C'est Quoi La Difference Entre Surface Roughness Model Groisse Et Huray

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  1. C'est Quoi La Difference Entre Surface Roughness Model Grosse Et Huray

tl;dr -I don’t remember how many games of Clue I’ve played but I do remember being surprised by Mrs White being the murderer in only 2 of those games. Can you give an estimate and an upper bound for the number of games I have played?
We solve this problem by using Bayes theorem and discussing the data generation mechanism, and illustrate the solution with R.

Making use of external information with Bayes theorem

It is shown that electrothermal (ET) nonlinearity, arising due to heating of imperfect conductors by high-power carriers in a multicarrier system, is correlated with conductor surface roughness.

Having been raised a frequentist, I first tried to solve this using a max likelihood method, but quickly gave up when I realized how intractable it actually was, especially for the upper bound.

See what G T (geotres) has discovered on Pinterest, the world's biggest collection of ideas. Preface to the Candid Reader, Studious of the Magnetick Philosophy. To the Most Eminent and Learned Man Dr. William Gilbert, a distinguished Doctor of Medicine amongst the Londoners, and Father of Magnetick Philosophy, an Encomiastic Preface of Edward Wright on the subject of these books Magnetical.

This is a problem where conditioning on external knowledge is key, so the most natural way to tackle it is to use Bayes theorem. This will directly yield an interpretable probability for what we’re looking for (most probable number of and uncertainty interval)
Denote an integer n>3 and:
C
What we want writes as a simple product of quantities that we can compute, thanks to Bayes:
Notice that there is an “proportional to” sign instead of an equal. This is because the denominator is just a normalization constant, which we can take care of easily after computing the likelihood and the prior.
Likelihood
The likelihood indicates the odds of us observing the data (in this case, that k_Mrs_White = 2) given the value of the unknown parameter (here the number of games played). Since at the beginning of each game the murderer is chosen at uniform random between 6 characters, the number of times Mrs White ends up being the culprit can be modeled as a binomial distribution with parameters n and 1/6.
This will be easily obtained using the dbinom function, which gives directly the exact value of P(x = k), for any x and a binomial distribution of parameters n and p. Let’s first import a few useful functions that I put in our GitHub repo to save some space on this post, and set a few useful parameters:
Note that we can’t exactly obtain the distribution for any game from 1 to infinity, so we actually compute the distribution for 1 to 200 games (this doesn’t matter much in practice):
easy enough 🙂
Side note: when I was a student, I kept forgetting that the distribution functions existed in R and whenever I needed them I used to re-generate them using the random generation function (rbinom in this case) 🤦‍♂️
Prior
There are a lot of possible choices for the prior but here I’m going to consider that I don’t have any real reason to believe and assume a uniform probability for any number of games between 3 and 200:
Model
First posterior
Using the likelihood and the prior, we can easily compute the posterior, normalize it and plot it:
We can also compute directly the estimates we’re looking for. The most probable number of games played is 11:
And there is a 95% chance that the number of games is less than 40:

A more realistic data generation mechanism

I find this result very unsatisfying. It doesn’t “feel” right to me that someone would be surprised by only 2 occurrences of Mrs White being guilty in such a small number of games! For example, I simulated 40 games, a number that was supposedly suspiciously high according to the model:
We observe that characters #4 and #5 are the murderers in respectively only 2 and 3 games!
In the end I think what really counts is not the likelihood that *Mrs White* was the murderer 2 times, but that the *minimum* number of times one of the characters was the culprit was 2 times!
I think it’s a cool example of a problem where just looking at the data available is not enough to make good inference – you also have to think about *how* the data was generated (in a way, it’s sort of a twist of the Monty Hall paradox, which is one of the most famous examples of problems where the data generation mechanism is critical to understand the result).
I wrote a quick and dirty function based on simulations to generate this likelihood, given a certain number of games. I saved the distribution directly in the GitHub (and called it Gumbel since it kinda looks like an extreme value problem) so that we can call it and do the same thing as above:
The new posterior has the same shape but appears shifted to the right. For example N_games = 50 seems much more likely now! The estimates are now 23 for the number of games:
And 51 for the max bound of the uncertainty interval

C'est Quoi La Difference Entre Surface Roughness Model Grosse Et Huray

Credits for title image: Yeonsang

Sleep aids such as earplugs, eye masks, sleeping pills, and white noise are all used to help you fall asleep soundly. However, these sleep aids can be costly and oftentimes provide short-term solutions as sleep disorders and sleep deprivation continue to interfere with a good night’s rest. Dr. Andrew Weil, a Harvard trained medical doctor with a focus on holistic health, believes getting the best sleep ever is as simple as breathing in and breathing out.

This breathing exercise claims to help you fall asleep in just 60 seconds by simply inhaling and exhaling.Photo courtesy of Shutterstock

AMERICA’S SLEEP PROBLEM

In the U.S., 40 million people suffer from chronic long-term sleep disorders each year, says the Centers for Disease Control and Prevention, while an additional 20 million people experience occasional sleep problems. Stimulants such as coffee and energy drinks, alarm clocks, and external lights, interfere with our “circadian rhythm,” also known as our natural sleep/wake cycle, which is why sleep deprivation is becoming more common. Although research cannot pinpoint the exact amount of sleep needed by people at different ages, eight or so hours for a healthy adult is a good “rule of thumb,” according to the National Sleep Foundation.

The 21st century’s digital revolution has made it increasingly difficult to get a sufficient amount of sleep, especially with the constant need to be connected 24/7. However, Weil, a huge advocate of holistic breathing practices to combat stress, anxiety, and insomnia, believes this can all be remedied with a simple breathing exercise. On his website, he writes: “Breathing strongly influences physiology and thought processes, including moods. By simply focusing your attention on your breathing and without doing anything to change it, you can move in the direction of relaxation.”

This same philosophy is used in his well-known “The 4-7-8 Breathing Exercise,” also called “The Relaxing Breath,” which promotes better sleep. This is based on pranayama, an ancient Indian practice that means “regulation of breath.” The exercise is described by Weil as “a natural tranquilizer for the nervous system” that eases the body into a state of calmness and relaxation.

Kevin Meehan, a holistic practitioner and founder of Meehan Formulations in Jackson, Wyo., believes this breathing technique could be effective because it encourages the fast removal of carbon dioxide. Appropriate respiration is effective in removing carbon dioxide from our systems. “Doing so equates into a better preservation of the bicarbonate pool; our reservoirs for helping maintain an appropriate pH balance,” Meehan told Medical Daily in an email.

HOW TO DO THE “4-7-8” EXERCISE

Weil’s technique is shockingly simple, takes hardly any time, and can be done anywhere in five steps. Although you can do the exercise in any position, it’s recommended to sit with your back straight while learning the exercise. Weil explains to “place the tip of your tongue against the ridge of tissue just behind your upper front teeth and keep it there through the entire exercise. You will be exhaling through your mouth around your tongue; try pursing your lips slightly if this seems awkward.” This is followed by the five-step procedure listed below:

  1. Exhale completely through your mouth, making a whoosh sound.
  2. Close your mouth and inhale quietly through your nose to a mental count of four.
  3. Hold your breath for a count of seven.
  4. Exhale completely through your mouth, making a whoosh sound to a count of eight.
  5. This is one breath. Now inhale again and repeat the cycle three more times for a total of four breaths.

Weil emphasizes the most important part of this process is holding your breath for eight seconds. This is because keeping the breath in will allow oxygen to fill your lungs and then circulate throughout the body. It is this that produces a relaxing effect in the body.

DOES THE SLEEP HACK REALLY WORK?

A life hack, especially a 60-second sleep hack, leads several experts to be skeptical about such a bold claim. Dr. Michelle E. Gordon, founder of Northern Westchester Surgical Associates General, acute and emergency surgery specialist, has tried Weil’s breathing technique and attests falling asleep in a minute did not work for her. However, she told Medical Daily in an email: “The breath does elicit a sense of relaxation and calm. I teach it to my patients as a means of keeping calm when having anxiety over surgery or post-operative anxiety. It works.”

Gordon believes the breathing exercise works because it works in the same way as meditation: It helps people quiet the mind and let go of preoccupying thoughts.

The truth behind Weil’s 4-7-8 exercise is it takes practicing this twice a day over two months to perfect the technique until you can truly fall asleep in a minute. Once you’ve mastered it, it will become more and more effective and even help you deal with anxiety and stress in your life. Soon, going to bed will be as simple as taking a deep breath