美国留学：学生保险拔智齿

Wisdom Teeth (source)

在快奔三的年纪，终于长出了最后一颗智齿。本来想着说这辈子不用拔智齿的——因为我25岁前就已经长完了三颗智齿，并且都 align 得非常好，并没有阻生。之前在中国时的医生也告诉我，没有必要拔掉，因为他们出来得迟，因此比起其他牙齿也会掉得迟。所以以后牙齿掉完后，他们还会在那里，可以做到固定镶牙的用途。当然我在美国没有听到有医生这样提起的，而且美国的习惯是 4 颗一起全部拔掉，一了百了！听起来有点 scary，只是他们的考虑也不是没有道理：智齿一般会长歪，即使没有长歪，也可能引发各种疾病，比如由于长得比较靠里，比较难清洁到，因此很容易蛀牙。更甚的是，蛀牙后，会引起正常的牙齿也蛀牙！这个情况就发生了在我身上：我的下面两颗支持都有蛀牙，并且引起了旁边的蛀牙！为了这个问题，我已经补过两次牙齿。这成为了我这次拔掉他们的最大原因。

我的最后一颗智齿是左上那颗，长歪了，好在不是顶着别的牙齿，而是横向的生长，朝着舌头方向长出来了。所以舌头蹭到很不舒服。大概5个多月前刚长出来时去检查过，还拍了 panarama 的 x-ray （学校的 dental delta 保险三年只 cover 一次，这次只能自费，花了大概 70 刀）。但由于只是刚长成，并不清楚趋势，因此我也带着侥幸的心理没有理他（考虑到别的三颗都乖乖的直直地长了出来！）。最近终于把找工、TA、论文的事情忙得差不多，感觉不拔不行了，赶紧联系医生。可惜之前去的 dental clinic 不能做 oral surgery，于是医生 refer 我去当地最大的 local hospital：carle。总结起来，大概 timeline 是这样的：

12月份看的牙医，拍 X-ray，医生诊断需要拔智齿，开 referal paper 让我去 carl 做『oral surgery』。我偷懒没有马上去做。

5月初打电话给 carle schedule 了一个 appointment。护士告诉我让 clinic 发 x-ray 给他们。于是我打电话让 clinic 发，他们说会在我 appointment 前发过去（结果后来没发！）

过了一个星期去做了 examination，竟然是免费的。护士帮我一检查，发觉 x-ray 竟然没发过来。于是我马上电话过去让他们发。护士和医生很好人，说如果他们不发，给我免费做一个。等了好久，终于给我发了过来。医生也是顺理成章地问了下我情况，问我要不要做 sedation，全身麻醉 (anesthesia，Dental IV)，还是做 local 的局部麻醉。作为一个小白，当然是咨询医生意见。医生说大家都做 IV，睡一觉醒来就拔好了。于是我就说好我也要（只是没想到后来麻醉竟然要 375）。由于我以为我保险马上要过期，于是眼泪汪汪地让他给我这周马上做手术。他们非常 accomodating，愣是给我 schedule 到了第二天。拔智齿在美国算是小手术了，因此要签一张 paper，类似于 disclosure。走之前，我拿着手术清单去 patient account 查价 （check against insurance），但是前台阿姨说不能马上知道结果，只能给我第二天打电话。回到家后，我对着 bill 大概估算了一下，一颗牙 285 x 4 = 1140 + 麻醉 375 = 1515，而保险的 upper limit 是 1000，即使 100% cover 也要自付 515。感觉还是太贵，于是打电话问他们能不能取消掉。得到的答复是，我必须跟医生商量。但是医生一直 busy，一直没有给我答复。直到他们下班前，护士才电话我说，第二天跟医生讲就好。整个流程持续了大概 2 个多小时，花了 3 刀 parking。

第二天早上收到医院电话，得到具体 insurance 的信息以及bill。我掐指一算：一颗牙 285 x 4 = 1140 + 麻醉 375 = 1515，但是保险 upper limit 是 1000，而且不！包！麻！醉！这样 quote 下来我的价格是 (285x4 - 45) * 30% + 375 + 45 = 748.5，其中 45 是保险的 deductible。并且由于 carle 不属于 delta dental 的 network，保险只 cover 70%，which means I pay 30%! 太贵了。于是我果断选择了只做局部麻醉，因为是免费的。这样下来就是我的 out of pocket 是 373.5, which is not too bad。果然穷人多受罪…… 不过换个角度想，全身麻醉怎么说还是比较伤身的，没用也好。不过为了预防万一，我还是做好了全身麻醉的准备。根据给我的资料，全身麻醉需要在术前8小时不能进食，任何水、candy、gum都不能吃！（据说是为了防止你大小便失禁？）由于我手术是下午1:45开始，那么算起来我最迟也要在凌晨 5 点时吃东西……要那么早爬起来准备+吃，还是算了吧。我昨天晚上是8点吃的晚饭，这样算起来我有将近 18 小时滴！水！未！进！T_T 并且由于全麻带来的作用，术后人会不清醒，还必须有人带你去医院负责把你运回家，非常严肃，当然也非常麻烦。

下午开车到了位于 champaign 的医院（carle 在 urbana 和 champaign 各有一间，医生轮岗）。check-in ，乖乖地贡献 373.5 后等了半小时进手术室。总的来说护士们都很 caring，会一直跟我聊天，也很详细地给我解释术后的一些注意事项。不久后，医生助手进来给我打麻药。老实说，整个过程中最痛的其实是这个环节，因为他们会给智齿附近的 gum 打针，扎进去恐怖+疼的感觉，一半一半吧。整个人也会不自觉地绷紧了，双手牢牢地按住自己大腿。不过其实局部麻醉对我来说也是常事了，之前补牙时也做过，所以多少有点心理准备。不久后，整个嘴麻了，连吞口水也感觉有点困难。

医生进来后手术正式开始。新出来的那颗（左上），我估计 5 秒就拔出来了，一点感觉都没有。医生会 count：this is one。我当时心里一阵窃喜，原来这么水啊！可惜如意算盘打错了，拔下面那颗时，我感觉整颗死死地嵌在牙腔里，怎么也拔不出来，牙根处有点隐隐作疼，但更疼的，是我的下巴。因为作用力太大，我感觉整个下巴都要被扯起来了…… 也许是因为太牢固，也许是因为补过牙，医生决定把它钻开再拔。于是就听到了钻头在口腔里巨大的声音。钻好后，医生估计是一片一片地拔出来的，其实我感觉不到具体手法，只知道他们一直在里面捣鼓。期间医生也会预警：你接下来会听到一些碎裂的声音…… 右上的智齿虽然也是 fully erupted，但是比起下面的好拔多了，虽然不如左上的容易，但是不需要钻就拔了出来。右下的是最 hard core 的，不仅要钻，而且钻完了也花了好大功夫才解决。估计下面的开口比较严重，所以医生都给我缝合了。没感觉到他给我穿针，但是能感觉到他拉线和打结时把牙肉缝起来。其实真正拔牙的整个流程估计不超过10分钟？老实说也没有网上写的那么恐怖，可能是我身体素质比较好吧 :)

完了后做起来歇息了一下便走了（说到这，我都佩服我自己了，没有过敏，没有烟酒，没有遗传病，没有重大病史，各种指标正常，拔牙不叫不闹，估计医生也喜欢我这种病人吧…… 感谢上天感谢爹娘给我的强壮体魄~）。回家后一直要咬着纸巾止血。大概3-4个小时候麻药效果过去了。根据护士说法，我可以服用一些 ibuprofen （美国常见止疼药）来止疼。把纸巾取出来后的大概半个小时，真的很疼。小时候牙疼的那种感觉又回来了。不过好在半小时过后就没怎么疼了，也许是止疼药功效上来了，也可能伤口愈合得好。总的来说，还是没什么大问题。

接下来要做的，就是看它恢复得如何了。刚拔完自然是不敢吃比较硬的食物的。乖乖地给自己熬了粥喝。希望身体赶紧回复过来，一周后还要去 DC 和 NY 旅行呢~

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Popular watches under $150

I've been looking around entry-level watches for some time. Recently, I answered a question in Zhihu (Chinese Quora), and I feel like to transcribe this collection in my blog.

Dress Watch

Rodina R005, $119 via Amazon

This watch is discussed in my previous blog post. It is a bit debatable as some people think it completely ripoff the NOMOS Tangente. However, considering there so many Rolex Submariner homages, this should also considered a homage. It uses a Seagull ST1701 movement, sapphire crystal, and display case back. At this price point, it is really a good deal. Get in on Amazon.

Orient Bambino, $130 via Amazon

I've always like the ORIENT logo, much more than SEIKO's. This watch features Roman literals, blue hands and white classic dial. Amazon

This has been quite popular in China, due to their successful marketing campaign. It is a quartz (Japanese) watch with multiple variation, and looks really good. Get the best looking ones here and here.

Diver's Watch

Now moves to my favorite category. Rolex designed the true classic look of today's diver's watch. However, the retail price for a submariner is probably too high for lots of people. Fortunately, Japanese brands SEIKO and ORIENT provide some affordable options here.

SEIKO skx007

A very popular one. Considered as a poor man's Rolex. You can get it around $180 at Amazon.

Orient Ray

Also a very popular one. As I said, I really like Orient's LOGO. I find it far more interesting to see the lions and shields rather than just the word "SEIKO". $130 at Amazon.

Orient Mako

Ray's brother, Mako. The watch face is slightly different, thinner hands, arabic numbers at 6, 9 and 12 o'clock. Also around $130 at Amazon.

Field/Flight/Pilot Watch

One of my favorite. It's lume is fantastic and got countless compliments. Only $100 at Amazon.

This is my favorite style. Look at the beautifully designed digits! It's lume is also awesome: lumes at all numbers! When it's on sale you can get it at $125.

SEIKO SNK 809

Bestseller in Amazon. Come with various colors (black, green, blue, beige). It's so cheap ($50) that people are getting all colors and rotate everyday. Also, since it's so affordable, it will become your workhorse. You won't treat it like million dollar watch that only put in your locker.

Skeleton Watch

Seagull M182SK

Quite popular in watchuseek forum. Very nice seagull movement with a complete see-through design. That said, it might be too busy to see the hands. $135 at Amazon.

Fossil Grant

This skeleton is cleaner than the Seagull's. Nevertheless, Seagull is more reputable than Fossil in watch making. Amazon.

Conclusion

So there you have it. These watches are very affordable and have the great quality that earn them reputation. You can see them in nearly every watch forums. If you just started watch collecting, consider getting one of them. Let me know if you have any other suggestions.

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Popular Watches Under Slash $150

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---

layout: post
title: "Popular watches under \$150"
date: 2015-05-04 13:24:35 -0500
comments: true
categories: [watches]

---

I've been looking around entry-level watches for some time. Recently,
I answered a question in Zhihu (Chinese Quora), and I feel like to
transcribe this collection in my blog.

Dress Watch

This watch is discussed in my previous blog post. It is a bit debatable as some people think it completely
ripoff the NOMOS Tangente. However, considering there so many Rolex Submariner
homages, this should also considered a homage. It uses a Seagull ST1701 movement,
sapphire crystal, and display case back. At this price point, it is really
a good deal. Get in on Amazon.

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Watch Review: Rodina R005GB

Tangente

So NOMOS has this awesome looking Bauhaus style watch: Tangente. Apparently everyone wants one, but not everyone wants to break their bank ($2330 USD).

Luckily, we have an alternative here: Rodina series watches.

The Review

Some people think it a copycat watch, while some others think it a homage. The truth is, with price only $139.99, it is a really affordable price. During Valentine's, it is on sale with $99.99 shipped. The website frequently has sales. Without further delay, I bought it when it's one sale. It is shipped from Tianjin, China via EMS, and USPS after it arrives in US. After 10 days of waiting, I finally received it!

It's funny that as others commented, the soft bag is supposed to be used to hold the watch, but after opening the case, the watch is not wrapped around it.

However, the watch itself is fine and intact. It is wrapped in plastic strips under good protection.

These are all the stuff in the box. I can understand that, as I don't think Rodina is not any famous big brand. Don't expect full service inside the box.

This is really how it should come:

It's transparent back, which is a perfect show-off for automatic watches. As you can see, it's 5ATM, which is slightly better than 3ATM that a lot of cheap watches have. It is said to have a Seagull ST1713 movement (with date function).

The crown is really a bummer. If you go to look for its pictures online, the 'R' will have a blue coating. However, the blue coating on mine is totally off. I wiped them clean instead. You can see there is still blue pieces in the cleaning cloth. Nevertheless, I like the letter 'R' in the crown.

The watch dial is unbeatable. Case is made with sapphire crystal, which is astonishing for this price. The hands are in blue dark blue, which looks really cool. The only problem as someone else pointed out is that the fonts does not match: the numbers are sans-serif, while the Rodina letters are serif fonts. Furthermore, 'CHINA MADE' sounds weird, although I can understand they may feel proud to say this.

The strap. Leather is of cheap quality as expected. Feels like plastic. However, the making is not bad. The stitching, the holes, are definitely satisfactory. I picked the brown one as I think black is too dressy for everyday wear. I have a skinny wrist, so I almost used the last hole.

This is how it looks like on my wrist. 39mm is a bit small for me. However, the winding piece is not stable enough. It creates noise and you can feel it moving when you move your arm and thus triggering the winding action. The ticking sound is pretty small though, compared to the notorious Timex Weekender.

Conclusion

With lots of imperfection, this watch is still worth buying. I really like it's style. I wish I get one with roman literals and dates (the one with Roman literal does not have dates). I wish the leather is of better quality. But with this price point, one cannot expect too much, and the quality of the watch itself is really good. Here's the pros and cons:

Pros:

• Affordable price
• Good style, similar to the famous NOMOS Bauhaus style
• Seagull ST1713 automatic movement
• 5ATM (instead of 3ATM)
• Stainless steel case
• Sapphire crystal!

Cons:

• Noisy winding action
• Low quality leather (notice that the strap is good, only the leather is bad quality)
• Fonts in the dial do not match
• Blue coating in the crown not printed at the perfect location
• Whether it is a copycat or homage is debatable.

In general, my first impression for the watch is good. Might need some more time wearing it to see if , what do you think?

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Notes on Maximum Likelihood, Maximum A Posteriori and Naive Bayes

Let \(\data\) be a set of data generated from some distribution parameterized by \(\theta\). We want to estimate the unknown parameter \(\theta\). What we can do?

Essentially, we want to find a most likely value of \(\theta\) given \(\data\), that is \(\arg \max P(\theta | \data)\). According to Bayes Rule, we have

\[ P(\theta \given \data) = \frac{P(\data \given \theta)P(\theta)}{P(\data)} \]

and the terms have the following meanings:

• \(P(\theta \given \data)\): Posterior
• \(P(\data \given \theta)\): Likelihood
• \(P(\theta)\): Prior
• \(P(\data)\): Evidence

Maximum Likelihood Estimation (MLE)

An easy way out is to use the MLE method. We want to find a \(\theta\) the best explains the data. That is, we maximize \(P(\data \given \theta)\). Denote such a value as \(\hat{\theta}_{ML}\). We have

\[ \hat{\theta}_{ML} = \argmax_\theta P(\data \given \theta) = \argmax_\theta P(\mathbf{x}_1, \ldots, \mathbf{x}_N \given \theta ) \]

Note that the above \(P\) is a joint distribution over the data. We usually assume the observations are independent. Thus, we have

\[ P(\mathbf{x}_1, \ldots, \mathbf{x}_N \given \theta ) = \prod_{i=1}^{N} P(\mathbf{x}_i \given \theta ) \]

We usually use logarithm to simplify the computation, as logarithm is monotonically increasing. Thus, we write:

\[ \mathcal{L}(\data \given \theta) = \sum_{i=1}^N \log P(\mathbf{x}_i \given \theta ) \]

Finally, we seek for the ML solution:

\[ \hat{\theta}_{ML} = \argmax_\theta \mathcal{L}(\data \given \theta) \]

If we know the distribution \(P\), we can usually solve the above by setting derivative of \(\theta\) to 0 and solve for \(\theta\), that is,

\[ \frac{\partial L}{\partial \theta} = 0 \]

Maximum A Posteriori (MAP)

In MAP, we maximize \(P(\theta \given \data)\) directly. Denote the MAP hypothesis as \(\hat{\theta}_{MAP}\), we have:

\[\begin{array}{rl} \hat{\theta}_{MAP} = & \argmax_\theta P(\theta \given \data) \\ = & \argmax_\theta \frac{P(\data \given \theta)P(\theta)}{P(\data)} \\ = & \argmax_\theta P(\data \given \theta)P(\theta) \end{array}\]

Note that the last step is due to the evidence (data) \(\data\) is constant, and thus can be omitted in \(\argmax\).

At this step, we notice that the only difference between \(\hat{\theta}_{ML}\) and \(\hat{\theta}_{MAP}\) is the prior term \(P(\theta)\). Another way to interpret is that we consider \(MAP\) is more general than \(MLE\), as if we assume all the possible \(\theta\) are equally probable a priori, e.g., they have the same prior probability, or uniform prior, we can effectively remove \(P(\theta)\) from the MAP formula, and it looks like exactly the same as MLE.

Finally, if the independent observation holds, again we can use logarithm and expand \(\hat{\theta}_{MAP}\) as:

\[ \begin{array}{rl} \hat{\theta}_{MAP} = & \argmax_\theta L(\data \given \theta) \\ = & \argmax_\theta \sum_{i=1}^{N} \log P(\mathbf{x}_i \given \theta ) + \log P(\theta) \end{array} \]

The extra prior term has the effect that we are essentially ‘pulling’ the \(\theta\) distribution towards prior value. This makes sense as we are putting our domain knowledge as prior and intuitively the estimation is biased towards the prior value.

Naive Bayes Classifier

Assume that we are given a set of data \(\data\), where each example \(\mathbf{x_j}=(a_1, a_2, \ldots, a_n)\), which can be viewed as conjunctions of attributes values. \(v_j \in V\) is the corresponding class value. Using MAP, we can classify an example \(\mathbf{x}\) as:

\[v_{MAP}=\argmax_{v_j\in V} P(v_j \given a_1, \ldots, a_n)\]

The problem is that it is hard to find a joint distribution for \(P(\mathbf{x} \given \theta)\). If we use the data to estimate the distribution, we typically don’t have enough data for each attribute. In other words, the data we have is very sparse compared to the whole distribution space.

Naive bayes makes the assumption that each attribute is conditionally independent given the target class \(v_j\), that is,

\[P(a_1, \ldots, a_n \given v_j) = \prod_{i=1}^n P(a_i \given v_j)\]

which can be easily estimated from the data. Thus, we have the following naive bayes classifier:

\[v_{NB} = \argmax_{v_j \in V} P(v_j) \prod_{i=1}^n P(a_i \given v_j)\]

Note that the learning of naive bayes simply involves in estimating \(P(a_i \given v_j)\) and \(P(v_j)\) based on the frequencies in the training data.

Normally the conditional independence assumption does not hold, but naive bayes performs well even if so. More importantly, when conditional independence is satisfied, Naive Bayes corresponds to MAP classification.

Conclusion

MLE, MAP and Naive Bayes are all connected. While MLE and MAP are parameter estimation methods that returns a single value of the paramter being estimated, NB is a classifier that predicts the probability of the class that an example belongs to. We also have the following insightes:

• Given the data, MLE considers the paramter to be a constant and estimates a value that provide maximum support for the data.
• MLE does not allow us to ‘inject’ our beliefs about the likely values for the parameter (prior) in the estimation process.
• MAP allows the fact that the paramter can take values from a prior (non-uniform) distribution that express our prior beliefs regarding the paramters.
• MAP returns paramter value where the probability is highest given data.
• Again, both MLE and MAP returns a single and specific value for the paramter. By contrast, bayesian estimation computes the full posterior distribution \(P(\theta \given \data)\).

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