The oft-repeated claim that polar bears are starving in Western Hudson Bay (e.g., here, here, here, and here) comes primarily from a 10 year old study that documented a declining trend in polar bear body condition (a biology euphemism for relative fatness) between 1980 and 2004, which appeared to correlate with earlier and earlier breakup dates for Hudson Bay.
The authors of that study (polar bear specialist Ian Stirling and NASA sea ice researcher Claire Parkinson) reported the body weights of lone female bears captured in Western Hudson Bay between 1980 and 2004. The trend over time in those bear weights was then correlated with the overall change in dates of sea ice breakup on Hudson Bay for that period.
However, it turns out that while the trend of body condition and the trend in breakup dates indeed correlated over time, the actual year to year data did not. The question is, what does that mean for the claim that polar bears in WHB are starving?