STFC-RAL-CR03 R61: 3.
STFC-RAL-CR03 R61: I've been here for about 8 months now, and numbers talk about yeah. Some work under Phd, and still some of them. Now, on taking a facing approach.
STFC-RAL-CR03 R61: So yeah, quick outline of this talk, I will start with a really brief overview of internal solutions. I'll introduce a few and some aspects.
STFC-RAL-CR03 R61: and I'll go into more detail about exactly how we performed these phase and sensitivities, what the results are a bit about what they mean, and then conclude with some work in progress on how to improve the sampling techniques for the next analysis.
STFC-RAL-CR03 R61: Okay, so few oscillations in a nutshell.
STFC-RAL-CR03 R61: So, as we all know, nequinos are extremely abundant.
STFC-RAL-CR03 R61: and there are multiple different sources, and these sources will live at different between our energy ranges.
STFC-RAL-CR03 R61: building sources, for example, all the way from Big Bang sources here on Earth, sun, supernova explosions, and even human sources like, however, nuclear reactors. But the source that is most relevant to this book are accelerators, neutrinos.
STFC-RAL-CR03 R61: and you can see
STFC-RAL-CR03 R61: a bit of this line with the X-axis. But these these neutrinos live in roughly the Ged range, but it is a very wide energy range, so we have neutrinosis 100 meb all the way up to some high end.
STFC-RAL-CR03 R61: So what are neutrino oscillations? Well, when a neutrino is produced, exists in a particular wheat, eigenstate, or flavor eigenstate, and this and these correspond to the 3 generations of Leprons, have.
STFC-RAL-CR03 R61: and these weak eigenstates are actually a linear combination of 3 mass eigenstates. And we can relate the flavor and mass eigenstates using a unitary mixing matrix that we call the Kns. Matrix.
STFC-RAL-CR03 R61: However, when these materials propagate, they propagate in their mass eigenstates, so provided that these mass eigenstates have masses. This results in a loss of the unique flavor identity that it was formed in. And now, as it propagates, it is in a superposition of these flavor eigenstates.
STFC-RAL-CR03 R61: and when neutrino reinteracts weekly.
STFC-RAL-CR03 R61: it collapses back to this weak eigenstate, and the probability of measuring a given flavor in our detector, for example, depends on the mass state measure at that point. And so phenociations refer to the fact that the probability of observing any given flavor oscillates. As the mass eigenstates or the mass States evolves.
STFC-RAL-CR03 R61: So we can see this oscillation.
STFC-RAL-CR03 R61: And so the question being is what these oscillations actually depend on, so on the right you can see the probability of observing a neural neutrino as a mu one neutrino, otherwise called the survival probability.
STFC-RAL-CR03 R61: and the 1st thing we can see is oscillates as a function of nuclear energy.
STFC-RAL-CR03 R61: But these oscillations also depend on the distance the neutrino has propagated, so we can see the probability for different distances which correspond to different long baseline experiments, and this is because the neutrino oscillations actually are a function of lov distance over energy.
STFC-RAL-CR03 R61: So the next thing between our stations depend on are the difference in the square of the masses of these mass eigenstates, so you can see on the right the square mass difference between the 3rd and second mass eigenstates, and if we increase this square mass difference, it has the effect of pushing the probability or the minimum of the probability to the right.
STFC-RAL-CR03 R61: And if you look at the bottom left semantic, we can see that there are actually 2 different configurations for these square mass splittings. We have one where the 3rd mass, eigenstate is the heaviest and one where it is the lightest. This is referred to personally between a hierarchy problem, and it can also be described as whether delta n squared 3, 2 is less than or greater than 0,
STFC-RAL-CR03 R61: and the interesting thing is neutrino oscillations actually are not affected in a vacuum by the sign of this mass splitting. And so we use matter effects to get sensitivity, so as neutrinos propagate through matter, they can coherently scatter off of electrons.
STFC-RAL-CR03 R61: and this is going to affect electron neutrinos more than the other planes neutrinos, and also affect electronutrinos differently to anti neutrinos. And this is exactly how we measured the sign and the magnitude of Delta M. Squared, t. 1. This square splitting affects solar neutrinos at the most, and so we measured solar oscillations. They experience significant matter effects as they oscillate out the sun. And so we're able to measure the sign and the magnitude of that form.
STFC-RAL-CR03 R61: It's okay.
STFC-RAL-CR03 R61: So the fuel stations also depend on the labor mixing. So the mixing between the flavor eigenstates and the mass eigenstates. And the way to view this is by view current pricing matrix, and we get 3 mixing angles.
STFC-RAL-CR03 R61: and these mixing angles can roughly correspond to the sourcing neutrinos that this mixing affects the most.
STFC-RAL-CR03 R61: and so on the top right, we can see how these 2 3, the atmospheric and accelerator mixing angle affects this probability plot, and you can see that maximum mixing. We really pulled this oscillation probability right down. And so it affects the depth of this minima
STFC-RAL-CR03 R61: and this parameterization also results in a Cp biased phase, Lcp.
STFC-RAL-CR03 R61: which is necessary for there to be a difference in vacuum oscillations between neutrinos and anti neutrinos. But if you look at the bottom top right, we can see that del Cp also affects the probability of a mule neutrino oscillating into an electron. And this is for a Dean baseline.
STFC-RAL-CR03 R61: Okay?
STFC-RAL-CR03 R61: So that is a very brief overview on human oscillations. But what do we know now?
STFC-RAL-CR03 R61: So these are the best fits and uncertainties for the oscillation parameters from a global fit.
STFC-RAL-CR03 R61: And as you can see, these are some pretty good measurements. These are the uncertainties are roughly the couple of percent level. And this is a result of decades worth of accelerator reactor solitary experiments, and we put them onto a global fit. The results come out pretty good.
STFC-RAL-CR03 R61: So the question is, what is left to know
STFC-RAL-CR03 R61: so arguably. The most important question in the neutrino sector right now is, Do neutrino oscillations violate Cp.
STFC-RAL-CR03 R61: as you can see, the best fit value is the same global fit with Lcp.
STFC-RAL-CR03 R61: and if we actually look at the plot.
STFC-RAL-CR03 R61: Cp conservation corresponds to value of Lcp, n, pi, so 0, 1 or 2 in the spot, and you can see that we actually don't have any great evidence that neutrinos currently do violate Cp or No. There enough to make the biasing statement that we want to be able to make
STFC-RAL-CR03 R61: the mass hierarchy, as I talked to earlier, is that 3rd trino acid heavier or the heaviest or the lightest
STFC-RAL-CR03 R61: and the the 2 3 Octant is theta, 2, 3, greater than or less than 45, which corresponds to maximum mixing. I'll touch a bit more on this later.
STFC-RAL-CR03 R61: And then, finally, is there new physics that we can explore by measuring between oscillations?
STFC-RAL-CR03 R61: Is the Pms actually unitary, or does there exist a hidden star. Neutrino
STFC-RAL-CR03 R61: do neutrinos exhibit monster interactions. And can we see that with map effects? And you can oscillations? And there's plenty of more that we can see
STFC-RAL-CR03 R61: right now our current baseline experiments are hitting a statistical wall, and we need a new high statistics, high precision based on experiment to be able to answer these questions.
STFC-RAL-CR03 R61: So Dude stands for the deep underground neutrino experiments.
STFC-RAL-CR03 R61: So to start with, dune is a large international collaboration with over 1,400 collaborators from 200 institutions in 35 different countries.
STFC-RAL-CR03 R61: Add to give a great overview
STFC-RAL-CR03 R61: due to aims that we keep being, or predominantly, the re one neutrinos, or anti neutrinos are firm enough.
STFC-RAL-CR03 R61: These neutrinos will 1st pass through in the detector. It's very close to neutrino source. These neutrinos will then propagate
STFC-RAL-CR03 R61: to the western side of Dakota, 1,300 kilometers away to the sanct underground resource. Facility, right? The fire detector will live 1,500 meters underground.
STFC-RAL-CR03 R61: so to go with some details about something, and it will produce a neutrino beam well needed power.
STFC-RAL-CR03 R61: So in the 1st phase of the dude experiments, we expect a beam power of about 1.2 megawatts, and in the second phase of the experiment we expect this to be upgraded to 2 megawatts.
STFC-RAL-CR03 R61: But the unique and cool thing about the zoom beam is that the detectors we placed on axis. And so if you look at the bottom right, which shows the blocks of neutrinos at the detector. You can see that this is quite a broad energy range.
STFC-RAL-CR03 R61: and the advantage of this is, it allows us to not only have a very high flux in preloads at the 1st ostation maximum, but also we have adhesive flux at the second, and so we can extract as much information as possible to infer our ostational values.
STFC-RAL-CR03 R61: Okay, so the principal technology that June will use to measure these neutrino interactions is with Argon.
STFC-RAL-CR03 R61: The reason being is that it provides us precise instruction of both electronic and hydronic energies, energy over a broad energy question.
STFC-RAL-CR03 R61: So the feature on the top right
STFC-RAL-CR03 R61: shows a simulated event. So what a typical view on events and feeling event will look like in liquid!
STFC-RAL-CR03 R61: We have this nice long neon track at the bottom, and then this hydraulic energy deposit at the top. And the granular detail here is really quite incredible, and this is precedented for a while detector at a neutral stage experiment.
STFC-RAL-CR03 R61: Now the actual design of the fire detector consists of 4 modules. You can see the cabin here at the bottom, right.
STFC-RAL-CR03 R61: The 1st of these modules will be a vertical drift argon time projection chamber, and the second will be a horizontal drift.
STFC-RAL-CR03 R61: and you can see there's 2 empty spaces for 2 more modules, and right now the the baseline design is that there'll be vertical drifties.
STFC-RAL-CR03 R61: Okay.
STFC-RAL-CR03 R61: so do you will also have a near detector suite. So, suite of detectors, the 1st of these is called Ndr. It'll be a liquid Argon time, protection chamber. And the reason being is that it's vital for us to have a liquid argon target at our near detector as to constrain the uncertainties that come from neutrino argon interactions that will affect our detector.
STFC-RAL-CR03 R61: However, this will have very little design
STFC-RAL-CR03 R61: the extremely high event rates detector because of the proximity to source means that we're gonna have native 3D readouts
STFC-RAL-CR03 R61: and optical modularity.
STFC-RAL-CR03 R61: And that is to to deal with the quite novel problem. First, st in printer physics of the preload events. Pilot
STFC-RAL-CR03 R61: the second vector is called Tms, which stands for the Muon spectrometer, and that'll be placed just behind Ndr, with the main purpose being to measure the neuron momentum and sign for neurons that escape Ndr. And that's vital to get the energy reconstruction right.
STFC-RAL-CR03 R61: In the second phase of this experiment we will replace Tms with a gaseous hard on time projecting Chamber.
STFC-RAL-CR03 R61: Reason being is that case is awesome.
STFC-RAL-CR03 R61: has a lower energy special of argon. So we have a much better view of the low energy particles. So we essentially get to look at the phenomen interactions with magnifying glass.
STFC-RAL-CR03 R61: So if you look at the picture on the top right again, that gives us a much better understanding of all things that we don't see in this picture.
STFC-RAL-CR03 R61: And the final detector in this suite is Tank.
STFC-RAL-CR03 R61: The primary purpose of sign is to monitor the characteristics of the latrina beam.
STFC-RAL-CR03 R61: But also it's quite fine. Grade has great particle by particle reconstruction and multiple targets within it, so we expect it to make some exclusive neutrino nuclear specialists as well.
STFC-RAL-CR03 R61: Okay.
STFC-RAL-CR03 R61: And then the last piece of this suite is the prism, and this refers to the capability of any law, and Tms to move horizontally with respect to the theme. Axis
STFC-RAL-CR03 R61: now going off, axis
STFC-RAL-CR03 R61: changes the shape of the neutrino flux has a lower lower energy energy and also a thin distribution. And so we can sample different true energy or true energy fluxes with the same detectors.
STFC-RAL-CR03 R61: And so this gives us a much better handle on the smearing between our observed energy and our true energy, which is a key systematic fault.
STFC-RAL-CR03 R61: Okay, so we have our new events.
STFC-RAL-CR03 R61: How do we infer our oscillation and its values?
STFC-RAL-CR03 R61: So what we measure with these detectors is an event rate, and this event rate is a product of both oscillations and our lux interaction, and detecting modules.
STFC-RAL-CR03 R61: Sorry mulch
STFC-RAL-CR03 R61: the near detector has lots of events, and we assume no oscillations because of the proximity to the source. And so we use these events to constrain these systematic uncertainties.
STFC-RAL-CR03 R61: Now by detector has oscillations but far fewer events. So we need to apply the systematic constraints. To be able to get a nice measurement of oscillation.
STFC-RAL-CR03 R61: Now, in 2020
STFC-RAL-CR03 R61: didn't produce a comprehensive set of sensitivities using a frequentis framework, and these results are readily available.
STFC-RAL-CR03 R61: and one of the key parts from this study is here on the right. So this is showing our sensitivity to Cp violation as a function of teams. Runtime.
STFC-RAL-CR03 R61: Now, our sensity to Cp violation depends on the true values of delta Cp.
STFC-RAL-CR03 R61: so if Lcp is actually maximal, so minus pi over 2. Then you can see how our sensitivity changes over. To use runtime.
STFC-RAL-CR03 R61: and the width of this line is the effect of other oscillation parameters, the systematic uncertainty and the statistical uncertainty.
STFC-RAL-CR03 R61: But what if Lcp is a maximum? So we want to know what identity looks like for certain ranges of Lcp values. So if you take the 50% of Lcp values because you have the most sensitivity, this now shows us the minimum sensitivity that we'll have.
STFC-RAL-CR03 R61: And then we also can show the same thing. But for 75% of delta values.
STFC-RAL-CR03 R61: And this bump here that you can see happens occurs for all these lines at about 6 years. That is the effect of the phase 2 I was talking about. I would make some improvements.
STFC-RAL-CR03 R61: Okay, so now onto the phrasing study that we and I have formed.
STFC-RAL-CR03 R61: So what was our analysis strategy?
STFC-RAL-CR03 R61: So if we look at this diagram at the bottom, we start with our unoscillated Monte Carlo events. We then apply an oscillation probability. Given a certain oscillation hypothesis, we then pass this through our Lux Cross section and detector models.
STFC-RAL-CR03 R61: and then we end up with a prediction of what the events rates will be at both our fire detector and our leadership.
STFC-RAL-CR03 R61: We can then change all of these parameters, and we end up with a likelihood space as a function of of all of our parameters, and we use Mcmc to explore the full likelihood space.
STFC-RAL-CR03 R61: and then we use Bayesian inference to make an actual estimate of what our oscillation counters, and even us are.
STFC-RAL-CR03 R61: So.
STFC-RAL-CR03 R61: We know that this next generation of experiments can have extremely high statistics. And so we're going to need to make sure that we have an accurate treatment of our systematic uncertainties.
STFC-RAL-CR03 R61: And so this is a bit of an overview of the examples of systematic parameters that we have in our bit.
STFC-RAL-CR03 R61: So one of these are swines. Swines are continuous response functions, using piecewise cubic interpolation.
STFC-RAL-CR03 R61: So we can either bin these lines in between a reconstructed entry variables, or we can have event by vent. So it's flying each event for each parameter.
STFC-RAL-CR03 R61: And these are really good for cross-section factors, where we know that the effect, as we change the value of a parameter could well be not non Gaussian.
STFC-RAL-CR03 R61: You also have normalization parameters. So these simply just shift bits up and down, depending on character movement, and these can apply to specific kinematic ranges between events and also just events like.
STFC-RAL-CR03 R61: And these are good for those parameters where we know that the shape. The given bin as a result of that parameter will be Gauss.
STFC-RAL-CR03 R61: and the final
STFC-RAL-CR03 R61: doesn't matter. All type of parameter are shift like parameters. And so these are actually parameters which move an event from one bin to another.
STFC-RAL-CR03 R61: and these are great schematics which we know. Change the reconstructed variable on events. So if your detector
STFC-RAL-CR03 R61: you're seeing 50 Mv. Or 100 Mv. Less energy than you thought it did, and that's a good chance that a lot of your events belong in a different.
STFC-RAL-CR03 R61: and the reason why this is really useful is that we want to be able to keep the cross section and blocks effects on a given event, the same when we shift a text systematic. These are these weights for the cross section blocks. They don't apply to bins. They apply to a given Monte Carlo event. So when we shift our text systematic, it brings as the event moves from one week to another, it brings its weights with it.
STFC-RAL-CR03 R61: and we know that cross-section effects are going to be extremely important in this next generation experiments. So we need to be able to keep the cross section weights associated with the event and not just have this average which, when we move a static, is now no longer true.
STFC-RAL-CR03 R61: Okay, so we've built this complicated and hopefully your space.
STFC-RAL-CR03 R61: How do we forward with Monte Carlo?
STFC-RAL-CR03 R61: So, very briefly. This is a semi random walk around the full counter space
STFC-RAL-CR03 R61: we use the Mr. 2 T, 2. Algorithm for accepting or rejecting steps.
STFC-RAL-CR03 R61: And this diagram on the right shows you that this builds up a distribution
STFC-RAL-CR03 R61: of steps in each of your fancy dimensions, which is proportional to the target distribution, the target in our case being
STFC-RAL-CR03 R61: the scales really well with dimensions.
STFC-RAL-CR03 R61: but it can also deal with discontinuous likelihoods unlike some minimizers. And that's quite important with our event shift thing. We move an event from one link to another. The likelihood gap is actually not continuous.
STFC-RAL-CR03 R61: And then now we have our posterior distribution in all of our parameters. How do we actually look at promise? We want? We only want to look at a few at a time.
STFC-RAL-CR03 R61: So to remove this exit modality, we integrate out our new sub parameters, and because Mcmc. Gives us a posterior which is discrete in bins, which are steps in them. All we have to do is add up the bins in a parameter axis that we don't care about, and so on.
STFC-RAL-CR03 R61: Okay, so that's the strategy. What are the actual details of the study that was performed?
STFC-RAL-CR03 R61: So it was, as I say, simultaneous fit to both biotech and analytic samples.
STFC-RAL-CR03 R61: The base data that we're fitting to use the new fit. 4 point. Oh, global bits count values in normal ordering.
STFC-RAL-CR03 R61: You can see the the current distributions on the right, but from this little bit further back.
STFC-RAL-CR03 R61: we we use flat priors in all of our oscillation parameters of interest.
STFC-RAL-CR03 R61: and for the solar parameters times 22, 1, 2, and Delta M. 21. We use a Gaussian constraint that comes from the
STFC-RAL-CR03 R61: the marketing ran for about 180 million steps, and that was sufficient for getting reliable. 3 Sigma Bayesian enforcement.
STFC-RAL-CR03 R61: The systematic model, has 288 characters in it. So that's cross section plus the vector
STFC-RAL-CR03 R61: and the bay data set is equivalent to a nominal space, 7 year exposure. So what we think our data will look like after 7 years of running. Given the current design plan.
STFC-RAL-CR03 R61: this is equivalent to 336 Kiloton. At what years?
STFC-RAL-CR03 R61: So these samples I'm talking about. We have 4 biotech samples
STFC-RAL-CR03 R61: for both neutrino mode and antithe mode and neuro neutreno like and electron neutrino like amounts.
STFC-RAL-CR03 R61: and then we also have 2 samples. So in neutrino mode and an anti neutrino mode for events that look like charge currents.
STFC-RAL-CR03 R61: So, having closer look at our samples.
STFC-RAL-CR03 R61: Our sensitivity to science. Grade 2. Theta, 2, 3 come from the dip
STFC-RAL-CR03 R61: in the discipline spectrum. So how deep it is. But this is where this optum problem comes from. This gives sensitivity to these 2, 3, which means we don't know which side of 45
STFC-RAL-CR03 R61: we are from the disappearance spectrum and the sensitivity. Delta M squared 3, 2 comes from the horizontal position of this step.
STFC-RAL-CR03 R61: So we get sensitivity to sine squared theta 2, 3, and sine squared theta, 1, 3 from the sensitivity. Sorry from the appearance spectrum.
STFC-RAL-CR03 R61: And that's how we are able to get some sensitivity on which options we are actually in.
STFC-RAL-CR03 R61: and our delta Cp sensitivity comes from the differences between our neutrino or neutrino mode and anti neutrino mode spectrum, and also, we get some sensitivity in the appearance rates and shape.
STFC-RAL-CR03 R61: Okay, so what are our actual sentences?
STFC-RAL-CR03 R61: So to start with, I'll show a Delta M squared 3, 2. So on the left you have the one d posterior with 1, 2, and 3 significant intervals on the right you have the 2D posterior. Again, sine squared, theta 2, 3.
STFC-RAL-CR03 R61: The 1st thing you can notice is that our true value, which is the fake data set generated at.
STFC-RAL-CR03 R61: and our best fit point agrees really? Well, and that's consistent across most or all of the plots I'll show you. But the second thing is that this 2D post area. Most of the one D is actually just in normal order.
STFC-RAL-CR03 R61: and so there is almost no posterior in the Advice board
STFC-RAL-CR03 R61: which suggests how strong gene sensitivity is, for how? How your sensitive he is yet to the, to the mass hierarchy.
STFC-RAL-CR03 R61: however, the caveat to this
STFC-RAL-CR03 R61: is that the normal ordering and the inverse ordering actually live extremely far away in counter space. If you consider Delta M squared 3, 2 axis.
STFC-RAL-CR03 R61: So even though Mcmc is good at exploring multimodal distributions. That gap is far too big for the Mcm to jump in in a reasonable amount of time. So we actually add directly into the proposal function, a way of flipping from normal to inverted ordering.
STFC-RAL-CR03 R61: and that's been used on previous experiments. But now the likelihood is so steep
STFC-RAL-CR03 R61: we might need a better way. Is there a way to go from this position? Normal ordering to that position in a vertical ring? That is the most likely place in that space to go to. And we're 100% sure, we've got that all
STFC-RAL-CR03 R61: work against.
STFC-RAL-CR03 R61: Okay. So next is Beta 2, 3, we have the stereo here on the left.
STFC-RAL-CR03 R61: and you can see this optive degeneracy I mentioned earlier.
STFC-RAL-CR03 R61: However, you can still see that we we do kind of pick the correct optics
STFC-RAL-CR03 R61: and in the Bayesian framework to quantify the evidence for a given hypothesis, we use the Bayes factor.
STFC-RAL-CR03 R61: and that's simply just the integral over one hypothesis divided by another, and with steps on this side, and then divide by the steps on this side and that gives us a ratio of 2.7 6, and using the Jeffrey scale.
STFC-RAL-CR03 R61: which turns us into sort of a qualitative statement, corresponds to light evidence or up
STFC-RAL-CR03 R61: for the yeah. So for the correct option
STFC-RAL-CR03 R61: and for future one free.
STFC-RAL-CR03 R61: as you can see again, you have the majority of our posterior is filled in the right place, but you also have this second peak at large. Values of science by p. 2, 1, 3.
STFC-RAL-CR03 R61: And this can be explained when we've got the sine squared against sine squared 1, 3, and you can see that when our chain is in the wrong octance, we then push up our value of sine squared B to 1, 3 to still observe the same, the same data.
STFC-RAL-CR03 R61: And so there was some degeneracy between times 52, 1, 3, and the options of these 2, 3,
STFC-RAL-CR03 R61: and then finally for Delta. Cp, you have a 1 d plus B on the left, and then the 2 B again signs of E to one B on the right.
STFC-RAL-CR03 R61: You can see. The 1st thing is that our reason interval does not contain Lcp equals 0,
STFC-RAL-CR03 R61: and we also have this asymmetry here in distribution of this tail towards 0, and that's caused by Delta generacy, but mostly sensitive to the sign of Del Cp. And so that's what creates this this drawing tail towards 0.
STFC-RAL-CR03 R61: So
STFC-RAL-CR03 R61: so that's our posterior distribution. But now I want to talk a bit about what are the advantages of having this posterior solution in all of our space.
STFC-RAL-CR03 R61: Well, Mcmc actually allows us the ability to reweight the post period distribution. If we decide to change what priors we want to use.
STFC-RAL-CR03 R61: So, for example, everything I've shown so far has a lap prior in science? 42, 1, 3. What if you want to change that? What if you want to add some information into our bit that isn't included.
STFC-RAL-CR03 R61: For example, the context of this could be, new experiment comes out with a new result, and I want to apply that information to my current results without running a whole new fit. Well, that's what Mcmc allows us to do.
STFC-RAL-CR03 R61: The caveat to this is that there has to be enough enough Mcmc steps in the region that this new posterior prefers. We can't just massively wait up some parts of the counter space that we didn't explore in the 1st place.
STFC-RAL-CR03 R61: and it's also trivial for us to produce a posterior in some new variable that wasn't included in our in our Mcmc. Fix, provided that it is a functional value. So if you have a posterior and 2D. Alpha and beta, we can produce any solution as long as it's a function of our parent.
STFC-RAL-CR03 R61: So the 1st example is the react constraints. So, as I said, we have currently shown, just flat fires in science 22, 1, 3.
STFC-RAL-CR03 R61: And that's good because we want to be able to check how sensitive is due to this parameter. But we know that currently science 51, 3 has been very well measured by multiple.
STFC-RAL-CR03 R61: And you can see from the new bit global fit. How well this parameter has been, has been constrained.
STFC-RAL-CR03 R61: And so all we need to do is take the central value of this, of this of their fit.
STFC-RAL-CR03 R61: take the uncertainty, and turn that into a Gaussian fire, and just slap that one to our posterior.
STFC-RAL-CR03 R61: So you can see that when we had this generacy between times 50 to 1, 3, and 52, 3. When we applied the react constraints. That second incorrect load really goes away.
STFC-RAL-CR03 R61: And so now we can have a look at so more directly, comparing the reaction strength with and without it.
STFC-RAL-CR03 R61: and so on the right, so on the left. You can see first, st that in this 2D these 2D printable intervals that that second load in sine squared d to 1, 3 is gone, and we've also even narrowed the width of the interval and the wanting interval in the correct sine of 1 3 area.
STFC-RAL-CR03 R61: and then in the has been completely suppressed. So previously, when we couldn't make any strong statement about which option 2, 3 was when we apply optic to one pre ref constraints, you basically know certain
STFC-RAL-CR03 R61: another interesting change prior, that you might want to consider is the Delta Cp. Prior. So so far, I've shown results that have a flat prior in Delta, Cp, but that actually results in a non flat prior in other quantities. So sign Belt, Cp and Cos del Cp, you actually have some information added to it.
STFC-RAL-CR03 R61: So why is this interesting. Well, Cp violation is actually a function of signed l cp, so be interesting for us to see what the effect of changing that privacy.
STFC-RAL-CR03 R61: So you can see here that the effect of changing this prior in Delta, Sansk, 2, 3
STFC-RAL-CR03 R61: is really significant. But if we look at Delta, Cp and study, there are some shape effects, especially here, because this is where that flat sine delta cp. Prior really disappears.
STFC-RAL-CR03 R61: And it kind of tells us that at 7 years exposure. We're not 100% robust to our choice of Lcp. Prior.
STFC-RAL-CR03 R61: And like, I said, we can now plot using Mcmc
STFC-RAL-CR03 R61: a posterior in a variable that you need to market, and as we probably know, the R screen variant is a very useful parameter to take a look at when we look at secret violation as it indicates the magnitude of synchronization which is independent of your parameterization from Pms matrix
STFC-RAL-CR03 R61: for a value of Jcp. Of 0 indicates no city violation.
STFC-RAL-CR03 R61: And so you can see here our one deep posterior and our 1, 2, and 3 credible intervals.
STFC-RAL-CR03 R61: and we noticed that there are 2 kind of odd features in this distribution you have this weird little dip occurring in the maximum. And we have this kind of solve that currents. And so it's interesting to take a look at how maybe our priors might have affected this distribution.
STFC-RAL-CR03 R61: So if you 1st apply a graph constraint, you 1st notice that that upper bump is gone. So that's what's causing that weird little bump on the left hand side. You also notice that Jcp. Equals 0. So Cp. Conservation is excluded for that 3 Sigma.
STFC-RAL-CR03 R61: Now, if we change from our black prior and signed in Lcp. To that and signed Lcp. We see that with regularity of the top is gone. And that's because, again, we have. We were including a prior and signed Lcp into our pit and massive disfabe of that region. Basically
STFC-RAL-CR03 R61: cool. Okay.
STFC-RAL-CR03 R61: so that's the end of the result of the base insensitivities. The final part I want to talk about today is some ongoing work on improving our sampling techniques for our next view analysis.
STFC-RAL-CR03 R61: So so far today, I just showed you 3 single consoles. But, as I mentioned at the beginning of the talk. Do you want to be able to make 5 single statements?
STFC-RAL-CR03 R61: So the question now is, how do we get from 3 sigma to 5 sigma?
STFC-RAL-CR03 R61: And to answer this question. First, st we say, or we consider the fact that our market change steps are correlated.
STFC-RAL-CR03 R61: And looking at the bottom right, which shows us how correlated any given step in marketing is with another, for the like is the difference between those 2 steps.
STFC-RAL-CR03 R61: We see that roughly around the 10 K. Region are stepped out to become unpredicted.
STFC-RAL-CR03 R61: So if we take the 180 new steps that were in our chain.
STFC-RAL-CR03 R61: we work out how many independent steps. They were so divide by 10,000, and then work out how many of those steps probably lie outside of the 3 cent contour? We get 40 independent ones, and given the fact that our credible intervals I showed you were nice and smooth.
STFC-RAL-CR03 R61: we can say that's enough, confidently determined where 3 single contour lies.
STFC-RAL-CR03 R61: so we can then do the same thing. So we've got 40 independent points outside of our bias in the console, and then work our way back.
STFC-RAL-CR03 R61: And that results in needing about 800 billion steps.
STFC-RAL-CR03 R61: And that would currently require more than a billion CPU hours. If we take how long it took to get 180 million.
STFC-RAL-CR03 R61: Now, that's pretty unfeasible. At the very least, it's unnecessary. And so we need a more efficient method of sampling the tail regions of our solution. So we know where our pricing and contour is with fewer steps.
STFC-RAL-CR03 R61: So one way of doing this is with a method called umbrella sampling.
STFC-RAL-CR03 R61: And the way this works is that you apply bias to your likelihood, which increases the probability in some region.
STFC-RAL-CR03 R61: You do this with multiple biases. And then you combine these samples
STFC-RAL-CR03 R61: using weights and the purpose of these weights as 2 things. First, st you want to undo the bias that you actually added, and the second is, you have to now account for the fact that you, over or under sampled some regions, because these biases overlap with each other.
STFC-RAL-CR03 R61: and there are several options for the kinds of biases you can use.
STFC-RAL-CR03 R61: As you can see, they've used a bunch of interesting functions here. But the 1st attempt that I've used is a template by view.
STFC-RAL-CR03 R61: So instead of saying, Okay, I want to raise the likelihood of
STFC-RAL-CR03 R61: of this region here which I want to explore more often. Instead, you just say I want to make everything more black, and so you just raise your likelihood by one to one over T,
STFC-RAL-CR03 R61: and essentially, it's the temperature. The marketing is hotter. And so it's more like to get over the potential bumps
STFC-RAL-CR03 R61: and so similar to the previous example. You sample of multiple different temperatures, and then you combine together, using another sampling, waiting.
STFC-RAL-CR03 R61: And so this hope it works is a gif
STFC-RAL-CR03 R61: which shows the effect of changing the temperature on the distribution of steps in science. 51 threep. You see, to begin with, we have a distribution that's kind of like the contours that we saw earlier. And then, when we increase the temperature, you can see the steps go wild, and we start exploring all these places that we know our bison contour is going to lie somewhere around.
STFC-RAL-CR03 R61: And so this is definitely a work in progress part, and is what I'm doing currently. But the next step now is to take these mark chains, activate the weights, apply them to each chain onto each step, combine, and hopefully, when we draw the critical intervals with the weights included. They look like they lie somewhere that we expect to.
STFC-RAL-CR03 R61: And so that is that as well.
STFC-RAL-CR03 R61: Okay. So to summarize you. We'll have insight into the program.
STFC-RAL-CR03 R61: You know. We aim to measure the mass ordering regardless of what the values of any other oscillation counters are, and we expect to have good sensitivity to supervisation, and also to the options of these 2, 3, which are an answer questions.
STFC-RAL-CR03 R61: The first, st tracing sensitivity. Study has now formed is completed.
STFC-RAL-CR03 R61: and we expect this is going to be complementary to existing and future. The crisis sensitivities.
STFC-RAL-CR03 R61: and the advantage of our baseline approach is that we have the ability to update any results
STFC-RAL-CR03 R61: based on any information that comes along and does not require a fit.
STFC-RAL-CR03 R61: And and the other thing is, we get to look at distributions in other quantities. And so this is our 1st in depth. Look at Jcp, which is massively important.
STFC-RAL-CR03 R61: And I'm currently exploring some new sampling methods so that we can bring down the computational cost of trying to get high significant measurements. Which is what do you? So thank you.