Week One Summary and Key Takeaways

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来自 University of London 的课程

Probability and Statistics: To p or not to p?

16 个评分

University of London

Probability and Statistics: To p or not to p?

16 个评分

We live in an uncertain and complex world, yet we continually have to make decisions in the present with uncertain future outcomes. Indeed, we should be on the look-out for "black swans" - low-probability high-impact events. To study, or not to study? To invest, or not to invest? To marry, or not to marry? While uncertainty makes decision-making difficult, it does at least make life exciting! If the entire future was known in advance, there would never be an element of surprise. Whether a good future or a bad future, it would be a known future. In this course we consider many useful tools to deal with uncertainty and help us to make informed (and hence better) decisions - essential skills for a lifetime of good decision-making. Key topics include quantifying uncertainty with probability, descriptive statistics, point and interval estimation of means and proportions, the basics of hypothesis testing, and a selection of multivariate applications of key terms and concepts seen throughout the course.

从本节课中

Dealing with Uncertainty and Complexity in a Chaotic World

1.1 The Monty Hall Problem9:25

1.2 Decision Making Under Uncertainty10:48

1.3 Uncertainty in the News9:49

1.4 Simplicity vs. Complexity - The Need for Models10:59

1.5 Safe to Assume? Beware, When Model Assumptions Go Wrong!9:05

1.6 Roadmap of the Course9:00

Week One Summary and Key Takeaways4:25

与讲师见面

Dr James Abdey
Assistant Professorial Lecturer, LSE
University of London

So, many congratulations for making it through our week one.

So lets just perhaps consider some of

our key takeaways from the first few sessions of this course.

So our main point is that,

I want you to recognize that we live in a highly complex and uncertain world.

Whether you like uncertainty or dislike it,

its a fact of life and we have to deal with it.

So our goal is to make

well-informed decisions and have to make those decisions under uncertainty.

So it's not an ideal situation.

But indeed we don't live in an ideal world.

We live in this real world of uncertainty.

So the best we can do,

is to try and quantify the uncertainty and take

optimal decisions based on what we know at a given point in time.

Now I think this was very well illustrated in

our introductory game of that Monty Hall problem,

whereby what we were really solving for was not probabilities per say but a strategy.

What was the right thing to do?

Well from a probabilistic perspective

the optimal strategy is to always switch to the other door each time.

And by doing so, you are maximizing your chance of success.

Whereby in that game,

you would have a two thirds probability of winning the sports car.

True in this play of the game you are unlucky.

But of course we shouldn't be concerned with just a one shot game,

but a multi-shot game.

Whereby we do things many many times,

we recognize we have a chance of good luck,

bad luck exists and we are all prone to experiencing both good and bad luck.

But if we play things optimally,

probabilistically, then we will tend to win far more often than we lose.

We have also introduced the concept of a model.

Our way of trying to describe some aspects of the real world

whereby this model should be a deliberate simplification of reality.

Of course the challenge is to decide,

what are the most important,

the most salient features of the real world we should feature

in our model and which things are less important and could be discarded.

We gave the London Underground map as

an excellent example of an attempt to deliberately simplify the real world.

I will leave it to our own judgment.

From the famous underground map from the geographically accurate

one both being models but which one did you feel was the better model.

Ultimately that's down to our own opinion and judgment.

But do appreciate the trade offs which we face;

being geographically accurate in one case and being an easier to

interpret map in the other case and think about the trade offs involved.

We've also considered uncertainty in the news.

And please do going forward,

listen out to that word uncertainty when it is mentioned by a reporter.

When you hear about interest rates being raised or decreased,

when you hear the latest inflation figures being reported,

when you hear about volatile movements in the financial markets,

think of this as being the markets reacting to new information.

And indeed when things do change,

how does it compare to our expectations?

Are things as we had expected?

Or do they differ from our expectations?

And hence should there be any revisions to our beliefs about the world?,

Lets say from a probabilistic perspective and

what consequences could this have on our decision making.

Also we touched on briefly the importance of assumptions in model building.

Yes, we introduce assumptions primarily to

simplify the real world which is a desirable goal.

However, please be aware of the pitfalls of making flawed assumptions.

Because any inferences or conclusions we draw from models,

could be severely affected by our choice of assumptions and may

lead us to doing something which leads to a very bad outcome in the end.

So there is already a key takeaways from week one.

So we get to that at a fairly light level.

The calculations and theory bits to come later on.

But hopefully this has given you a nice introduction,

into how we have to deal with the uncertainty that we will face on a daily basis.

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