I'm curious if there are applications of MCMC outside of Bayesian Inference? this conversation started when discussing Monte Carlo methods vs Markov Chain Monte Carlo methods with a coworker. He asked what the difference was, and the best I could summarize was (A) MCMC is a subset of MC, and (B) MCMC has stricter assumptions about what is or isn't allowed. I used the example of Casino-style games. Consider a game where a player rolls a die 1-3 times and keeps winnings equal to the final throw. We can price the &quot;fair value&quot; of the game through monte carlo simulations. However, this requires definition of strategy. For example, one simple but effective strategy is to only take a subsequent throw if the previous value is less than the expectation of a given roll (3.5). Once you throw &gt;= 4 you quit. Otherwise, you throw again. This works well, but makes no assumptions of priors, likelihoods, etc. Conversely, if you want to use an MCMC, the best example that comes to mind is posterior inference. For example, if you're modeling linear regression of weights on heights of men, you supply a prior and likelihood and the sampler is able to return the posterior. In the discrete case, a markov chain can be represented as a matrix of transitions from one state to another. If you let a bot bounce around according to this matrix, it would converge on the &quot;stable distribution&quot; over time. (A simpler method is simply the leading eigenvector of the transition matrix.) Anyway, in the continuous case, we don't have a transition matrix, and so we use a transition kernel to make movement decisions (which generally means comparing the previous/subsequent likelihoods and making a probabilistic decision.) All that to say, MCMC methods appear to require a transition kernel, which means it requires likelihoods for movements, and this info will converge on the stable distribution given enough movements. By contrast, vanilla MC methods make less assumptions about what the end result should look like. This sounds like a bad working definition and so I'm curious if there are other use cases of MCMC methods? This might help expand my idea of how MCMC and vanilla MC are different.
I have been trying to get a sense of the different problems in frequentist settings where MCMC is used. I am familiar that MCMC (or Monte Carlo) is used in fitting GLMMs and in maybe Monte Carlo EM algorithms. Are there more frequentist problems where MCMC is used?
We are Indian passport holders, with valid visas for Canada. Plan is to take the EgyptAir flight Mumbai to Toronto, via Cairo. Problem is Egypt embassy website says we don't need Transit Visa if transit is up to 12 hours but here transit is 14 hours.    Has anyone with a Indian passport traveled this route? What was your experience at Cairo? Did you need a transit visa? Could we please be a bit nicer to new users? There is a distinct decline in the level of civility on all the sites here.  Some of this is due to new users coming in and posting spam and other nonsense, but the off-topic and downvote buttons are doing a pretty good job of keeping this under control. Unfortunately, a lot of this is coming from more experienced users, and the site's built-in moderation system does not (and probably cannot) handle this very well.  Folks are rushing to pound new users down with &quot;this belongs on meta!&quot;, &quot;this is off topic&quot;, &quot;this is a duplicate!&quot; and &quot;read the Help!&quot;. (Which is correct, but should be done nicer) All this, of course, is accompanied by a flurry of downvotes.  This is not very welcoming to new users who don't know about meta, the Help, or what counts as off-topic. Now I am not proposing that we just allow off-topic, meta, or duplicate questions.  However, I think we could be gentler in the way we express these sorts of things.  Explain what meta and the FAQ are and provide useful links.  Just using please and thank-you when asking folks to read the FAQ or post something on meta would be an improvement.  I also think we could rein in the downvoting a bit.  Not that we shouldn't vote stuff down, but unless a new user's post is clearly spam, voting it down to -1 or -2 should be sufficient to send a message without piling on. I like Stack Exchange and I want it to become a resource for everyone, not just an elitist site for high-rep users on the sites. Language Options -> Spell Checking in Windows 10 version 1803 Questions about a commutative ring with exactly three ideals Let $R$ be a commutative ring with identity. Assume that $R$ has exactly three distinct ideals: $\{0\},I, R.$      1) Show that if $a \in R-I$, then $a$ is a unit in $R$.      2) Let $a,b\ne0$ in $I$. Show that $ab=0$. Are we slightly lighter during the day and slightly heavier at night, owing to the force of the Sun's gravity? I have email addresses encoded with HTML character entities. Is there anything in .NET that can convert them to plain strings? NORMAL label in top right of some applications Laptop battery charge management I work on a HP laptop plugged in most of the time, and after a few months the battery went off-duty.  Of course, I could remove the battery each time the laptop is plugged and replace it each time I must move to where no sockets are around. But I think that:   It would be really BORING! The computer would not avail itself of the useful backup power supply a battery can provide in case of black out.   It should simply switch off the battery charging when a safe power level is reached (i.e. 95%) and start recharging it, not every five minutes, but only under a certain safe threshold (i.e. 40% - 50%).  In its energy-saving profiles, Windows 7 only allows for setting up screen brightness, screen fadeout, screen deactivation and the suspension, not managing any charging issue.  Is there a way to accomplish this? The space $ C^1[0,1] $- the space of all continuously differentiable functions on $ [0,1]$ is not a Banach space with respect to the sup norm,$ \|.\|_{\infty} $ since the uniform limit of a continuously differentiable function need not be differentiable.  How can I illustate this statement using a counter example? Can I use $ f_{n}=\frac1 n \sin nx $ as a counter example?  Also, is $ C^1[0,1] $ is same as the space given by $ X=\{f\in C^1[0,1]:f(0)=0 \}$. Can I use the same example to show that this is not a Banach space?  More help is appreciated! Thanks! I am wanting to find the correlation between two variables: a categorical vegetation variable (with categories 1-4)  and a continuous variable of erosion (with values anywhere between 0.2 and 9). I think I would be required to use a non parametric test to find the correlation, but bit of a newby to stats so could anyone suggest the best test to use? I also wanted to know how sample size can affect these tests, ie with a sample size of 100 or 1000? At least two questions (, ) on this site indicate that in more than a few isolated cases at least, letters of recommendation are in fact written by the applicant and only signed off (or perhaps rephrased somewhat) by the recommender, who would actually be responsible for writing the letter.  Is there any evidence about the prevalence of this practice that goes beyond anecdotes? I realize that cross-country (cultural) difference may play a role. show that $x$ is in $\ell^1$ if $\sum x_ny_n$ is convergent for all $y=(y_n)\in{c_0}$ If $x=(x_n)$ is a sequence of complex numbers such that the series $\sum  x_ny_n$ is convergent for all $y=(y_n)\in{c_0}$. Then prove that $x\in{\ell^1}$. Can anyone tell me what is the meaning of $c_0$  in this question and how to proceed on proving it. Sugar as a defence against bacteria? mentions that sugar "at a certain level acts as a preservative". I've always been taught that microorganisms eat sugar and expel acids, that is why sugary food are damaging to teeth. How is it that sugar acts as a preservative, then?  Googling the question I've found   though I don't credit the sources as being especially reputable. What is the real reason that sugar can act as a preservative? Why use the Conjure Minor Elemental spell when its results are so unpredictable? The  spell states:  You summon elementals that appear in unoccupied spaces that you can see within range. You choose one the following options for what appears:  One elemental of challenge rating 2 or lower Two elementals of challenge rating 1 or lower Four elementals of challenge rating 1/2 or lower Eight elementals of challenge rating 1/4 or lower.   It seems like the only two things a player can select are the maximum CR of the elemental conjured, and, arguably, the location its summoned in. I am confused as to why you would want to use this spell given that its results are so unpredictable. Why would a wizard cast a spell that's essentially an open invitation to whatever elemental from a list decides to show up? You can't strategize around the spell very much because, as written, you don't choose what gets summoned, and you can easily end up with something you weren't counting on. It won't be useless, but why would you cast a spell that has such an unpredictable result? It's like the difference between the chromatic orb and chaotic bolt - if the chaotic bolt didnt have the chance to bounce. You'd never pick a random damage type over a damage type of choice. Why would you choose a spell that might do something you want over something that does exactly what you intend it to do? What are the situations in which you would use this spell that wouldn't be better solved by a spell of equal or lower level that has more predictable results? Is "funnest" a word? We seem to be stuck at an impasse on this issue.  Is funnest a word or not?  If so, does it mean "most fun"? Resume a process via a PID number I wanted a daemon to start on boot so I added a line to /etc/rc.local that ended in "&amp;"  I did that so it would run in the background.  The daemon is loaded and working fine but when the daemon is running you can press keys that do other important things.  When I am finally logged in I wanted to resume process or send it a terminal (tty2) so I can do a couple of things.  I'm new to linux and not sure how to do this.  I do a ps -aux |grep uox to work out which PID it is. But not sure how to resume. How can I increase the mouse pointer speed beyond the limits set by the Mouse preferences dialog? In the Mouse preferences dialog I've set the acceleration to max and the sensitivity to min and the mouse pointer is not exactly sluggish, but I'd like to make it even faster. Is it possible to be done by setting some value in the procfs or something?  Thanks! What's the simplest way to add a click event handler to a canvas element that will return the x and y coordinates of the click (relative to the canvas element)?  No legacy browser compatibility required, Safari, Opera and Firefox will do. De Rham Cohomology of the tangent bundle of a manifold I would like to compute the de Rham cohomology of the tangent bundle $TM$ of a manifold $M$. It seems to me that we can just homotopy each fibre to a point, and that this would give a homotopy equivalence between $TM$ and $M$. Since de Rham cohomology is a homotopy invariant, this would imply that $H^*_{\text{dR}}(TM) \cong H^*_{\text{dR}}(M)$.     Is it always true that the tangent bundle of a manifold is homotopic to the manifold itself by the homotopy of each fibre with a point? If the $n^{th}$ partial sum of a series $\sum a_n$ is $S_n = \dfrac{n-1}{n+1}$, find $a_n$ and the sum.  By definition,  the sum of the series is the $\lim n\to\infty$ of it's $n^{th}$ partial sum.  $$\text{ Sum = } \lim_{n\to\infty} = \dfrac{n-1}{n+1} = 1$$  I am asked to find $a_n$. How do I do this? What is the procedure?