Computer architectures are becoming more and more complicated to meet the continuouslyincreasing demand on performance, security and sustainability from applications. Many factorsexist in the design and engineering space of various components and policies in the architectures,and it is not intuitive how these factors interact with each other and how they make impactson the architecture behaviors. Seeking for the best architectures for specific applicationsand requirements automatically is even more challenging. Meanwhile, the architecture designneed to deal with more and more non-determinism from lower level technologies. Emergingtechnologies exhibit statistical properties inherently, such as the wearout phenomenon inNEMs, PCM, ReRAM, etc. Due to the manufacturing and processing variations, there alsoexists variability among different devices or within the same device (e.g. different cells onthe same memory chip). Hence, to better understand and control the architecture behaviors,we introduce the statistical perspective of architecture design: by specifying the architecturaldesign goals and the desired statistical properties, we guide the architecture design with thesestatistical properties and exploit a series of techniques to achieve these properties.In the first part of the thesis, we introduce Herniated Hash Tables. Our architectural designgoal is that the hash table implementation is highly scalable in both storage efficiency andperformance, while the desired statistical property is to achieve as good storage efficiencyand performance as with uniform distributions given non-uniform distributions across hashbuckets. Herniated Hash Tables exploit multi-level phase change memory (PCM) to in-placeexpand storage for each hash bucket to accommodate asymmetrically chained entries. Theorganization, coupled with an addressing and prefetching scheme, also improves performancesignificantly by creating more memory parallelism.In the second part of the thesis, we introduce Lemonade from Lemons, harnessing devicewearout to create limited-use security architectures. The architectural design goal is tocreate hardware security architectures that resist attacks by statistically enforcing an upperbound on hardware uses, and consequently attacks. The desired statistical property is that thesystem-level minimum and maximum uses can be guaranteed with high probabilities despite ofdevice-level variability. We introduce techniques for architecturally controlling these boundsand explore the cost in area, energy and latency of using these techniques to achieve systemlevelusage targets given device-level wearout distributions.In the third part of the thesis, we demonstrate Memory Cocktail Therapy: A General,Learning-Based Framework to Optimize Dynamic Tradeoffs in NVMs. Limited write enduranceand long latencies remain the primary challenges of building practical memory systems fromNVMs. Researchers have proposed a variety of architectural techniques to achieve differenttradeoffs between lifetime, performance and energy efficiency; however, no individual techniquecan satisfy requirements for all applications and different objectives. Our architecturaldesign goal is that NVM systems can achieve optimal tradeoffs for specific applications andobjectives, and the statistical goal is that the selected NVM configuration is nearly optimal.Memory Cocktail Therapy uses machine learning techniques to model the architecture behaviorsin terms of all the configurable parameters based on a small number of sample configurations.Then, it selects the optimal configuration according to user-defined objectives whichleads to the desired tradeoff between performance, lifetime and energy efficiency.