T2K (from Tokai-to-Kamioka) is a long-baseline neutrino experiment using an off-axis neutrino beam to produce a narrow neutrino energy spectrum. T2K uses a near detector (ND280) to constrain the neutrino cross-section and beam flux systematics for the neutrino oscillation analyses, and provides some of the world's leading cross-section measurements. The neutrino beam is directed to, and detected at, Super-Kamiokande, a large 50\,kT Water Cherenkov detector that is also being used to study atmospheric, cosmic, supernovae neutrinos and more.

We describe the oscillation analysis for the T2K experiment that uses both near and far detector data, using Markov Chain Monte Carlo techniques to construct the Bayesian posterior probability distributions for the oscillation parameters. The analysis of the full T2K run 1–9 data with the reactor constraint on $sin^2\theta_{13}$ show that the CP conserving values of $\delta_{CP}$ are rejected with at least 2\,$\sigma$ confidence and intervals between -2.95 and -0.50 with the best fit point -1.82\,rad, whereas the 3\,$\sigma$ intervals are -$\pi$ – 0.13 \& 2.80 – $\pi$. The Normal Mass hierarchy has 88.9\% of the total Markov Chain Monte Carlo steps, corresponding to the likelihood-ratio of the two hypotheses, Bayes Factor, of 8.0. This can be considered as “substantial” on the Jeffreys scale, which is an interpretation the strength of Bayes Factors. The best fit point of $sin^2\theta_{23}$ is 0.537, preferring higher octant with 79.5\% Markov Chain Monte Carlo steps. This corresponds to the Bayes Factor of 3.4, again “substantial” on the Jeffreys scale.

Neither run 1–9c nor full run 1–9d data are incompatible with the PMNS model. The 1\,$\sigma$ intervals for $P(\nu_{\mu} \rightarrow \nu_e)$ and $P(\bar{\nu}_{\mu} \rightarrow \bar{\nu}_e)$ posterior probability distributions for both PMNS and non-PMNS analyses comfortably overlap. Far more data from the T2K's far detector, Super-K, is needed to see any potential deviations; we are currently statistically limited.

We also describe the development of a novel neutrino event reconstruction method for large Water Cherenkov detectors using similar Bayesian methods as in the oscillation analysis.