向日葵视频

In a novel use of statistics, researchers estimate the number of unattributed paintings, known as ‘sleepers’, by the famous 20^th Century Italian artist Amedeo Modigliani to be at between 20 and 120.

Modigliani’s works are among those that fetch some of the highest prices in the art world, with his ‘Nu couché’ painting having sold under the hammer for $170 million.

Though the exact number of Modigliani paintings (Modigliani also produced drawings and sculpture but they were not part of this study) are unknown. His work only gained popularity after his death, aged 35, in 1920. During his lifetime, he would give his paintings away or, due to financial hardship, sell them for pittances. His landlord is even said to have used them to patch-up old mattresses. Estimating a precise figure is also complicated by a large number of fakes that exist.

A ‘sleeper’ is a Modigliani painting that is in known circulation but where it has not yet been determined that it is a genuine Modigliani work.

In this new study, published by the journal Statistical Methods and Applications, Dr James Jackson, who undertook the research while at the Alan Turing Institute and now works at the Office for National Statistics, and Professor Brian Francis of 向日葵视频’s School of Mathematical Sciences, attempted to provide an estimate for the number of Modigliani sleepers by using a statistical method called multiple systems estimation (MSE).

MSE is a long-established statistical technique that has been used to estimate the effects of the plague in the 17^th Century, the population of France in the 19^th Century, and more recently to estimate the scale of human trafficking, the prevalence of drug usage as well as population estimates in official statistics. However, MSE is not commonly used in the context of art history.

Statisticians can use MSE when there are at least two incomplete lists on a given subject.

Artists’ works tend to be documented in comprehensive lists called Catalogue Raisoneé (CR). Most artists tend to have one definitive CR compiled by a leading expert.

However, Modigliani is unusual in that there are five CR of his work. The existence of these multiple lists enabled Dr Jackson and Professor Francis to apply the MSE technique to discover an estimate of unattributed Modigliani paintings.

Dr Jackson, who studied for a PhD at 向日葵视频 under supervision of Professor Francis, said the idea for the research came to him while watching a television programme.

“I was watching an episode of Fake or Fortune? on Modigliani and early on in the episode it mentions the unusual situation of there being five Modigliani catalogues raisoneés, and that’s when I had the idea,” he said. “I think I had subconsciously been on the lookout for potential applications of MSE. I had previously worked with Brian (Francis) on MSE in relation to modern slavery.”

Under the MSE technique, each Modigliani painting will fall under one of a possible 32 capture patterns. It could appear on one CR list, multiple lists, all five CR lists or none at all.

The researchers used a dataset called the ‘Secret Modigliani’ website which has cross classified most of the Modigliani paintings to show which appear within each Catalogue Raisoneé. In total there are 488 paintings attributed to one or more Modigliani CR.

Importantly, the researchers assumed that each painting included on each list is genuine and there are no fakes or wrongly attributed works.

Using MSE the researchers calculated the number of sleeping Modigliani paintings that likely do not appear on any of the five CR to be between 20 and 120.

These results suggest that, when added to the number of works that appear in at least one CR, there are between 500 and 600 Modigliani paintings.

However, the authors recognise that their calculations do have some limitations. It only factors for known unattributed works and does not account for any currently unknown paintings that are yet to be re-discovered.

The researchers believe that their study shows the potential MSE offers for estimating the number of unattributed art works.

Professor Francis said: “There is a lot of untapped potential in gathering data from art history, and this work offers an insight into other possibilities.”

Dr Jackson said: “There is definitely scope to apply this MSE approach to other artists. To apply MSE you only need two or more catalogues raisoneés. There are actually quite a few artists who have two or more catalogues, such as Renoir – but few have as many as Modigliani’s five."

The research is outlined in the paper ‘’.

DOI: 10.1007/s10260-024-00774-w