Barbata was born in Mexico City in 1958 and now lives and works in New York. A self-taught artist, she also studied sculpture and engraving at the School of Visual Arts at the University of Rio de Janeiro, architecture in Mexico City, and sociology at the University of California in San Diego. She has participated in more than 60 group exhibitions and biennials in Mexico, Brazil, Cuba, Europe and the United States, including at such major museums as the Metropolitan Museum of Art in New York, the Museum of Modern Art in Mexico City, and the Museum of Modern Art in Rio de Janeiro.

Anderson's drawings, sculpture and installations have been presented in solo exhibitions throughout Mexico and in Venezuela, Colombia, and the United States. "In the Order of Chaos", a 1998 solo exhibition at the Austin Museum of Art in Texas, inaugurated the museum's new series presenting the work of innovative younger artists. Since 1992, Anderson has worked with native communities in the Venezuelan Amazon and Ecuador, training them in the fabrication of hand-made paper. She incorporates the paper in her work, along with gourds, wax, and human teeth. Anderson is represented in corporate and museum collections, including those of the American Express Company, the Metropolitan Museum of Art, the Bozano-Simonsen Foundation in Rio de Janeiro, and the Museum of Modern Art in Mexico City.