  Simplicity bias is an intriguing phenomenon prevalent in various input-output
maps, characterized by a preference for simpler, more regular, or symmetric
outputs. Notably, these maps typically feature high-probability outputs with
simple patterns, whereas complex patterns are exponentially less probable. This
bias has been extensively examined and attributed to principles derived from
algorithmic information theory and algorithmic probability. In a significant
advancement, it has been demonstrated that the renowned logistic map and other
one-dimensional maps exhibit simplicity bias when conceptualized as
input-output systems. Building upon this work, our research delves into the
manifestations of simplicity bias within the random logistic map, specifically
focusing on scenarios involving additive noise.
  We discover that simplicity bias is observable in the random logistic map for
specific ranges of $\mu$ and noise magnitudes. Additionally, we find that this
bias persists even with the introduction of small measurement noise, though it
diminishes as noise levels increase. Our studies also revisit the phenomenon of
noise-induced chaos, particularly when $\mu=3.83$, revealing its
characteristics through complexity-probability plots. Intriguingly, we employ
the logistic map to illustrate a paradoxical aspect of data analysis: more data
adhering to a consistent trend can occasionally lead to \emph{reduced}
confidence in extrapolation predictions, challenging conventional wisdom.
  We propose that adopting a probability-complexity perspective in analyzing
dynamical systems could significantly enrich statistical learning theories
related to series prediction and analysis. This approach not only facilitates a
deeper understanding of simplicity bias and its implications but also paves the
way for novel methodologies in forecasting complex systems behavior.
