Question about Withings Sleep Analyser

Answer: Not at all.
The "measurements" that the device makes for me are largely implausible and deviate enormously from those recorded by another device (which works with EEG electrodes on the head, among other things).

According to the manufacturers: Our sleep algorithm has been calibrated against clinical records of sleep and polysomnography (PSG) at Paris-Béclère Hospital. It determines wake, rem, deep and light sleep phases by tracking a user's heart rate, respiratory rate and movement at high frequency and without disturbing the user's sleep.

I have been using this device for a month now and already feel that it is pretty accurate.