
ncm_stats_vec_get_mean_vector
Copy the current value of the means to the vector mean starting from parameter offset.
ncm_stats_vec_get_param_at
Gets the p-th parameter in the i-th data row used in the statistics, this function fails if the object was not created with save_x == TRUE;.
ncm_stats_vec_get_quantile
Returns the current estimate of the quantile initialized through ncm_stats_vec_enable_quantile().
ncm_stats_vec_get_quantile_all
Returns the current estimate of the quantile initialized through ncm_stats_vec_enable_quantile(). It returns an array containing the minimum, p/2, p, (p + 1)/2 and maximum value.
ncm_stats_vec_get_quantile_spread
Returns the current estimate of the quantile spread, from the probability $p$ initialized through ncm_stats_vec_enable_quantile(), i.e., it returns the difference between $(p + 1)/2$ quantile and the $p/2$. For example, if $p = 0.5$ then it returns the inter-quartile range.
ncm_stats_vec_get_sd
Return the current value of the variable standard deviation, i.e., $\sigma_n \equiv sqrt (Var_n)$.
ncm_stats_vec_get_subsample_autocorr
Calculates the autocorrelation vector, the j-th element represent
the self-correlation with lag-j using the subsample parameter.
ncm_stats_vec_get_subsample_autocorr_tau
Calculates the integrated autocorrelation time for the parameter p
using the subsample parameter.
ncm_stats_vec_get_weight
Return the current value of the weight, for non-weighted means this is simply the number of elements.
ncm_stats_vec_heidel_diag
Applies the Heidelberger and Welch’s convergence diagnostic
applying ntests Schruben tests sequentially, if ntests == 0
it will use the default 10 tests. The variable bindex will
contains the smallest index where all p-values are smaller than
pvalue, if pvalue is zero it used the default value of $0.05$.
ncm_stats_vec_max_ess_time
Calculates the time $t_m$ that maximizes the Effective Sample Size (ESS).
The variable ntests control the number of divisions where the ESS
will be calculated, if it is zero the default 10 tests will be used.
ncm_stats_vec_nrows
Gets the number of saved rows, this function fails if the object was not created with save_x == TRUE;.
ncm_stats_vec_peek_cov_matrix
Gets the internal covariance matrix starting from paramenter offset.
This is the internal matrix of svec and can change with further
additions to svec. It is not guaranteed to be valid after new additions.
ncm_stats_vec_peek_row
The i-th data row used in the statistics, this function fails if the object was not created with save_x == TRUE;.
ncm_stats_vec_prepend
Prepends and updates the statistics using the vector x and weight 1.0.
It assumes that NcmVector is of same size NcmStatsVec:length and
with continuous allocation. i.e., NcmVector:stride == 1.
ncm_stats_vec_prepend_data
Prepends and updates the statistics using the data contained in data and weight == 1.0.
It assumes that each element of data is a NcmVector of same size NcmStatsVec:length and
with continuous allocation. i.e., NcmVector:stride == 1.
ncm_stats_vec_prepend_weight
Prepends and updates the statistics using the vector x and weight w.
It assumes that NcmVector is of same size NcmStatsVec:length and
with continuous allocation. i.e., NcmVector:stride == 1.
ncm_stats_vec_reset
Reset all data in svec. If rm_saved is TRUE and svec has
saved data, it will be also removed from the object.
ncm_stats_vec_update_weight
Updates the statistics using svec->x set in svec and weight, then reset
svec->x to zero.
ncm_stats_vec_visual_heidel_diag
Computes the empirical cumulative and the mean used to build the Heidelberger and Welch’s convergence diagnostic.
Signals
Signals inherited from GObject (1)
GObject::notify
The notify signal is emitted on an object when one of its properties has its value set through g_object_set_property(), g_object_set(), et al.