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I am familiar with Bayes Theorem and hypothesis testing, but not much above that.

However, I have a problem that I cannot seem to formulate in frequentist terms - to my knowledge. From what I know of the Bayesian definition of probability, I hope to research some stuff about hypothesis testing in Bayesian statistics.

However I need some help to get there.

I am looking at room temperatures in a room, for which I have enough to build a linear heat model. I also know how much sunlight enters the room in the day and if the windows are open.

It is possible to build a first order fourier heat equation with this data.

However, the radiator was changed sometime last year. But I do not know when.

Question 1. Can I formulate a statistic or a posterior probability given the data, when the change happened?

I do not know any of the parameters involved, since where the change happened would affect my linear coefficients if we were to fit this data to the multivariate linear model of whether heating was on, if windows were open and if there was sunlight in the room.

I hope that it is possible to come up with a Bayesian posterior probability that confirms the changepoint and the coefficients of the fit as more data is fed to it.

Question 2. If I wanted to solve this problem really efficiently, where would I look for a succinct theoretical background? Some monograph, or survey article would be amazing.

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The residuals from your model could be used as input to an analysis program that would evaluate 1) significant deviation of the observed values versus the expected values and suggest either pulse, level/step shift or the need for time trend indicators in the presence of possibly auto-correlated residuals 2) whether or not a deterministic error variance change was detected and when .

This could be accomplished following http://docplayer.net/12080848-Outliers-level-shifts-and-variance-changes-in-time-series.html .

I have been involved with developing/advancing what had been published and if you post your residuals from your theoretical model based upon real or fabricated/simulated data I might be able to help further .

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