Speaker
Description
Likelihood-ratio statistics play a central role in assessing detection significance in cosmological analyses. Under regularity conditions, Wilks’ theorem predicts that these statistics follow a $\chi^2$ distribution in the asymptotic limit. When a parameter is restricted to a physical boundary, this result no longer holds, and Chernoff’s theorem provides the corresponding mixed distribution. In practice, however, cosmological likelihoods often involve several parameters that are both bounded and strongly correlated, and the extent to which standard asymptotic results apply in these settings remains unclear.
In this work, I investigate how parameter correlations and positivity constraints modify likelihood-ratio statistics in the context of CMB $B$-mode searches. These analyses typically involve the tensor-to-scalar ratio together with foreground amplitudes that are physically required to be non-negative, leading to a likelihood geometry that differs from the assumptions underlying the usual asymptotic results. Using simplified likelihood models, I examine the behaviour of profile likelihoods and likelihood-ratio tests in the presence of such correlated boundaries.
The results reproduce qualitative features seen in recent CMB analyses, where the empirical distribution of likelihood-ratio statistics deviates from the standard Chernoff prediction. I show that correlations between bounded parameters modify the probability that the likelihood peaks at the boundary, thereby altering the expected survival curves used to assess detection significance.
Understanding these effects is important for interpreting likelihood-ratio tests in current and upcoming high-precision CMB experiments, where increasingly sensitive measurements make the statistical behaviour of constrained likelihoods particularly relevant.