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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Fix Mid 2009 MBP RAM not recognized issue

Possible cause of unrecoganized RAM

A few days ago, I encountered an issue which seems to be common among mid-2009 MBPs: one of the RAM (in slot 1) is not recognized anymore. Or, sometimes it is recognized, but after sleep and wake up, the computer freezes and impossible to recover but force power off.

It turns out this is a common issue in this model. See the discussion in this thread and this thread. In the following, I am going to present my temporary fix for this problem. For those of you that still want to stick to the old MBP, the fix shall last for a while. But I do recomend you backup all the files and prepare to migrate some day soon.

As I suggested in my reply, this may due to a RAM slot degradation. My guess is, the RAM slot cannot align the RAM to a correct contact positions any more. Precisely, see the post image above. Notice that the two clips on the left and right are used to hold the rams in a horizontal position, otherwise they will bend upwards. I took a close look at those clips and found that the plastic wore out and cannot hold them as original. I don't have great ways to fix them, so I just cropped some papers and insert them between the RAMs and the back edges on the body, hoping they can help tucking the RAMs.

As I am fixing it, I accidentally broke the left holder. So I have to customized a plastic holder and stuck it with the logic board to hold the inner ram (slot 1).

To verify my theory, I then taped a padding at the corresponding RAM position in the back cover:

And they look like the following before I close:

Note that you have to screw it real tight to create the pressure such that the RAM is aligned. That said, there will be a 'bump' at that position, and will easily cause scratch. So I use an apple sticker to cover my ass:

This method worked for me, well, at 99% of the time. Sometimes after sleep, the MBP still won't wake up. I notice that this usually due to running the MBP for a long time, and it's hot inside. Nevertheless, this is the best solution I can come up with by now. If you have any other cheap solution that does not require replacing the logic board, please let me know in the comments.

Finally, Zach Clawson created a dedicated page for this issue, which lists lots of reference and provides explanation to it. Make sure you check it out if you have encountered similar issue.

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There are other common issues for this model, and they can be easily fixed. See my following posts:

• Fix frayed Magsafe cable
• Replace faulty SATA cable

If you have similar experience, do not hesitate to let me know. If you find my instruction helpful, leave a comment and share it!

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Replacing SATA cable in Mid 2009 MBP

Replacing MBP cable

Recently, my mid 2009 MBP (Model A1278) fails to recognize the hard drive. My first bet was another disk failure on me, but it was not the case. I took down the hard drive and put it to a mobile hard drive case and it can be read smoothly.

It turns out that it is due to the SATA cable fault, which is a notorious problem for mid 2009 MBP model. See the threads and discussions here, here, here and here.

Luckily, the solution is simple, just go ahead and purchase a replacement cable and replace it. iFixit has a very detailed illustrated document on the procedures. However, Amazon has a cheaper option, and it works fine for me. I didn't test the infra-red though, since I never and not plan to use it.

There are other common issues for this model, and they can be easily fixed. See my following posts:

• Fix frayed Magsafe cable
• Fix unrecognized RAM

If you have similar experience, do not hesitate to let me know. If you find my instruction helpful, leave a comment and share it!

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