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A reference in a recent Magazine article to the Monty Hall problem - where a contestant has to pick one of three boxes - left readers scratching their heads. Why does this probability scenario hurt everyone's brain so much, asks maths lecturer Dr John Moriarty.
Imagine Deal or No Deal with only three sealed red boxes.
The three cash prizes, one randomly inserted into each box, are 50p, £1 and £10,000. You pick a box, let's say box two, and the dreaded telephone rings.
The Banker tempts you with an offer but this one is unusual. Box three is opened in front of you revealing the £1 prize, and he offers you the chance to change your mind and choose box one. Does switching improve your chances of winning the £10,000?
Marcus du Sautoy explains probability and the Monty Hall problem to Alan Davies on Horizon
Each year at my university we hold open days for hordes of keen A-level students. We want to sell them a place on our mathematics degree, and I unashamedly have an ulterior motive - to excite the best students about probability using this problem, usually referred to as the Monty Hall Problem.
This mind-melter was alluded to in an AL Kennedy piece on change this week and dates back to Steve Selvin in 1975 when it was published in the academic journal American Statistician.
It imagines a TV game show not unlike Deal or No Deal in which you choose one of three closed doors and win whatever is behind it.
One door conceals a Cadillac - behind the other two doors are goats. The game show host, Monty Hall (of Let's Make a Deal fame), knows where the Cadillac is and opens one of the doors that you did not choose. You are duly greeted by a goat, and then offered the chance to switch your choice to the other remaining door.
Most people will think that with two choices remaining and one Cadillac, the chances are 50-50.
The most eloquent reasoning I could find is from Emerson Kamarose of San Jose, California (from the Chicago Reader's Straight Dope column in 1991): "As any fool can plainly see, when the game-show host opens a door you did not pick and then gives you a chance to change your pick, he is starting a new game. It makes no difference whether you stay or switch, the odds are 50-50."
But the inconvenient truth here is that it's not 50-50 - in fact, switching doubles your chances of winning. Why?
Let's not get confused by the assumptions. To be clear, Monty Hall knows the location of the prize, he always opens a different door from the one you chose, and he will only open a door that does not conceal the prize.
For the purists, we also assume that you prefer Cadillacs to goats. There is a beautiful logical point here and, as the peddler of probability, I really don't want you to miss it.
In the game you will either stick or switch. If you stick with your first choice, you will end up with the Caddy if and only if you initially picked the door concealing the car. If you switch, you will win that beautiful automobile if and only if you initially picked one of the two doors with goats behind them.
If you can accept this logic then you're home and dry, because working out the odds is now as easy as pie - sticking succeeds 1/3 of the time, while switching works 2/3 of the time.
Kamarose was wrong because he fell for the deception - after opening the door, the host is not starting a new 50-50 game. The actions of the host have already stacked the odds in favor of switching.
The mistake is to think that two choices always means a 50-50 chance. If Manchester United play Accrington Stanley in the Cup then, with the greatest respect to proud Stanley, it's more likely that United will progress to the next round.
Still not convinced? You are in good company. The paradox of the Monty Hall Problem has been incredibly powerful, busting the brains of scientists since 1975.
In 1990 the problem and a solution were published in Parade magazine in the US, generating thousands of furious responses from readers, many with distinguished scientific credentials.
Part of the difficulty was that, as usual, there was fault on both sides as the published solution was arguably unclear in stating its assumptions. Subtly changing the assumptions can change the conclusion, and as a result this topic has attracted sustained interest from mathematicians and riddlers alike.
Even Paul Erdos, an eccentric and brilliant Hungarian mathematician and one-time guest lecturer at Manchester, was taken in.
So what happens on our university's open days? We do a Monty Hall flash mob. The students split into hosts and contestants and pair up. While the hosts set up the game, half the contestants are asked to stick and the other half to switch.
The switchers are normally roughly twice as successful. Last time we had 60 pairs in 30 of which the contestants were always stickers and in the other 30 pairs always switchers:
Among the 30 switcher contestants, the Cadillac was won 18 times out of 30 - a strike rate of 60%
Among the 30 sticker contestants, there were 11 successes out of 30, a strike rate of about 36%
So switching proved to be nearly twice as successful in our rough and ready experiment and I breathed a sigh of relief.
I had calculated beforehand the chances of ending up with egg on my face and the team of 30 stickers beating the 30 switchers. It was a risk worth taking, but one shouldn't play Russian Roulette too often.
Next year we will need something different, perhaps Simpson's Paradox. Imagine that 1% of people have a certain disease.
A diagnostic test has been developed which performs as follows - if you have the disease, the test has a 99% chance of giving the result "positive", while if you do not have the disease, the test has 2% chance of (falsely) giving the result "positive".
A randomly chosen person takes the test. If they get the result "positive", what is the probability that they actually have the disease? The answer, 1/3, is perhaps surprisingly low.
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We make micro adjustments every day to what we wear, how we shop, and how we drive. Our healthcare and industrial verticals are working with AI and Computer Vision to enhance our experiences from the user to the professional. There are a variety of computer vision applications to make life easier, more efficient, and safer. In other words, our computers have eyes. Every industry, it seems, is now touched by Computer Vision. From retail to healthcare to agriculture to banking, AI technology combines with deep learning and machine learning to help computers “see” where a car goes, an individual’s health, and what outfit might look best for any given outing. So, let’s take a look at some of the industries currently using Computer Vision. AUTOMOTIVE Human error and distractions often lead to car accidents and fatalities. According to the WHO, it’s estimated traffic accidents will be the seventh leading cause of death by 2030. To help alleviate this prediction, there is work being done on a self-driving car with sensor technology. Though autonomous cars have been tried before, this next incarnation has worked to ensure it can detect not only other cars and other large obstacles, but also pedestrians and cyclists at a distance. As it navigates through the streets autonomously, it follows traffic regulations as well as detect hand signals, and more. Efforts to train the vehicles use deep learning to predict, plan, and map its way through various scenarios. HEALTHCARE The advent of Computer Vision in technology has been a boon to the industry. It can help determine conditions of illness, reduce or eliminate misdiagnoses, and can even monitor blood loss during medical situations. Captured images on items such as surgical sponges can be processed using Computer Vision using Machine Learning. In comparison with the human eye, the computer’s estimates were more accurate. RETAIL Retail has been at the forefront of many changes within the tech industry. And now, as online shopping, e-commerce, and virtual events take over traditional venues and brick-and-mortar stores, even the task of trying on clothes has gone virtual. From a virtual mirror which uses Computer Vision to help identify what outfit looks best. What may be most appropriate in what situation. Something like a movie montage, but in real time for a real person. Retail takes things a step further by stepping up security. Using Computer Vision, retail security apps can monitor what is being recorded, what has been taken from shelves, and items being fake scanned. This information and knowledge can lead to reduced theft and other losses in stores. While other industries such as banking and agriculture have also seen a rise in Computer Vision, it’s the above which we might see in our day-to-day lives sooner rather than later. ONE FINAL THOUGHT Business processes have shifted online, looking for your next job has become more daunting than ever before. But here’s the good news. Everyone’s on the same page. Leaders, hiring managers, recruiters, and prospective employees are all navigating a new way of doing business and finding talent to keep those businesses running. In the wake of work-from-home policies, remote working, and the shifting landscape of working outside the office, technology, and particularly biotechnology careers are prime opportunities to both gain increased knowledge in your chosen field or begin your career path. If you’re interested in Big Data & Analytics or other Data professional opportunities, check out our current vacancies or contact one of our recruitment consultants to learn more. For our West Coast Team, contact us at (415) 614 - 4999 or send an email to email@example.com. For our Mid-West and East Coast teams contact us at (212) 796-6070 or send an email to firstname.lastname@example.org.
25. June 2020
What does Data tell us? Why do we want to know the information we collect and analyze? How can Data help us now? Well, sometimes you have to go back to basics. Knowing your Data helps you make better decisions for the future. This is the transformative nature of Data Science. The Data Scientists have collected is leading toward a vaccine for a novel virus. Our massive shift from in-house workers to working from home showed us where the gaps in our internet infrastructure existed. But, the information we gathered wasn’t just where the gaps occurred, it also offers a jumping off point for how we can use what we’ve learned to improve. We know Data is essential to business today, but how we use it, and gathering what we can learn from it, offer transformative advantages we might have otherwise missed. WHERE DO WE GO FROM HERE? Data Science is what helps us interpret the massive amounts of Data we’ve collected. With an estimated 90 percent of Data created just in the last couple of years, and an estimated dearth of connected devices estimated to grow over 75 billion by 2025, the sheer volume is daunting. Yet we still have need for change. Technologies to interpret Data at such a massive scale still need someone to gather, collect, analyze, and interpret the information. What we’ve learned so far with Data Science shows us what must change to support health workers, the health of our employees, the support of remote workers and gig workers, and how businesses can differentiate themselves from their competitors in a post pandemic world. SEVEN WAYS ORGANIZATIONS CAN PREPARE FOR THE FUTURE Prioritize Digital Collaboration As employees begin to return to ‘normal’ work hours, Gartner suggests 48% of employees will work remotely. This is an 18% increase pre-pandemic. So, when hiring managers take stock of their employees, they’ll want to consider things such as productivity and performance management and how workers are evaluated based remote working touchpoints rather than established criteria of employee performance management.Ensure Inclusivity of Employees Bring employees into more critical roles and give them the freedom to make mission critical decisions. Open Up Opportunities and Develop Critical Skillsets Coach employees on how to develop critical skills for a variety of roles, rather than focusing on one particular role.Be Flexible The days of doing things ‘the way we we’ve always done’ are gone. It’s time to reassess, reevaluate, and prepare your employees for success. How? Consider what may may be needed for a given role’s development path. Do your employees need reskilling or upskilling? Flexible careers. The gig economy. The freelance economy. Contractors. All these titles and labels offer flexible learning and training allowing your business to pivot smoothly and efficiently as needed. Training is the key here and it will help employees transition into other organizations, into roles with greater responsibility, and allow both your employees and your organization to adapt to changes more quickly.Teach Employees to Respond Rather than React Structure your organization and employee response to quickly course correct. Don’t assume or target a core set of future skills. We don’t know what the future holds or what skills may be needed. But if you have employees with wide interests, your business may be better positioned to make changes as needed. Implement a Culture of Inclusiveness – Remote vs. In-House Employees Diversity is an important part of any business. But with the rise of remote workers, it’s time to ensure all workers are supported in regard to healthcare coverage, mental support, and financial health pre-and post-pandemic. Inclusiveness can help to engage those workers both in-house and remote to ensure everyone feels part of the team. Devices such as VR, AR, video calls, and more can help to make every employee feel part of the company culture.Encourage Data Literacy Throughout Your Organization Everyone in your organization will need to be Data literate. Yet everyone will be at a different level of literacy. Here it’s important to define both the skills and capability. Once your leadership has a firm grasp of the Data provided to them by your Data Scientists and business intelligence analysts, then they’ll have a starting point from which to make informed decisions. Building a culture of Data begins with leadership. Are you ready for the role or are you an organization looking for someone to fill this role? Business processes have shifted online, looking for your next job has become more daunting than ever before. But here’s the good news. Everyone’s on the same page. Leaders, hiring managers, recruiters, and prospective employees are all navigating a new way of doing business and finding talent to keep those businesses running. If you’re interested in Big Data and Analytics or other Data professional opportunities, check out our current vacancies or contact one of our expert consultants to learn more. For our West Coast Team, contact us at (415) 614 - 4999 or send an email to email@example.com. For our Mid-West and East Coast teams contact us at (212) 796-6070 or send an email to firstname.lastname@example.org.
18. June 2020
COVID-19 has reshaped the way we do business, how we interact with each other, closed and opened opportunities. Essential workers are on the frontlines and scientists work feverishly in the background to help flatten the curve and find a cure. The Life Sciences industry has seen a surge in demand, but can those needs be met in time? New York, California, and Boston, face the highest demand and the biggest shortage of workers to fill the jobs. In Massachusetts alone, it’s estimated that though 74,000 people filled Life Science jobs by the end of 2018, there would be a need for an additional 12,000 by 2024. This was before the pandemic struck. The need is ever greater now. So, what skills do you need to enter the Biotech and Life Sciences field and if you’re in the field, how can you upskill or reskill to fill the most in demand roles? THREE ADVANCED SKILLSETS FOR A POST-PANDEMIC WORLD Computer Vision – A subset of AI, Computer Vision can help the healthcare industry in a variety of ways. It can help identify anomalies in x-rays, help craft prediction models for things like tracking and vaccine solutions, and enhance technology workflows. Data Storytelling – One key element businesses look for in a Data professional is someone who has good data storytelling skills. The ability to translate complex numbers and statistics into something executives and stakeholders can understand is becoming ever more important and ensures sustainability of business continuity. Not only does Data Storytelling make information more digestible for non-technical professionals, it also helps business leaders to make powerful insights about where they are and what steps they need to make moving forward.Skills in Healthcare Technologies – Healthcare technology skills are in high demand. Data professionals who can use and understand medical data in real-time to get results will be highly sought after. Advanced skill sets in healthcare, biotechnology, and similar areas within Life Sciences will see a surge in demand and would be most relevant to companies now more than ever before. Computer Vision, Data Storytelling, and Healthcare Technology skills have become three of the top skillsets needed for today’s world. Each one feeds to the other, and as important as technical skills are, it’s just as important to have soft skills. Especially now. Thankfully, both soft skills and technical skills can be taught. But there still exists a gap between school and business. Below are some ideas on how to bridge that gap. BRIDGING THE GAP BETWEEN SCHOOL & BUSINESS STEM and STEAM skills will be in higher demand now more than ever before. As important as it is to ensure students with the desire to move into these fields, it’s more important to begin with the schools. For the professionals already in the industry, there are other ways to encourage bridging the gap. Draw more students into STEM programming careers and sustain encouragement as they progress in their studies and career.Emphasize skills with a focus toward the life sciences field.Emphasize that students don’t have to choose a business career over a science career. There is crossover leading to more opportunities.And for those life long learners (read: already in the field), ensure opportunities for professional development.Find talent in other creative ways. Consider ‘non-traditional’ candidates. Business processes have shifted online, looking for your next job has become more daunting than ever before. But here’s the good news. Everyone’s on the same page. Leaders, hiring managers, recruiters, and prospective employees are all navigating a new way of doing business and finding talent to keep those businesses running. In the wake of work-from-home policies, remote working, and the shifting landscape of working outside the office, technology, and particularly biotechnology careers are prime opportunities to both gain increased knowledge in your chosen field or begin your career path. If you’re interested in Big Data & Analytics professional opportunities, check out our current vacancies or contact one of our recruitment consultants to learn more. For our West Coast Team, contact us at (415) 614 - 4999 or send an email to email@example.com. For our Mid-West and East Coast teams contact us at (212) 796-6070 or send an email to firstname.lastname@example.org.
04. June 2020
When Ford first introduced the assembly line, he could only imagine how it would affect the automotive industry. But what about how it could affect supply and demand within the life sciences industry? Automotive and similar factories have been converted before to help build items most needed. Not the least of which, today, is to help supply those in the life sciences industry with the PPE and medical devices they need. Demand is high. Supply is not. Enter blockchain technologies. As health systems become overburdened and disruptions to ‘normal’ life occur on a global scale, it’s important to ensure critical resources are prioritized. So, what can businesses do to help ensure supply and demand are met in not only these critical times, but for the future. FIVE WAYS TO ENSURE SUPPLY MEETS DEMAND When it’s difficult to supply even the most in demand products, it’s time to take an assessment of various scenarios. These scenarios can help leaders predict what and when they’ll need certain products and critical items. Assess your scenario within the framework of increased disruption.What are your capabilities?Identify the most immediate needs to meet, any risks to be aware of, and take action.Determine any structural changes you’ll need to make.Prepare to pivot. Be aware you may be in a continuous cycle of determining risk, assessing where you are and need to go, any configurations you’ll need to make to get there, and any operational procedures to improve and move forward. By assessing, prioritizing, and visualizing, companies are able to craft a clearer scope of vision. The scenarios created can offer insight into key pieces of planning to help mitigate disruptions of supply chain processes. This crisis will have long-lasting effects and implications from how we work to how we assure supply and demand. It’s in these strange crosshairs, the life sciences industry finds itself at the center of this pandemic, and at the same time is the life force which has given blockchain technologies fuel to improve. No matter where you are on the spectrum of supply chain technology, there is calculated risk to every decision. Just because we’re easing restrictions now, doesn’t mean there won’t be an about face in the next few months, and what companies do between now and then is critical. Supply is already short. Now is the time to take immediate action to help mitigate risk for patients, providers, your clients, and your communities WHAT TO DO NOW AND HOW TO PREPARE FOR THE FUTURE The scale of risk is unlike any leaders have seen in recent years. Its speed adds to the uncertainty as numbers rise, decisions change, and most are left wondering what’s next. Businesses who respond quickly and confidently can help to alleviate some uncertainties, but can craft a plan crucial to understanding the complexities of blockchain within the industry. Strong data, analysis, predictive modelling can help to anticipate any further or potential disruption. Taking these steps can help make businesses more resilient in the future and also help them manage future challenges. It’s integral to have strong, responsive, and resilient risk management capabilities. To do this, your business will want to ensure their capabilities are technology-led platforms which support analytics, machine learning, and artificial intelligence. Whether you’re mitigating risk, preparing an assessment, or determining your capabilities, it’s important to ensure you’re transparent. We are all in this together. Even in business. Transparency builds trust as does assuring supply and demand by mitigating risk. It’s these things which will soon become the basics of business protocols. Business processes have shifted online, looking for your next job has become more daunting than ever before. But here’s the good news. Leaders, hiring managers, recruiters, and prospective employees are all navigating a new way of doing business and finding talent to keep those businesses running. In the wake of work-from-home policies, remote working, and the shifting landscape of working outside the office, technology careers are prime opportunities to both gain increased knowledge in your chosen field or begin your career path. If you’re interested in Big Data & Analytics professional opportunities, check out our current vacancies or contact one of our recruitment consultants to learn more. For our West Coast Team, contact us at (415) 614 - 4999 or send an email to email@example.com. For our Mid-West and East Coast teams contact us at (212) 796-6070 or send an email to firstname.lastname@example.org.
28. May 2020