  Roy and Bhattacharya (2020) provided Bayesian characterization of infinite
series, and their most important application, namely, to the Dirichlet series
characterizing the (in)famous Riemann Hypothesis, revealed insights that are
not in support of the most celebrated conjecture for over 150 years.
  In contrast with deterministic series considered by Roy and Bhattacharya
(2020), in this article we take up random infinite series for our
investigation. Remarkably, our method does not require any simplifying
assumption. Albeit the Bayesian characterization theory for random series is no
different from that for the deterministic setup, construction of effective
upper bounds for partial sums, required for implementation, turns out to be a
challenging undertaking in the random setup. In this article, we construct
parametric and nonparametric upper bound forms for the partial sums of random
infinite series and demonstrate the generality of the latter in comparison to
the former. Simulation studies exhibit high accuracy and efficiency of the
nonparametric bound in all the setups that we consider.
  Finally, exploiting the property that the summands tend to zero in the case
of series convergence, we consider application of our nonparametric bound
driven Bayesian method to global climate change analysis. Specifically,
analyzing the global average temperature record over the years 1850--2016 and
Holocene global average temperature reconstruction data 12,000 years before
present, we conclude, in spite of the current global warming situation, that
global climate dynamics is subject to temporary variability only, the current
global warming being an instance, and long term global warming or cooling
either in the past or in the future, are highly unlikely.
