Painoarvo

Painoarvo is a Finnish term that refers to a numeric value assigned to a data item, criterion, or observation to express its relative importance, frequency, reliability, or probability in a calculation or model. It is used to modify contributions in calculations such as weighted averages, sums, estimations, and decision models.

In statistics and data collection, painoarvot help correct for uneven sampling or nonresponse. Weights w_i are often related to the inverse probability of inclusion or adjusted for post-stratification. A weighted mean is computed as x̄_w = (sum w_i x_i) / (sum w_i). Weighted variance and other estimators similarly use weights to reflect the varying influence of observations. In some applications, weights are normalized so that their sum equals one.

In machine learning and data analysis, painoarvot appear as sample weights or instance weights in loss functions, giving more influence to certain observations, such as rare classes or difficult examples. Weights are also used to address class imbalance or to prioritize particular outcomes in training.

In decision analysis and multi-criteria evaluation, painoarvot quantify the relative importance of criteria. Techniques such as simple weighting, entropy weighting, and the Analytic Hierarchy Process (AHP) produce weights that are often normalized to sum to one. These weights are then applied in aggregation methods like the weighted sum model to produce overall scores or rankings.

Determining weights involves expert judgment, data-driven methods, or optimization, and practitioners commonly perform sensitivity analyses to assess how changes in weights affect conclusions. Potential issues include subjectivity, redundancy among criteria, and overemphasis on correlated factors.